Recent zbMATH articles in MSC 76Dhttps://zbmath.org/atom/cc/76D2021-06-15T18:09:00+00:00WerkzeugLift and drag forces acting on a particle moving with zero slip in a linear shear flow near a wall.https://zbmath.org/1460.768312021-06-15T18:09:00+00:00"Ekanayake, Nilanka I. K."https://zbmath.org/authors/?q=ai:ekanayake.nilanka-i-k"Berry, Joseph D."https://zbmath.org/authors/?q=ai:berry.joseph-d"Stickland, Anthony D."https://zbmath.org/authors/?q=ai:stickland.anthony-d"Dunstan, David E."https://zbmath.org/authors/?q=ai:dunstan.david-e"Muir, Ineke L."https://zbmath.org/authors/?q=ai:muir.ineke-l"Dower, Steven K."https://zbmath.org/authors/?q=ai:dower.steven-k"Harvie, Dalton J. E."https://zbmath.org/authors/?q=ai:harvie.dalton-james-ericSummary: The lift and drag forces acting on a small spherical particle in a single wall-bounded linear shear flow are examined via numerical computation. The effects of shear rate are isolated from those of slip by setting the particle velocity equal to the local fluid velocity (zero slip), and examining the resulting hydrodynamic forces as a function of separation distance. In contrast to much of the previous numerical literature, low shear Reynolds numbers are considered \((10^{-3} \lesssim Re_\gamma \lesssim 10^{-1})\). This shear rate range is relevant when dealing with particulate flows within small channels, for example particle migration in microfluidic devices being used or developed for the biotech industry. We demonstrate a strong dependence of both the lift and drag forces on shear rate. Building on previous theoretical \(Re_\gamma \ll 1\) studies, a wall-shear-based zero-slip lift correlation is proposed that is applicable when the wall lies both within the inner and outer regions of the disturbed flow. Similarly, we validate an improved wall-shear-based zero-slip drag correlation that more accurately captures the drag force when the particle is close to, but not touching, the wall. Application of the new correlations to predict the movement of a force-free particle shows that the examined shear-based lift force is as important as the previously examined slip-based lift force, highlighting the need to accurately account for shear when predicting the near-wall movement of force-free particles.Electric-field-induced transitions from spherical to discocyte and lens-shaped drops.https://zbmath.org/1460.769402021-06-15T18:09:00+00:00"Wagoner, Brayden W."https://zbmath.org/authors/?q=ai:wagoner.brayden-w"Vlahovska, Petia M."https://zbmath.org/authors/?q=ai:vlahovska.petia-m"Harris, Michael T."https://zbmath.org/authors/?q=ai:harris.michael-t"Basaran, Osman A."https://zbmath.org/authors/?q=ai:basaran.osman-aSummary: When a poorly conducting drop that is surrounded by a more conducting exterior fluid is subjected to an electric field, the drop can deform into an oblate shape at low field strengths. Such drops become unstable at high field strengths and display two types of dynamics, dimpling and equatorial streaming, the physics of which is currently not understood. If the drop is more viscous, dimples form and grow at the poles of the drop and eventually the discocyte-shaped drop breaks up to form a torus. If the exterior fluid is more viscous, the drop deforms into a lens and sheds rings from the equator that subsequently break into a number of smaller droplets. A theoretical explanation as to why dimple- and lens-shaped drops occur, and the mechanisms for the onset of these instabilities, are provided by determining steady-state solutions by simulation and inferring their stability from bifurcation analysis. For large drop viscosities, electric shear stress is shown to play a dominant role and to result in dimpling. For small drop viscosities, equatorial normal stresses (electric, hydrodynamic and capillary) become unbounded and lead to the lens shape.Morphological evolution of microscopic dewetting droplets with slip.https://zbmath.org/1460.762632021-06-15T18:09:00+00:00"Chan, Tak Shing"https://zbmath.org/authors/?q=ai:chan.tak-shing-t"Mcgraw, Joshua D."https://zbmath.org/authors/?q=ai:mcgraw.joshua-d"Salez, Thomas"https://zbmath.org/authors/?q=ai:salez.thomas"Seemann, Ralf"https://zbmath.org/authors/?q=ai:seemann.ralf"Brinkmann, Martin"https://zbmath.org/authors/?q=ai:brinkmann.martinSummary: We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length \(\tilde{b}\) with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length \(\tilde{b}_m\approx O(0.1-1)\) and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than \(\tilde{b}_m\). Around \(\tilde{b}_m\), the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for \(\tilde{b}\gg \tilde{b}_m\), friction at the substrate for \(\tilde{b}\approx \tilde{b}_m\) and shear flows for \(\tilde{b}\ll \tilde{b}_m\). Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when \(\tilde{b}\) is many orders of magnitude smaller than \(\tilde{b}_m\).Effect of an internal nonlinear rotational dissipative element on vortex shedding and vortex-induced vibration of a sprung circular cylinder.https://zbmath.org/1460.762242021-06-15T18:09:00+00:00"Tumkur, Ravi Kumar R."https://zbmath.org/authors/?q=ai:tumkur.ravi-kumar-r"Pearlstein, Arne J."https://zbmath.org/authors/?q=ai:pearlstein.arne-j"Masud, Arif"https://zbmath.org/authors/?q=ai:masud.arif"Gendelman, Oleg V."https://zbmath.org/authors/?q=ai:gendelman.oleg-v"Blanchard, Antoine B."https://zbmath.org/authors/?q=ai:blanchard.antoine-b"Bergman, Lawrence A."https://zbmath.org/authors/?q=ai:bergman.lawrence-a"Vakakis, Alexander F."https://zbmath.org/authors/?q=ai:vakakis.alexander-fSummary: We computationally investigate coupling of a nonlinear rotational dissipative element to a sprung circular cylinder allowed to undergo transverse vortex-induced vibration (VIV) in an incompressible flow. The dissipative element is a `nonlinear energy sink' (NES), consisting of a mass rotating at fixed radius about the cylinder axis and a linear viscous damper that dissipates energy from the motion of the rotating mass. We consider the Reynolds number range \(20\leqslant Re\leqslant 120\), with \(Re\) based on cylinder diameter and free-stream velocity, and the cylinder restricted to rectilinear motion transverse to the mean flow. Interaction of this NES with the flow is mediated by the cylinder, whose rectilinear motion is mechanically linked to rotational motion of the NES mass through nonlinear inertial coupling. The rotational NES provides significant `passive' suppression of VIV. Beyond suppression however, the rotational NES gives rise to a range of qualitatively new behaviours not found in transverse VIV of a sprung cylinder without an NES, or one with a `rectilinear NES', considered previously. Specifically, the NES can either stabilize or destabilize the steady, symmetric, motionless-cylinder solution and can induce conditions under which suppression of VIV (and concomitant reduction in lift and drag) is accompanied by a greatly elongated region of attached vorticity in the wake, as well as conditions in which the cylinder motion and flow are temporally chaotic at relatively low \(Re\).Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition.https://zbmath.org/1460.762752021-06-15T18:09:00+00:00"Ali, N."https://zbmath.org/authors/?q=ai:ali.naseem"Cortina, G."https://zbmath.org/authors/?q=ai:cortina.g"Hamilton, N."https://zbmath.org/authors/?q=ai:hamilton.norman-t|hamilton.nicholas-a|hamilton.nathaniel"Calaf, M."https://zbmath.org/authors/?q=ai:calaf.marc"Cal, R. B."https://zbmath.org/authors/?q=ai:cal.raul-bayoanSummary: A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.Two-degree-of-freedom flow-induced vibrations of a rotating cylinder.https://zbmath.org/1460.762062021-06-15T18:09:00+00:00"Bourguet, Rémi"https://zbmath.org/authors/?q=ai:bourguet.remiSummary: The flow-induced vibrations of an elastically mounted circular cylinder, free to oscillate in the streamwise and cross-flow directions, and forced to rotate about its axis, are investigated via two- and three-dimensional simulations. The Reynolds number based on the body diameter and inflow velocity is equal to \(100\). The impact of the imposed rotation on the flow-structure system behaviour is explored over wide ranges of values of the rotation rate (ratio between the cylinder surface and inflow velocities, \(\alpha \in [0,5.5])\) and of the reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by the inflow velocity and body diameter, \(U^\star \in [1,25])\). Flow-induced vibrations are found to develop over the entire range of \(\alpha\), including in the intervals where the imposed rotation cancels flow unsteadiness when the body is rigidly mounted (i.e. not allowed to translate). The responses of the two-degree-of-freedom oscillator substantially depart from their one-degree-of-freedom counterparts. Up to a rotation rate close to \(2\), the body exhibits oscillations comparable to the vortex-induced vibrations usually reported for a non-rotating circular cylinder: they develop under flow-body synchronization and their amplitudes present bell-shaped evolutions as functions of \(U^\star\). They are, however, enhanced by the rotation as they can reach \(1\) body diameter in each direction, which represents twice the peak amplitude of cross-flow response for \(\alpha =0\). The symmetry breaking due to the rotation results in deviations from the typical figure-eight orbits. The flow remains close to that observed in the rigidly mounted body case, i.e. two-dimensional with two spanwise vortices shed per cycle. Beyond \(\alpha =2\), the structural responses resemble the galloping oscillations generally encountered for non-axisymmetric bodies, with amplitudes growing unboundedly with \(U^\star\). The response growth rate increases with \(\alpha\) and amplitudes larger than \(20\) diameters are observed. The cylinder describes, at low frequencies, elliptical orbits oriented in the opposite sense compared to the imposed rotation. The emergence of subharmonic components of body displacements, leading to period doubling or quadrupling, induces slight variations about this canonical shape. These responses are not predicted by a quasi-steady modelling of fluid forcing, i.e. based on the evolution of the mean flow at each step of body motion; this suggests that the interaction with flow unsteadiness cannot be neglected. It is shown that flow-body synchronization persists, which is not expected for galloping oscillations. Within this region of the parameter space, the flow undergoes a major reconfiguration. A myriad of novel spatio-temporal structures arise with up to \(20\) vortices formed per cycle. The flow three-dimensional transition occurs down to \(\alpha \approx 2\), versus \(3.7\) for the rigidly mounted body. It is, however, shown that it has only a limited influence on the system behaviour.On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum.https://zbmath.org/1460.352932021-06-15T18:09:00+00:00"Liu, Yang"https://zbmath.org/authors/?q=ai:liu.yang.6|liu.yang.17|liu.yang.21|liu.yang.3|liu.yang.1|liu.yang.8|liu.yang.9|liu.yang.16|liu.yang.13|liu.yang.20|liu.yang.23|liu.yang.11|liu.yang.15|liu.yang|liu.yang.10|liu.yang.12|liu.yang.2|liu.yang.18|liu.yang.19|liu.yang.5|liu.yang.4|liu.yang.22|liu.yang.14"Zhong, Xin"https://zbmath.org/authors/?q=ai:zhong.xinSummary: This paper deals with the Cauchy problem of three-dimensional (3D) nonhomogeneous incompressible nematic liquid crystal flows. The global well-posedness of strong solutions with large velocity is established provided that \(\|\rho_0\|_{L^\infty}+\|\nabla d_0\|_{L^3}\) is suitably small. In particular, the initial density may contain vacuum states and even have compact support. Furthermore, the large time behavior of the solution is also obtained.Linear hydrodynamics and stability of the discrete velocity Boltzmann equations.https://zbmath.org/1460.766842021-06-15T18:09:00+00:00"Masset, Pierre-Alexandre"https://zbmath.org/authors/?q=ai:masset.pierre-alexandre"Wissocq, G."https://zbmath.org/authors/?q=ai:wissocq.gauthierSummary: The discrete velocity Boltzmann equations (DVBE) underlie the attainable properties of all numerical lattice Boltzmann methods (LBM). To that regard, a thorough understanding of their intrinsic hydrodynamic limits and stability properties is mandatory. To achieve this, we propose an analytical study of the eigenvalues obtained by a von Neumann perturbative analysis. It is shown that the Knudsen number, naturally defined as a particular dimensionless wavenumber in the athermal case, is sufficient to expand rigorously the eigenvalues of the DVBE and other fluidic systems such as Euler, Navier-Stokes and all Burnett equations. These expansions are therefore compared directly to one another. With this methodology, the influences of the lattice closure and equilibrium on the hydrodynamic limits and Galilean invariance are pointed out for the D1Q3 and D1Q4 lattices, without any \textit{ansatz}. An analytical study of multi-relaxation time (MRT) models warns us of the errors and instabilities associated with the choice of arbitrarily large ratios of relaxation frequencies. Importantly, the notion of the Knudsen-Shannon number is introduced to understand which physics can be solved by a given LBM numerical scheme. This number is also shown to drive the practical stability of MRT schemes. In the light of the proposed methodology, the meaning of the Chapman-Enskog expansion applied to the DVBE in the linear case is clarified.Artificial intelligence control of a turbulent jet.https://zbmath.org/1460.765742021-06-15T18:09:00+00:00"Zhou, Yu"https://zbmath.org/authors/?q=ai:zhou.yu"Fan, Dewei"https://zbmath.org/authors/?q=ai:fan.dewei"Zhang, Bingfu"https://zbmath.org/authors/?q=ai:zhang.bingfu"Li, Ruiying"https://zbmath.org/authors/?q=ai:li.ruiying"Noack, Bernd R."https://zbmath.org/authors/?q=ai:noack.bernd-rSummary: An artificial intelligence (AI) control system is developed to maximize the mixing rate of a turbulent jet. This system comprises of six independently operated unsteady minijet actuators, two hot-wire sensors placed in the jet and genetic programming for the unsupervised learning of a near-optimal control law. The ansatz of this law includes multi-frequency open-loop forcing, sensor feedback and nonlinear combinations thereof. Mixing performance is quantified by the decay rate of the centreline mean velocity of the jet. Intriguingly, the learning process of AI control discovers the classical forcings, i.e. axisymmetric, helical and flapping achievable from conventional control techniques, one by one in the order of increased performance, and finally converges to a hitherto unexplored forcing. Careful examination of the control landscape unveils typical control laws, generated in the learning process, and their evolutions. The best AI forcing produces a complex turbulent flow structure that is characterized by periodically generated mushroom structures, helical motion and an oscillating jet column, all enhancing the mixing rate and vastly outperforming others. Being never reported before, this flow structure is examined in various aspects, including the velocity spectra, mean and fluctuating velocity fields and their downstream evolution, and flow visualization images in three orthogonal planes, all compared with other classical flow structures. Along with the knowledge of the minijet-produced flow and its effect on the initial condition of the main jet, these aspects cast valuable insight into the physics behind the highly effective mixing of this newly found flow structure. The results point to the great potential of AI in conquering the vast opportunity space of control laws for many actuators and sensors and in optimizing turbulence.Feedback control of vortex shedding using a resolvent-based modelling approach.https://zbmath.org/1460.762892021-06-15T18:09:00+00:00"Jin, Bo"https://zbmath.org/authors/?q=ai:jin.bo"Illingworth, Simon J."https://zbmath.org/authors/?q=ai:illingworth.simon-j"Sandberg, Richard D."https://zbmath.org/authors/?q=ai:sandberg.richard-dSummary: An investigation of optimal feedback controllers' performance and robustness is carried out for vortex shedding behind a two-dimensional cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier-Stokes equations into an input-output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to high-dimensional flow systems is overcome by using low-order models identified from frequency responses. These low-order models are used to design optimal controllers using \(\mathcal{H}_\infty\) loop shaping. Two distinct single-input single-output control arrangements are considered. In the first arrangement, a velocity sensor located in the wake drives a pair of body forces near the cylinder. Complete suppression of shedding is observed up to \(Re=110\). Due to the convective nature of vortex shedding and the corresponding time delays, we observe a fundamental trade-off: the sensor should be close enough to the cylinder to avoid excessive time lag, but it should be kept sufficiently far from the cylinder to measure unstable modes developing downstream. These two conflicting requirements become more difficult to satisfy for larger Reynolds numbers. In the second arrangement, we consider a practical set-up with an actuator that oscillates the cylinder according to the lift measurement. The system is stabilised up to \(Re=100\), and we demonstrate why the performance of the resulting feedback controllers deteriorates more rapidly with increasing Reynolds number. The challenges of designing robust controllers for each control set-up are also analysed and discussed.Rolling of non-wetting droplets down a gently inclined plane.https://zbmath.org/1460.760672021-06-15T18:09:00+00:00"Schnitzer, Ory"https://zbmath.org/authors/?q=ai:schnitzer.ory"Davis, Anthony M. J."https://zbmath.org/authors/?q=ai:davis.anthony-m-j"Yariv, Ehud"https://zbmath.org/authors/?q=ai:yariv.ehudSummary: We analyse the near-rolling motion of non-wetting droplets down a gently inclined plane. Inspired by the scaling analysis of \textit{L. Mahadevan} and \textit{Y. Pomeau} [Phys. Fluids 11, No. 9, 2449--2453 (1999; Zbl 1149.76466)], we focus upon the limit of small Bond numbers, where the drop shape is nearly spherical and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop. In that region, where the fluid interface appears flat, we obtain an analytical approximation for the flow field. By evaluating the dissipation associated with that flow we obtain a closed-form approximation for the drop speed. This approximation reveals that the missing prefactor in the Mahadevan-Pomeau scaling law is \((3\pi/6)\sqrt{3/2}\approx 0.72\) -- in good agreement with experiments. An unexpected feature of the flow field is that it happens to satisfy the no-slip and shear-free conditions simultaneously over both the solid flat spot and the mobile fluid interface in its vicinity. Furthermore, we show that close to the near-circular contact line the velocity field lies primarily in the plane locally normal to the contact line; it is analogous there to the local solution in the comparable problem of a two-dimensional rolling drop. This analogy breaks down near the two points where the contact line propagates parallel to itself, the local flow being there genuinely three dimensional. These observations illuminate a unique `peeling' mechanism by which a rolling droplet avoids the familiar non-integrable stress singularity at a moving contact line.Acoustic receptivity simulations of flow past a flat plate with elliptic leading edge.https://zbmath.org/1460.762022021-06-15T18:09:00+00:00"Shahriari, Nima"https://zbmath.org/authors/?q=ai:shahriari.nima"Bodony, Daniel J."https://zbmath.org/authors/?q=ai:bodony.daniel-j"Hanifi, Ardeshir"https://zbmath.org/authors/?q=ai:hanifi.ardeshir"Henningson, Dan S."https://zbmath.org/authors/?q=ai:henningson.dan-sSummary: We present results of numerical simulations of leading-edge acoustic receptivity for acoustic waves impinging on the leading edge of a finite-thickness flat plate. We use both compressible and incompressible flow solvers fitted with high-order high-accuracy numerical methods and independent methods of estimating the receptivity coefficient. The results show that the level of acoustic receptivity in the existing literature appears to be one order of magnitude too high. Our review of previous numerical simulations and experiments clearly identifies some contradictory trends. In the limit of an infinitely thin flat plate, our results are consistent with asymptotic theory and numerical simulations.Görtler vortices and streaks in boundary layer subject to pressure gradient: excitation by free stream vortical disturbances, nonlinear evolution and secondary instability.https://zbmath.org/1460.762272021-06-15T18:09:00+00:00"Xu, Dongdong"https://zbmath.org/authors/?q=ai:xu.dongdong"Liu, Jianxin"https://zbmath.org/authors/?q=ai:liu.jianxin"Wu, Xuesong"https://zbmath.org/authors/?q=ai:wu.xuesongSummary: This paper investigates streaks and Görtler vortices in a boundary layer over a flat or concave wall in a contracting or expanding stream, which provides a favourable or adverse pressure gradient, respectively. We consider first the excitation of streaks and Görtler vortices by free stream vortical disturbances (FSVD), and their nonlinear evolution. The focus is on FSVD with sufficiently long wavelength, to which the boundary layer is most receptive. The formulation is directed at the general case where the Görtler number \(G_\Lambda\) (based on the spanwise length scale \(\Lambda\) of FSVD) is of order one, and the FSVD is strong enough that the induced vortices acquire an \(O(1)\) streamwise velocity in the region where the boundary layer thickness becomes comparable with \(\Lambda\), and the vortices are governed by the nonlinear boundary region equations (NBRE). An important effect of a pressure gradient is that the oncoming FSVD are distorted by the non-uniform inviscid flow outside the boundary layer through convection and stretching. This process is accounted for by using the rapid distortion theory. The impact of the distorting FSVD is analysed to provide the appropriate initial and boundary conditions, which form, along with the NBRE, the appropriate initial boundary value problem describing the excitation and nonlinear evolution of the vortices. Numerical results show that an adverse/favourable pressure gradient cause the Görtler vortices to saturate earlier/later, but at a lower/higher amplitude than that in the case of zero-pressure-gradient. On the other hand, for the same pressure gradient and at low levels of FSVD, the vortices saturate earlier and at a higher amplitude as \(G_\Lambda\) increases. Raising FSVD intensity reduces the effects of the pressure gradient and curvature. At a high FSVD level of 14\%, the curvature has no impact on the vortices, while the pressure gradient only influences the saturation intensity. The unsteadiness of FSVD is found to reduce the boundary layer response significantly at FSVD levels, but that effect weakens as the turbulence level increases. A secondary instability analysis of the vortices is performed for moderate adverse and favourable pressure gradients. Three families of unstable modes have been identified, which may become dominant depending on the frequency and streamwise location. In the presence of an adverse pressure gradient, the secondary instability occurs earlier, but the unstable modes appear in a smaller band of frequency, and have smaller growth rates. The opposite is true for a favourable pressure gradient. The present theoretical framework, which accounts for the influence of the curvature, turbulence level and pressure gradient, allows for a detailed and integrated description of the key transition processes, and represents a useful step towards predicting the pretransitional flow and transition itself of the boundary layer over a blade in turbomachinery.Linear feedback control of invariant solutions in channel flow.https://zbmath.org/1460.765262021-06-15T18:09:00+00:00"Linkmann, Moritz"https://zbmath.org/authors/?q=ai:linkmann.moritz"Knierim, Florian"https://zbmath.org/authors/?q=ai:knierim.florian"Zammert, Stefan"https://zbmath.org/authors/?q=ai:zammert.stefan"Eckhardt, Bruno"https://zbmath.org/authors/?q=ai:eckhardt.brunoSummary: Considering channel flow at Reynolds numbers below the linear stability threshold of the laminar profile as a generic example system showing a subcritical transition to turbulence connected with the existence of simple invariant solutions, we here discuss issues that arise in the application of linear feedback control of invariant solutions of the Navier-Stokes equations. We focus on the simplest possible problem, that is, travelling waves with one unstable direction. In view of potential experimental applicability we construct a pressure-based feedback strategy and study its effect on the stable, marginal and unstable directions of these solutions in different periodic cells. Even though the original instability can be removed, new instabilities emerge as the feedback procedure affects not only the unstable but also the stable directions. We quantify these adverse effects and discuss their implications for the design of successful control strategies. In order to highlight the challenges that arise in the application of feedback control methods in principle and concerning potential applications in the search for simple invariant solutions of the Navier-Stokes equations in particular, we consider an explicitly constructed analogue to closed-loop linear optimal control that leaves the stable directions unaffected.Ambiguity in mean-flow-based linear analysis.https://zbmath.org/1460.767002021-06-15T18:09:00+00:00"Karban, Ugur"https://zbmath.org/authors/?q=ai:karban.ugur"Bugeat, B."https://zbmath.org/authors/?q=ai:bugeat.b"Martini, E."https://zbmath.org/authors/?q=ai:martini.eduardo"Towne, A."https://zbmath.org/authors/?q=ai:towne.aaron"Cavalieri, A. V. G."https://zbmath.org/authors/?q=ai:cavalieri.andre-v-g"Lesshafft, L."https://zbmath.org/authors/?q=ai:lesshafft.lutz"Agarwal, A."https://zbmath.org/authors/?q=ai:agarwal.anurag"Jordan, P."https://zbmath.org/authors/?q=ai:jordan.peter"Colonius, T."https://zbmath.org/authors/?q=ai:colonius.timSummary: Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and can be modified under nonlinear transformation of variables. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimising models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator.Separation scaling for viscous vortex reconnection.https://zbmath.org/1460.762292021-06-15T18:09:00+00:00"Yao, Jie"https://zbmath.org/authors/?q=ai:yao.jie"Hussain, Fazle"https://zbmath.org/authors/?q=ai:hussain.fazleSummary: Reconnection plays a significant role in the dynamics of plasmas, polymers and macromolecules, as well as in numerous laminar and turbulent flow phenomena in both classical and quantum fluids. Extensive studies in quantum vortex reconnection show that the minimum separation distance \(\delta\) between interacting vortices follows a \(\delta(t) \sim t^{1/2}\) scaling. Due to the complex nature of the dynamics (e.g. the formation of bridges and threads as well as successive reconnections and avalanche), such scaling has never been reported for (classical) viscous vortex reconnection. Using direct numerical simulation of the Navier-Stokes equations, we study viscous reconnection of slender vortices, whose core size is much smaller than the radius of the vortex curvature. For separations that are large compared to the vortex core size, we discover that \(\delta (t)\) between the two interacting viscous vortices surprisingly also follows the 1/2-power scaling for both pre- and post-reconnection events. The prefactors in this 1/2-power law are found to depend not only on the initial configuration but also on the vortex Reynolds number (or viscosity). Our finding in viscous reconnection, complementing numerous works on quantum vortex reconnection, suggests that there is indeed a universal route for reconnection -- an essential result for understanding the various facets of the vortex reconnection phenomena and their potential modelling, as well as possibly explaining turbulence cascade physics.Parametrically forced stably stratified flow in a three-dimensional rectangular container.https://zbmath.org/1460.762852021-06-15T18:09:00+00:00"Yalim, Jason"https://zbmath.org/authors/?q=ai:yalim.jason"Lopez, Juan M."https://zbmath.org/authors/?q=ai:lopez.juan-manuel|lopez.juan-m|lopez.juan-manuel.1"Welfert, Bruno D."https://zbmath.org/authors/?q=ai:welfert.bruno-dSummary: The dynamics of a stably and thermally stratified fluid-filled cavity harmonically forced in the vertical direction, resulting in a periodic gravity modulation, is studied numerically. Prior simulations in a two-dimensional cavity showed a myriad of complex dynamic behaviours near the onset of instabilities, and here we address the extent to which these persist in three dimensions. Focusing on a parameter regime where the primary subharmonic mode is resonantly driven, we demonstrate comprehensive qualitative agreement between the dynamics in two and three dimensions; the quantitative difference is due to the larger forcing amplitudes needed in three dimensions to overcome the additional viscous damping from the spanwise walls. Using a small detuning of the forcing frequency, together with a relatively large forcing amplitude, leads to a wave-breaking regime where the qualitative agreement between two and three dimensions breaks down.The flow dynamics of the garden-hose instability.https://zbmath.org/1460.762262021-06-15T18:09:00+00:00"Xie, Fangfang"https://zbmath.org/authors/?q=ai:xie.fangfang"Zheng, Xiaoning"https://zbmath.org/authors/?q=ai:zheng.xiaoning"Triantafyllou, Michael S."https://zbmath.org/authors/?q=ai:triantafyllou.michael-s"Constantinides, Yiannis"https://zbmath.org/authors/?q=ai:constantinides.yiannis"Karniadakis, George Em."https://zbmath.org/authors/?q=ai:karniadakis.george-emSummary: We present fully resolved simulations of the flow-structure interaction in a flexible pipe conveying incompressible fluid. It is shown that the Reynolds number plays a significant role in the onset of flutter for a fluid-conveying pipe modelled through the classic garden-hose problem. We investigate the complex interaction between structural and internal flow dynamics and obtain a phase diagram of the transition between states as function of three non-dimensional quantities: the fluid-tension parameter, the dimensionless fluid velocity and the Reynolds number. We find that the flow patterns inside the pipe strongly affect the type of induced motion. For unsteady flow, if there is symmetry along a direction, this leads to in-plane motion whereas breaking of the flow symmetry results in both in-plane and out-of-plane motions. Hence, above a critical Reynolds number, complex flow patterns result for the vibrating pipe as there is continuous generation of new vorticity due to the pipe wall acceleration, which is subsequently shed in the confined space of the interior of the pipe.Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm.https://zbmath.org/1460.762312021-06-15T18:09:00+00:00"Yao, W."https://zbmath.org/authors/?q=ai:yao.wangjin|yao.wenhao|yao.wancong|yao.wenpo|yao.wang.1|yao.weigang|yao.wanying|yao.wangshu|yao.weiguo|yao.wenying|yao.weixin|yao.wensong|yao.wenlin|yao.weiping|yao.weiwei|yao.weijie|yao.weihong|yao.weiguang|yao.wen-li|yao.wei.1|yao.weixing|yao.weilie|yao.weifeng|yao.wen|yao.weiran|yao.weili|yao.wei|yao.wenqing|yao.wanghe|yao.wenqi|yao.weijian|yao.wenqiang|yao.wenxiu|yao.wang|yao.wenjuan|yao.wensheng|yao.weian|yao.wensu|yao.weijia|yao.wenju"Jaiman, R. K."https://zbmath.org/authors/?q=ai:jaiman.rajeev-kumarSummary: We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid-structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.Model reduction and mechanism for the vortex-induced vibrations of bluff bodies.https://zbmath.org/1460.762302021-06-15T18:09:00+00:00"Yao, W."https://zbmath.org/authors/?q=ai:yao.wangjin|yao.wenhao|yao.wancong|yao.wenpo|yao.wensong|yao.weiguo|yao.wenjuan|yao.weifeng|yao.wen|yao.wensheng|yao.weijian|yao.wenqing|yao.wanying|yao.wei.1|yao.wenlin|yao.weijie|yao.weiran|yao.wang.1|yao.wanghe|yao.weiwei|yao.wensu|yao.wenqi|yao.weian|yao.weilie|yao.weixing|yao.weigang|yao.wangshu|yao.wenying|yao.weiguang|yao.weili|yao.weixin|yao.wei|yao.wen-li|yao.weiping|yao.wang|yao.wenxiu|yao.wenqiang|yao.weihong|yao.weijia|yao.wenju"Jaiman, R. K."https://zbmath.org/authors/?q=ai:jaiman.rajeev-kumarSummary: We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier-Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency \((F_s)\), while maintaining fixed values of the Reynolds number \((Re)\) and mass ratio \((m^*)\). The effects of the Reynolds number \(Re\), the mass ratio \(m^*\) and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance-flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for \(30\leqslant Re\leqslant 100\) at \(m^*=10. In\) the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with \(1:3\) synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.Mathematical model to analyze the flow and heat transfer problem in U-shaped geothermal exchangers.https://zbmath.org/1460.800082021-06-15T18:09:00+00:00"Egidi, Nadaniela"https://zbmath.org/authors/?q=ai:egidi.nadaniela"Giacomini, Josephin"https://zbmath.org/authors/?q=ai:giacomini.josephin"Maponi, Pierluigi"https://zbmath.org/authors/?q=ai:maponi.pierluigiSummary: In this study, we propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier-Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger.The interaction of Blasius boundary-layer flow with a compliant panel: global, local and transient analyses.https://zbmath.org/1460.762032021-06-15T18:09:00+00:00"Tsigklifis, Konstantinos"https://zbmath.org/authors/?q=ai:tsigklifis.konstantinos"Lucey, Anthony D."https://zbmath.org/authors/?q=ai:lucey.anthony-dSummary: We study the fluid-structure interaction (FSI) of a compliant panel with developing Blasius boundary-layer flow. The linearised Navier-Stokes equations in velocity-vorticity form are solved using a Helmholtz decomposition coupled with the dynamics of a plate-spring compliant panel couched in finite-difference form. The FSI system is written as an eigenvalue problem and the various flow- and wall-based instabilities are analysed. It is shown that global temporal instability can occur through the interaction of travelling wave flutter (TWF) with a structural mode or as a resonance between Tollmien-Schlichting wave (TSW) instability and discrete structural modes of the compliant panel. The former is independent of compliant panel length and upstream inflow disturbances while the specific behaviour arising from the latter phenomenon is dependent upon the frequency of a disturbance introduced upstream of the compliant panel. The inclusion of axial displacements in the wall model does not lead to any further global instabilities. The dependence of instability-onset Reynolds numbers with structural stiffness and damping for the global modes is quantified. It is also shown that the TWF-based global instability is stabilised as the boundary layer progresses downstream while the TSW-based global instability exhibits discrete resonance-type behaviour as Reynolds number increases. At sufficiently high Reynolds numbers, a globally unstable divergence instability is identified when the wavelength of its wall-based mode is longer than that of the least stable TSW mode. Finally, a non-modal analysis reveals a high level of transient growth when the flow interacts with a compliant panel which has structural properties capable of reducing TSW growth but which is prone to global instability through wall-based modes.Existence of a sharp transition in the peak propulsive efficiency of a low-\(Re\) pitching foil.https://zbmath.org/1460.765792021-06-15T18:09:00+00:00"Das, Anil"https://zbmath.org/authors/?q=ai:das.anil-kuman"Shukla, Ratnesh K."https://zbmath.org/authors/?q=ai:shukla.ratnesh-k"Govardhan, Raghuraman N."https://zbmath.org/authors/?q=ai:govardhan.raghuraman-n(no abstract)A tumor growth model of Hele-Shaw type as a gradient flow.https://zbmath.org/1460.920502021-06-15T18:09:00+00:00"Di Marino, Simone"https://zbmath.org/authors/?q=ai:di-marino.simone"Chizat, Lénaïc"https://zbmath.org/authors/?q=ai:chizat.lenaicSummary: In this paper, we characterize a degenerate PDE as the gradient flow in the space of nonnegative measures endowed with an optimal transport-growth metric. The PDE of concern, of Hele-Shaw type, was introduced by \textit{B. Perthame} et al. [Arch. Ration. Mech. Anal. 212, No. 1, 93--127 (2014; Zbl 1293.35347)] as a mechanical model for tumor growth and the metric was introduced recently in several articles as the analogue of the Wasserstein metric for nonnegative measures. We show existence of solutions using minimizing movements and show uniqueness of solutions on convex domains by proving the evolutional variational inequality. Our analysis does not require any regularity assumption on the initial condition. We also derive a numerical scheme based on the discretization of the gradient flow and the idea of entropic regularization. We assess the convergence of the scheme on explicit solutions. In doing this analysis, we prove several new properties of the optimal transport-growth metric, which generally have a known counterpart for the Wasserstein metric.Local feedback stabilization of time-periodic evolution equations by finite dimensional controls.https://zbmath.org/1460.930792021-06-15T18:09:00+00:00"Badra, Mehdi"https://zbmath.org/authors/?q=ai:badra.mehdi"Mitra, Debanjana"https://zbmath.org/authors/?q=ai:mitra.debanjana"Ramaswamy, Mythily"https://zbmath.org/authors/?q=ai:ramaswamy.mythily"Raymond, Jean-Pierre"https://zbmath.org/authors/?q=ai:raymond.jean-pierreSummary: We study the feedback stabilization around periodic solutions of parabolic control systems with unbounded control operators, by controls of finite dimension. We prove that the stabilization of the infinite dimensional system relies on the stabilization of a finite dimensional control system obtained by projection and next transformed via its Floquet-Lyapunov representation. We emphasize that this approach allows us to define feedback control laws by solving Riccati equations of finite dimension. This approach, which has been developed in the recent years for the boundary stabilization of autonomous parabolic systems, seems to be totally new for the stabilization of periodic systems of infinite dimension. We apply results obtained for the linearized system to prove a local stabilization result, around periodic solutions, of the Navier-Stokes equations, by finite dimensional Dirichlet boundary controls.Modelling a surfactant-covered droplet on a solid surface in three-dimensional shear flow.https://zbmath.org/1460.762702021-06-15T18:09:00+00:00"Liu, Haihu"https://zbmath.org/authors/?q=ai:liu.haihu"Zhang, Jinggang"https://zbmath.org/authors/?q=ai:zhang.jinggang"Ba, Yan"https://zbmath.org/authors/?q=ai:ba.yan"Wang, Ningning"https://zbmath.org/authors/?q=ai:wang.ningning"Wu, Lei"https://zbmath.org/authors/?q=ai:wu.lei.2Summary: A surfactant-covered droplet on a solid surface subject to a three-dimensional shear flow is studied using a lattice-Boltzmann and finite-difference hybrid method, which allows for the surfactant concentration beyond the critical micelle concentration. We first focus on low values of the effective capillary number \((Ca_e)\) and study the effect of \(Ca_e\), viscosity ratio \((\lambda)\) and surfactant coverage on the droplet behaviour. Results show that at low \(Ca_e\) the droplet eventually reaches steady deformation and a constant moving velocity \(u_d\). The presence of surfactants not only increases droplet deformation but also promotes droplet motion. For each \(\lambda\), a linear relationship is found between contact-line capillary number and \(Ca_e\), but not between wall stress and \(u_d\) due to Marangoni effects. As \(\lambda\) increases, \(u_d\) decreases monotonically, but the deformation first increases and then decreases for each \(Ca_e\). Moreover, increasing surfactant coverage enhances droplet deformation and motion, although the surfactant distribution becomes less non-uniform. We then increase \(Ca_e\) and study droplet breakup for varying \(\lambda\), where the role of surfactants on the critical \(Ca_e (Ca_{e,c})\) of droplet breakup is identified by comparing with the clean case. As in the clean case, \(Ca_{e,c}\) first decreases and then increases with increasing \(\lambda\), but its minima occurs at \(\lambda =0.5\) instead of \(\lambda =1\) in the clean case. The presence of surfactants always decreases \(Ca_{e,c}\), and its effect is more pronounced at low \(\lambda\). Moreover, a decreasing viscosity ratio is found to favour ternary breakup in both clean and surfactant-covered cases, and tip streaming is observed at the lowest \(\lambda\) in the surfactant-covered case.On the flow separation mechanism in the inverse Leidenfrost regime.https://zbmath.org/1460.761962021-06-15T18:09:00+00:00"Arrieta, J."https://zbmath.org/authors/?q=ai:arrieta.jose-m"Sevilla, Alejandro"https://zbmath.org/authors/?q=ai:sevilla.alejandroSummary: The inverse Leidenfrost regime occurs when a heated object in relative motion with a liquid is surrounded by a stable vapour layer, drastically reducing the hydrodynamic drag at large Reynolds numbers due to a delayed separation of the flow. To elucidate the physical mechanisms that control separation, here we report a numerical study of the boundary layer equations describing the liquid-vapour flow around a solid sphere whose surface temperature is above the Leidenfrost point. Our analysis reveals that the dynamics of the thin layer of vaporised liquid controls the downstream evolution of the flow, which cannot be properly described substituting the vapour layer by an effective slip length. In particular, the dominant mechanism responsible for the separation of the flow is the onset of vapour recirculation caused by the adverse pressure gradient in the rearward half of the sphere, leading to an explosive growth of the vapour-layer thickness due to the accumulation of vapour mass. Buoyancy forces are shown to have an important effect on the onset of recirculation, and thus on the separation angle. Our results compare favourably with previous experiments.Erratum: ``Wake behind contaminated bubbles in a solid-body rotating flow''.https://zbmath.org/1460.762472021-06-15T18:09:00+00:00"Rastello, Marie"https://zbmath.org/authors/?q=ai:rastello.marie"Marié, Jean-Louis"https://zbmath.org/authors/?q=ai:marie.jean-louisFigure 2 in the authors' paper [ibid. 884, A17, 23 p. (2020; Zbl 1460.76246)] is corrected.Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system.https://zbmath.org/1460.352852021-06-15T18:09:00+00:00"Han, Bin"https://zbmath.org/authors/?q=ai:han.bin|han.bin.1"Zhao, Na"https://zbmath.org/authors/?q=ai:zhao.naSummary: In this work, we study the regularity criterion for the 3D incompressible MHD equations. By making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one component of the velocity vector field, both in scaling invariant spaces. Moreover, the norms imposed on the magnetic vector field are the Lebesgue and anisotropic Lebesgue norms. This improved the result of our previous blow up criterion in [the authors, Nonlinear Anal., Real World Appl. 51, Article ID 103000, 26 p. (2020; Zbl 1430.35035)], in which the magnetic vector field is bounded in critical Sobolev spaces.Besov regularity for the stationary Navier-Stokes equation on bounded Lipschitz domains.https://zbmath.org/1460.352532021-06-15T18:09:00+00:00"Eckhardt, Frank"https://zbmath.org/authors/?q=ai:eckhardt.frank"Cioica-Licht, Petru A."https://zbmath.org/authors/?q=ai:cioica-licht.petru-a"Dahlke, Stephan"https://zbmath.org/authors/?q=ai:dahlke.stephanSummary: We use the scale \(B^s_\tau(L_\tau(\Omega)), 1/\tau=s/d+1/2,s> 0\), to study the regularity of the stationary Stokes equation on bounded Lipschitz domains \(\Omega\subset\mathbb{R}^d,d\geq 3\), with connected boundary. The regularity in these Besov spaces determines the order of convergence of nonlinear approximation schemes. Our proofs rely on a combination of weighted Sobolev estimates and wavelet characterizations of Besov spaces. Using Banach's fixed point theorem, we extend this analysis to the stationary Navier-Stokes equation with suitable Reynolds number and data, respectively.On singular solutions of time-periodic and steady Stokes problems in a power cusp domain.https://zbmath.org/1460.352542021-06-15T18:09:00+00:00"Eismontaite, Alicija"https://zbmath.org/authors/?q=ai:eismontaite.alicija"Pileckas, Konstantin"https://zbmath.org/authors/?q=ai:pileckas.konstantinSummary: The time-periodic and steady Stokes problems with the boundary value having a nonzero flux are considered in the power cusp domains. The asymptotic expansion near the singularity point is constructed in order to reduce the problem to the case where the energy solution exists. The solution of the problem is found then as the sum of the asymptotic expansion and the term with finite dissipation of energy.The circular capillary jump.https://zbmath.org/1460.760382021-06-15T18:09:00+00:00"Bhagat, Rajesh K."https://zbmath.org/authors/?q=ai:bhagat.rajesh-k"Linden, P. F."https://zbmath.org/authors/?q=ai:linden.paul-fSummary: In this paper we re-examine the flow produced by the normal impact of a laminar liquid jet onto an infinite plane when the flow is dominated by surface tension. Over the range of parameters we consider, which are typical of water from a tap over a kitchen sink, it is observed experimentally that after impact the liquid spreads radially over the plane away from the point of impact in a thin film. It is also observed that, at a finite radius, there is an abrupt increase in thickness of the film which has been identified as a hydraulic jump. Once the jump is formed this radius remains constant in time and, further, is independent of the orientation of the surface showing that gravity is unimportant [\textit{R. K. Bhagat} et al., ibid. 851, R5, 11 p. (2018; Zbl 1415.76031)]. We show that the application of conservation of momentum in the film, subject only to viscosity and surface tension and ignoring gravity completely, predicts a singularity in the curvature of the liquid film and consequently a jump in the depth of the film at a finite radius. This location is almost identical to the radius of the jump predicted by conservation of energy and agrees with experimental observations. We also provide the correct boundary condition to be applied at an interface, where there is a change in interfacial area as a result of the fluid flow, that accounts for the energy change associated with fluid molecules' exchange between the interface and the bulk.Fluid-structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow.https://zbmath.org/1460.762452021-06-15T18:09:00+00:00"Pfister, Jean-Lou"https://zbmath.org/authors/?q=ai:pfister.jean-lou"Marquet, O."https://zbmath.org/authors/?q=ai:marquet.olivierSummary: The dynamics of a hyperelastic splitter plate interacting with the laminar wake flow of a circular cylinder is investigated numerically at a Reynolds number of 80. By decreasing the plate's stiffness, four regimes of flow-induced vibrations are identified: two regimes of periodic oscillation about a symmetric position, separated by a regime of periodic oscillation about asymmetric positions, and finally a regime of quasi-periodic oscillation occurring at very low stiffness and characterized by two fundamental (high and low) frequencies. A linear fully coupled fluid-solid analysis is then performed and reveals the destabilization of a steady symmetry-breaking mode, two high-frequency unsteady modes and one low-frequency unsteady mode, when varying the plate's stiffness. These unstable eigenmodes explain the emergence of the nonlinear self-sustained oscillating states and provide a good prediction of the oscillation frequencies. A comparison with nonlinear calculations is provided to show the limits of the linear approach. Finally, two simplified analyses, based on the quiescent-fluid or quasi-static assumption, are proposed to further identify the linear mechanisms at play in the destabilization of the fully coupled modes. The quasi-static static analysis allows an understanding of the behaviour of the symmetry-breaking and low-frequency modes. The quiescent-fluid stability analysis provides a good prediction of the high-frequency vibrations, unlike the bending modes of the splitter plate in vacuum, as a result of the fluid added-mass correction. The emergence of the high-frequency periodic oscillations can thus be predicted based on a resonance condition between the frequencies of the hydrodynamic vortex-shedding mode and of the quiescent-fluid solid modes.A general criterion for the release of background potential energy through double diffusion.https://zbmath.org/1460.767402021-06-15T18:09:00+00:00"Middleton, Leo"https://zbmath.org/authors/?q=ai:middleton.leo"Taylor, John R."https://zbmath.org/authors/?q=ai:taylor.john-r.1|taylor.john-rSummary: Double diffusion occurs when the fluid density depends on two components that diffuse at different rates (e.g. heat and salt in the ocean). Double diffusion can lead to an up-gradient buoyancy flux and drive motion at the expense of potential energy. Here, we follow the work of \textit{E. N. Lorenz} [``Available potential energy and the maintenance of the general circulation'', Tellus 7, No. 2 2, 157--167 (1955; \url{doi:10.3402/tellusa.v7i2.8796})] and \textit{K. B. Winters} et al. [J. Fluid Mech. 289, 115--128 (1995; Zbl 0858.76095)] for a single-component fluid and define the background potential energy (BPE) as the energy associated with an adiabatically sorted density field and derive its budget for a double-diffusive fluid. We find that double diffusion can convert BPE into available potential energy (APE), unlike in a single-component fluid, where the transfer of APE to BPE is irreversible. We also derive an evolution equation for the sorted buoyancy in a double-diffusive fluid, extending the work of \textit{K. B. Winters} and \textit{E. A. D'Asaro} [ibid. 317, 179--193 (1996; Zbl 0894.76082)] and \textit{N. Nakamura} [``Two-dimensional mixing, edge formation, and permeability diagnosed in an area coordinate'', J. Atmos. Sci. 53, No. 11, 1524--1537 (1996; \url{doi:10.1175/1520-0469(1996)053<1524:TDMEFA>2.0.CO;2})]. The criterion we develop for a release of BPE can be used to analyse the energetics of mixing and double diffusion in the ocean and other multiple-component fluids, and we illustrate its application using two-dimensional simulations of salt fingering.Generalised solutions to the Benjamin problem.https://zbmath.org/1460.762192021-06-15T18:09:00+00:00"Ostapenko, Vladimir V."https://zbmath.org/authors/?q=ai:ostapenko.vladimir-vSummary: We generalise the classical [\textit{T. B. Benjamin}, ibid. 31, 209--248 (1968; Zbl 0169.28503)] modelling the flow in a horizontal duct of finite depth in situations where the flow contains a region spanning the depth of the duct, and a region in which the surface detaches from the ceiling of the duct as a free surface. It is shown that the Benjamin solution belongs to a one-parameter family of similar solutions, which are divided into two types: solutions that describe potential flows where the free surface of the fluid is deflected from the duct ceiling at a zero angle; and solutions that admit the formation of a vortex flow region in the vicinity of the point of fluid separation from the duct ceiling. It is shown that this one-parameter family of solutions is the limit of a two-parameter family of solutions in which part of the uniform flow energy is converted into energy of the small-scale fluid motion. Based on the local hydrostatic approximation, the applicability of the constructed solutions is discussed.How non-Darcy effects influence scaling laws in Hele-Shaw convection experiments.https://zbmath.org/1460.762522021-06-15T18:09:00+00:00"De Paoli, Marco"https://zbmath.org/authors/?q=ai:de-paoli.marco"Alipour, Mobin"https://zbmath.org/authors/?q=ai:alipour.mobin"Soldati, Alfredo"https://zbmath.org/authors/?q=ai:soldati.alfredoSummary: We examine experimentally the influence of non-Darcy effects on convective dissolution in Hele-Shaw cells. We focus on buoyancy-driven convection, where the flow is controlled by the Rayleigh-Darcy number, \(Ra\), which measures the strength of convection compared to diffusion. The Hele-Shaw cell is suitable to mimic Darcy flows only under certain geometrical constraints, and a recent theoretical work [\textit{J. A. Letelier} et al., ibid. 864, 746--767 (2019; Zbl 1415.76606)] demonstrated that a precise limit exists for the parameter \(\epsilon^2 Ra - \epsilon \sim\) thickness-to-height ratio -- beyond which the flow exhibits non-Darcy effects. In this work, we run experiments for solute convection in Rayleigh-Bénard-like configuration. We examine a wide range of the parameters space \((Ra, \epsilon)\) and we clearly identify the application limits of Darcy flow assumptions. Besides confirming previous theoretical predictions, current results are of relevance in the context of porous media flows -- which are often studied experimentally with Hele-Shaw set-ups. Using our original datasets, we have been able to explain and reconcile the discrepancies observed between scaling laws previously proposed for Rayleigh-Bénard-like experiments and simulations in similar contexts. Specifically, we attribute an important role to the parameter \(\epsilon^2 Ra\), which clearly establishes thresholds beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.Bound on the drag coefficient for a flat plate in a uniform flow.https://zbmath.org/1460.761702021-06-15T18:09:00+00:00"Kumar, Anuj"https://zbmath.org/authors/?q=ai:kumar.anuj"Garaud, Pascale"https://zbmath.org/authors/?q=ai:garaud.pascaleSummary: The background method has been a successful tool in obtaining strict bounds on global quantities such as the rate of energy dissipation and heat transfer in turbulent flows. However, all applications of this method until now have focused on flows confined between solid boundaries. An important class of problems that, by contrast, has received no attention is the class of external flows, i.e. flow past a body. In this context, obtaining the dependence of the drag coefficient on the Reynolds number is of crucial relevance for many engineering applications. In this paper, we consider the classical problem of flow past a flat plate of finite length at zero angle of incidence and use the background method to obtain a bound on the drag coefficient. Assuming a statistically steady state and appropriate far-field decay rates for the flow variables, we show that at large Reynolds numbers, the drag coefficient \((C_D)\) is bounded by a constant, a bound that is within a logarithmic factor of experimental data.Resolvent-based optimal estimation of transitional and turbulent flows.https://zbmath.org/1460.765692021-06-15T18:09:00+00:00"Martini, Eduardo"https://zbmath.org/authors/?q=ai:martini.eduardo"Cavalieri, André V. G."https://zbmath.org/authors/?q=ai:cavalieri.andre-v-g"Jordan, Peter"https://zbmath.org/authors/?q=ai:jordan.peter"Towne, Aaron"https://zbmath.org/authors/?q=ai:towne.aaron"Lesshafft, Lutz"https://zbmath.org/authors/?q=ai:lesshafft.lutzSummary: We extend the resolvent-based estimation approach recently introduced by \textit{A. Towne} et al. [ibid. 883, A17, 27 p. (2020; Zbl 1430.76127)] to obtain optimal, non-causal estimates of time-varying flow quantities from low-rank measurements. We derive optimal transfer functions between the measurements and certain nonlinear terms that act as a forcing on the linearised Navier-Stokes equations, and show that the resulting transfer function to the flow state is equivalent to a multiple-input, multiple-output Wiener filter if the colour of the forcing statistics is known. A matrix-free implementation is developed based on integration of the direct and adjoint linearised Navier-Stokes operators, enabling application to the large systems encountered for transitional and turbulent flows without the need for \textit{a priori} model reduction. Using a linearised Ginzburg-Landau problem, we show that the non-casual resolvent-based method outperforms a casual Kalman filter for general sensor configurations and recovers the Kalman filter transfer function in specific cases, leading to causal estimates at a significantly reduced computational cost. Additionally, our method is shown to be more accurate and robust than popular approaches based on truncation of the resolvent operator to its leading modes. The applicability of the method to transitional and turbulent flows is demonstrated via application to a (linearised) transitional boundary layer and a (nonlinear) turbulent channel flow. Errors on the order of 2\% are achieved for the boundary layer, and the channel flow case highlights the need to account for the forcing colour to achieve accurate flow estimates. In practice, our method can be used as a post-processing tool to reconstruct unmeasured quantities from limited experimental data, and, in cases where the transfer function can be accurately truncated to its causal components, as a low-cost estimator for flow control.Deformation of ambient chemical gradients by sinking spheres.https://zbmath.org/1460.768402021-06-15T18:09:00+00:00"Inman, Bryce G."https://zbmath.org/authors/?q=ai:inman.bryce-g"Davies, Christopher J."https://zbmath.org/authors/?q=ai:davies.christopher-j"Torres, Carlos R."https://zbmath.org/authors/?q=ai:torres.carlos-r"Franks, Peter J. S."https://zbmath.org/authors/?q=ai:franks.peter-j-sSummary: A sphere sinking through a chemical gradient drags fluid with it, deforming the gradient. The sphere leaves a trail of gradient enhancement that persists longer than the velocity disturbance in the Reynolds \(10^{-2}\leqslant Re\leqslant 10^2\), Froude \(10^{-1}\leqslant Fr\leqslant 10^3\) and Péclet \(10^2<Pe\leqslant 10^6\) regime considered here. We quantify the enhancement of the gradient and the diffusive flux in the trail of disturbed chemical left by the passing sphere using a combination of numerical simulations and scaling analyses. When \(Fr\) is large and buoyancy forces are negligible, dragged isosurfaces of chemical form a boundary layer of thickness \(\delta_\rho\) around the sphere with diameter \(l\). We derive the scaling \(\delta_\rho /l\sim Pe^{-1/3}\) from the balance of advection and diffusion in the chemical boundary layer. The sphere displaces a single isosurface of chemical a maximum distance \(L_{Def}\) that increases as \(L_{Def}/l\sim l/\delta_\rho \sim Pe^{1/3} \). Increased flux through the chemical boundary layer moving with the sphere is described by a Sherwood number, \(Sh\sim l/\delta_\rho \sim Pe^{1/3}\). The gradient enhancement trail extends much farther than \(L_{Def}\) as displaced isosurfaces slowly return to their original positions through diffusion. In the reference frame of a chemical isosurface moving past the sphere, a new quantity describing the Lagrangian flux is found to scale as \(M\sim (L_{Def}/l)^2\sim Pe^{2/3}\). The greater \(Pe\) dependence of \(M\) versus \(Sh\) demonstrates the importance of the deformation trail for determining the total flux of chemical in the system. For \(Fr \geqslant 10\), buoyancy forces are weak compared to the motion of the sphere and the preceding results are retained. Below \(Fr=10\), an additional Froude dependence is found and \(l/\delta_\rho \sim Sh\sim Re^{1/6} Fr^{-1/6} Pe^{1/3}\). Buoyancy forces suppress gradient deformation downstream, resulting in \(L_{Def}/l\sim Re^{-1/3} Fr^{1/3} Pe^{1/3}\) and \(M\sim Re^{-1/3} Fr^{1/3} Pe^{2/3}\). The productivity of marine plankton -- and therefore global carbon and oxygen cycles -- depends on the availability of microscale gradients of chemicals. Because most plankton exist in the fluids regime under consideration, this work describes a new mechanism by which sinking particles and plankton can stir weak ambient chemical gradients a distance \(L_{Def}\) and increase chemical flux in the trail by a factor of \(M\).Drag reduction on drop during impact on multiscale superhydrophobic surfaces.https://zbmath.org/1460.762712021-06-15T18:09:00+00:00"Martouzet, Grégoire"https://zbmath.org/authors/?q=ai:martouzet.gregoire"Lee, Choongyeop"https://zbmath.org/authors/?q=ai:lee.choongyeop"Pirat, Christophe"https://zbmath.org/authors/?q=ai:pirat.christophe"Ybert, Christophe"https://zbmath.org/authors/?q=ai:ybert.christophe"Biance, Anne-Laure"https://zbmath.org/authors/?q=ai:biance.anne-laureSummary: Liquid drop impact dynamics depends on the liquid-substrate interaction. In particular, when liquid-solid friction is decreased, the spreading of the impacting drop lasts longer. We characterise this effect by using two types of superhydrophobic surfaces, with similar wetting properties but different friction coefficients. It is found that, for large enough impact velocities, a reduced friction delays the buildup of a viscous boundary layer, and leads to an increase of the time required to reach the maximal radius of the impacting drop. An asymptotic analysis is carried out to quantify this effect, and agrees well with the experimental findings. Interestingly, this novel description complements the general picture of drop impact on solid surfaces, and more generally addresses the issue of drag reduction in the presence of slippage for non-stationary flows.Numerical simulations of thermals with and without stratification.https://zbmath.org/1460.762822021-06-15T18:09:00+00:00"Orlandi, Paolo"https://zbmath.org/authors/?q=ai:orlandi.paolo"Carnevale, G. F."https://zbmath.org/authors/?q=ai:carnevale.george-fSummary: The evolution of vertical and horizontal thermals is examined via three-dimensional numerical simulations. The two types of thermals are distinguished by the geometry of their sources: respectively spherical and horizontal cylindrical. How the evolution of a vertical thermal is affected by varying the Reynolds number from the laminar regime into the fully turbulent regime is examined. Although the rate of rise of a thermal increases with increasing Reynolds number in the laminar regime, it is shown here that it decreases with increasing Reynolds number in the turbulent regime. Known instabilities of vortex rings and vortex dipoles are shown to affect the evolution of the vertical and horizontal thermals, respectively. In particular, the short-wave cooperative instability, commonly seen in the evolution of contrails behind aircraft, is a major influence on the evolution of the horizontal thermal. The vortex dynamics during the encounter of both types of thermals with a strong thermocline is examined. It is found that, when blocked by a thermocline, the head of the vertical thermal is dispersed laterally by the action of small compact vortex dipoles that are produced during the collision. Evidence is presented for the propagation of circular waves in the thermocline that spread out horizontally moving away from the impact site. In the case of the horizontal thermal, the collision with the thermocline results in vortex dynamics similar to that which occurs when a dipole impinges on a no-slip wall.Quadrupolar flows around spots in internal shear flows.https://zbmath.org/1460.764052021-06-15T18:09:00+00:00"Wang, Zhe"https://zbmath.org/authors/?q=ai:wang.zhe"Guet, Claude"https://zbmath.org/authors/?q=ai:guet.claude"Monchaux, Romain"https://zbmath.org/authors/?q=ai:monchaux.romain"Duguet, Yohann"https://zbmath.org/authors/?q=ai:duguet.yohann"Eckhardt, Bruno"https://zbmath.org/authors/?q=ai:eckhardt.brunoSummary: Turbulent spots occur in shear flows confined between two walls and are surrounded by robust quadrupolar flows. Although the far-field decay of such large-scale flows has been reported to be exponential, we predict a different algebraic decay for the case of plane Couette flow. We address this problem theoretically, by modelling an isolated spot as an obstacle in a linear plane shear flow with free-slip boundary conditions at the walls. By seeking invariant solutions in a co-moving Lagrangian frame and using geometric scale separation, a set of differential equations governing large-scale flows is derived from the Navier-Stokes equations and solved analytically. The wall-normal velocity turns out to be exponentially localised in the plane, while the quadrupolar in-plane velocity field, after wall-normal averaging, features a superposition of algebraic and exponential decays. The algebraic decay exponent is \(-3\). The quadrupolar angular dependence stems from (i) the shearing of the streamwise velocity and (ii) the breaking of the spanwise homogeneity. Near the spot, exponentially decaying solutions can generate reversed quadrupolar flows. Eventually, by noting that the algebraically decaying in-plane flow is two-dimensional and harmonic, we suggest a topological origin to the quadrupolar large-scale flow.Optimal suppression of a separation bubble in a laminar boundary layer.https://zbmath.org/1460.761982021-06-15T18:09:00+00:00"Karp, Michael"https://zbmath.org/authors/?q=ai:karp.michael"Hack, M. J. Philipp"https://zbmath.org/authors/?q=ai:hack.m-j-philippSummary: By means of nonlinear optimization, we seek the velocity disturbances at a given upstream position that suppress a laminar separation bubble as effectively as possible. Both steady and unsteady disturbances are examined and compared. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. It is found that the linear analysis largely captures the suppression of the separation bubble attained by the nonlinear optimal perturbations. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during the perturbation growth. The mean flow distortion enhances the momentum close to the wall, counteracting the deceleration of the flow in that region. An examination of the effect of the disturbance spanwise wavenumber reveals that perturbations maximizing the mean flow distortion also approximately maximize the peak wall pressure, which is beneficial for lowering form drag. The optimal spanwise wavenumber leading to maximal peak wall pressure is significantly larger than the one maximizing the shift in separation onset. For unsteady disturbances, the mechanism of separation delay relies on enhancing wall-normal momentum transfer by triggering instabilities of the separated shear layer. It is found that Tollmien-Schlichting waves obtained from linear stability theory provide accurate estimates of the nonlinearly optimal disturbances. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.Breathers in a three-layer fluid.https://zbmath.org/1460.762812021-06-15T18:09:00+00:00"Nakayama, K."https://zbmath.org/authors/?q=ai:nakayama.keisuke|nakayama.keiichi|nakayama.kentaro|nakayama.kenichiro|nakayama.katsumasa|nakayama.kunji|nakayama.kenji|nakayama.keita|nakayama.kazuaki|nakayama.koji|nakayama.kazunori|nakayama.kazuyuki"Lamb, K. G."https://zbmath.org/authors/?q=ai:lamb.kevin-gSummary: In a three-layer system, weakly nonlinear theory predicts that breathers exist under certain conditions which, under the Boussinesq approximation, include symmetric stratifications in which the density jump across each interface is the same and the upper and lower layer thicknesses are equal and less than 9/26 of the total water depth. The existence and characteristics of fully nonlinear breathers in this symmetric stratification are poorly understood. Therefore, this study investigates fully nonlinear breathers in a three-layer symmetric stratification in order to clarify their characteristics by making direct comparisons between numerical simulation results and theoretical solutions. A normalization of the breather profiles is introduced using theoretical solutions of a breather and a new energy scale is proposed to evaluate their potential and kinetic energy. We apply fully nonlinear and strongly dispersive internal wave equations in a three-layer system using a variational principle. The computational results show that the larger the amplitude, the shorter the length of the envelope of breathers, which agrees with the theoretical solution. However, breathers based on the theoretical solutions cannot progress without deformation and decay due to the emission of short small-amplitude internal waves. Furthermore we demonstrate that the shedding of larger amplitude waves occurs, and the amplitude of the envelope decays more strongly when the density interface crosses the critical depth where the ratio of the upper layer thickness and the total water depth is 9/26 suggesting a limiting amplitude for fully nonlinear breathers.Marangoni-driven film climbing on a draining pre-wetted film.https://zbmath.org/1460.760702021-06-15T18:09:00+00:00"Xue, Nan"https://zbmath.org/authors/?q=ai:xue.nan"Pack, Min Y."https://zbmath.org/authors/?q=ai:pack.min-y"Stone, Howard A."https://zbmath.org/authors/?q=ai:stone.howard-aSummary: Marangoni flow is the motion induced by a surface tension gradient along a fluid-fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.Modes of synchronisation around a near-wall oscillating cylinder in streamwise directions.https://zbmath.org/1460.761672021-06-15T18:09:00+00:00"Ju, Xiaoying"https://zbmath.org/authors/?q=ai:ju.xiaoying"An, Hongwei"https://zbmath.org/authors/?q=ai:an.hongwei"Cheng, Liang"https://zbmath.org/authors/?q=ai:cheng.liang"Tong, Feifei"https://zbmath.org/authors/?q=ai:tong.feifeiSummary: Two-dimensional direct numerical simulations of a cylinder undergoing forced streamwise oscillations in steady approaching flow are conducted over ranges of oscillation amplitude, oscillation frequency and gap distance between the cylinder and the wall at a Reynolds number of 175. The flow characteristics are found to be strongly affected by the gap distance, compared to those observed around an isolated cylinder \textit{G. Tang} et al. [ibid. 832, 146--169 (2017; Zbl 1419.76182)]. The synchronisation modes are mapped out in the parameter ranges. The existence of the plane wall leads to an increased chance of occurrence of high-order modes with the denominator being an odd number. Two new flow phenomena, namely the period doubling and transition to quasi-periodic states through cascade of period doubling within the primary synchronisation region, are observed. The interaction of the plane-wall boundary layer with vortices shed from the cylinder and the asymmetry of the flow through the gap and around the top side of the cylinder are identified as the primary physical mechanisms responsible for the observed behaviours. The influence of velocity gradient in the plane-wall boundary layer on the two new phenomena is quantified through a numerical test involving linear shear flow around an isolated cylinder. The period-doubling phenomenon occurs only when the velocity gradient is larger than a critical value. The results obtained through three-dimensional simulations suggest that the synchronisation modes identified through two-dimensional simulations are not significantly affected by the three-dimensionality of the flow over the parameter ranges covered in the present study.Work-minimizing kinematics for small displacement of an infinitely long cylinder.https://zbmath.org/1460.762002021-06-15T18:09:00+00:00"Mandre, Shreyas"https://zbmath.org/authors/?q=ai:mandre.shreyas-dSummary: We consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If \(t\) represents the time since the commencement of motion and \(T\) the final time, then the optimum speed profile is \(Ct^{1/4}(T-t)^{1/4}\), where \(C\) is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves.Upstream actuation for bluff-body wake control driven by a genetically inspired optimization.https://zbmath.org/1460.762432021-06-15T18:09:00+00:00"Minelli, G."https://zbmath.org/authors/?q=ai:minelli.guglielmo"Dong, T."https://zbmath.org/authors/?q=ai:dong.teng|dong.tingting|dong.tianhang|dong.tao|dong.thinh|dong.ting|dong.tianzhen|dong.tuochuan|dong.tianxue|dong.tianxin|dong.tong|dong.tianwen|dong.tiansi|dong.tiandu|dong.tianbao|dong.tian|dong.tianyu|dong.taiheng"Noack, B. R."https://zbmath.org/authors/?q=ai:noack.bernd-r"Krajnović, S."https://zbmath.org/authors/?q=ai:krajnovic.sinisaSummary: The control of bluff-body wakes for reduced drag and enhanced stability has traditionally relied on the so-called direct-wake control approach. By the use of actuators or passive devices, one can manipulate the aerodynamic loads that act on the rear of the model. An alternative approach for the manipulation of the flow is to move the position of the actuator upstream, hence interacting with an easier-to-manipulate boundary layer. The present paper comprises a bluff-body flow study via large-eddy simulations to investigate the effectiveness of an upstream actuator (positioned at the leading edge) with regard to the manipulation of the wake dynamics and its aerodynamic loads. A rectangular cylinder with rounded leading edges, equipped with actuators positioned at the front curvatures, is simulated at \(Re=40\,000\). A genetic algorithm (GA) optimization is performed to find an effective actuation that minimizes drag. It is shown that the GA selects superharmonic frequencies of the natural vortex shedding. Hence, the induced disturbances, penetrating downstream in the wake, significantly reduce drag and lateral instability. A comparison with a side-recirculation-suppression approach is also presented, the latter case being worse in terms of reduced drag (only 8 \% drag reduction achieved), despite the total suppression of the side recirculation bubble. In contrast, the GA optimized case contributes to a 20 \% drag reduction with respect to the unactuated case. In addition, the large drag reduction is associated with a reduced shedding motion and an improved lateral stability.Maximum amplification of enstrophy in three-dimensional Navier-Stokes flows.https://zbmath.org/1460.761682021-06-15T18:09:00+00:00"Kang, Di"https://zbmath.org/authors/?q=ai:kang.di"Yun, Dongfang"https://zbmath.org/authors/?q=ai:yun.dongfang"Protas, Bartosz"https://zbmath.org/authors/?q=ai:protas.bartoszSummary: This investigation concerns a systematic search for potentially singular behaviour in three-dimensional (3-D) Navier-Stokes flows. Enstrophy serves as a convenient indicator of the regularity of solutions to the Navier Stokes system -- as long as this quantity remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. However, there are no estimates available with finite \textit{a priori} bounds on the growth of enstrophy and, hence, the regularity problem for the 3-D Navier-Stokes system remains open. In order to quantify the maximum possible growth of enstrophy, we consider a family of optimization problems in which initial conditions with prescribed enstrophy \(\mathcal{E}_0\) are sought such that the enstrophy in the resulting Navier-Stokes flow is maximized at some time \(T\). Such problems are solved computationally using a large-scale adjoint-based gradient approach derived in the continuous setting. By solving these problems for a broad range of values of \({\mathcal{E}}_0\) and \(T\), we demonstrate that the maximum growth of enstrophy is in fact finite and scales in proportion to \(\mathcal{E}_0^{3/2}\) as \(\mathcal{E}_0\) becomes large. Thus, in such a worst-case scenario the enstrophy still remains bounded for all times and there is no evidence for formation of singularity in finite time. We also analyse properties of the Navier-Stokes flows leading to the extreme enstrophy values and show that this behaviour is realized by a series of vortex reconnection events.Axisymmetric inertial modes in a spherical shell at low Ekman numbers.https://zbmath.org/1460.768952021-06-15T18:09:00+00:00"Rieutord, M."https://zbmath.org/authors/?q=ai:rieutord.michel"Valdettaro, L."https://zbmath.org/authors/?q=ai:valdettaro.lorenzoSummary: We investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero. We identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number \(E\) becomes very small. First are modes associated with attractors of characteristics that are made of thin shear layers closely following the periodic orbit traced by the characteristic attractor. Second are modes made of shear layers that connect the critical latitude singularities of the two hemispheres of the inner boundary of the spherical shell. Third are quasi-regular modes associated with the frequency of neutral periodic orbits of characteristics. We thoroughly analyse a subset of attractor modes for which numerical solutions point to an asymptotic law governing the eigenvalues. We show that three length scales proportional to \(E^{1/6}\), \(E^{1/4}\) and \(E^{1/3}\) control the shape of the shear layers that are associated with these modes. These scales point out the key role of the small parameter \(E^{1/12}\) in these oscillatory flows. With a simplified model of the viscous Poincaré equation, we can give an approximate analytical formula that reproduces the velocity field in such shear layers. Finally, we also present an analysis of the quasi-regular modes whose frequencies are close to \(\sin (\pi/4)\) and explain why a fluid inside a spherical shell cannot respond to any periodic forcing at this frequency when viscosity vanishes.Decay of turbulent wakes behind a disk in homogeneous and stratified fluids.https://zbmath.org/1460.762352021-06-15T18:09:00+00:00"Chongsiripinyo, Karu"https://zbmath.org/authors/?q=ai:chongsiripinyo.karu"Sarkar, Sutanu"https://zbmath.org/authors/?q=ai:sarkar.sutanuSummary: Body-inclusive large-eddy simulations of disk wakes are performed for a homogeneous fluid and for different levels of stratification. The Reynolds number is \(5 \times 10^4\) and the Froude number \((Fr)\) takes the values of \(\infty , 50, 10\) and 2. In the axisymmetric wake of a disk with diameter \(L_b\) in a homogeneous fluid, it is found that the mean streamwise velocity deficit \((U_0)\) decays in two stages: \(U_0\propto x^{-0.9}\) during \(10<x/L_b<65\) and, subsequently, \(U_0\propto x^{-2/3}\). Consequently, none of the simulated stratified wakes is able to exhibit the classical 2/3 decay exponent of \(U_0\) in the interval before buoyancy effects set in. Stratification affects the wake within approximately one buoyancy time scale, after which, we find three regimes: weakly stratified turbulence (WST), intermediately stratified turbulence (IST) and strongly stratified turbulence (SST). WST begins when the turbulent Froude number \((Fr_h)\) decreases to \(O(1)\), spans \(1\lesssim Nt_b\lesssim 5\) and, while the mean flow is strongly affected by buoyancy in WST, turbulence is not. During IST, which commences at \(Nt_b\approx 5\) when \(Fr_h=O(0.1)\), the mean flow has arrived into the non-equilibrium (NEQ) regime with \(U_0\propto x^{-0.18}\), but the turbulence state is still in transition, as indicated by progressively increasing turbulence anisotropy. When \(Fr_h\sim O(0.01)\) at \(Nt_b\approx 20\), the wake transitions into SST, where the turbulent vertical Froude number \((Fr_v)\) asymptotes to a \(O(1)\) constant. There is strong anisotropy \((u_z'\ll u_h')\), and both \(u_h'\) and \(U_0\) satisfy \(x^{-0.18}\) decay, signifying the arrival of the NEQ regime for both turbulence and mean flow. Turbulence is patchy and temporal spectra are broadband in the SST wake. The wake height decreases as \(L_V\sim O(U_0/N)\) in IST/SST. Energy budgets reveal that stratification prolongs wake life during WST/early-IST by both an energy transfer from mean potential energy to mean kinetic energy and reduction of turbulent production. In the late-IST/early-SST stages, production is enhanced and, additionally, there is injection from turbulent potential energy slowing down turbulent kinetic energy (TKE) decay. Only in the SST stage, when NEQ is realized for both the mean and turbulence, does the turbulent buoyancy flux become negative again, acting as a sink of TKE.Experimental investigation of unsteady separation in the rotor-oscillator flow.https://zbmath.org/1460.760012021-06-15T18:09:00+00:00"Lamarche-Gagnon, Marc-Étienne"https://zbmath.org/authors/?q=ai:lamarche-gagnon.marc-etienne"Vétel, Jérôme"https://zbmath.org/authors/?q=ai:vetel.jeromeSummary: Visualisations of various types of flow separation are presented in an experimental set-up that translates a rotating cylinder parallel to a wall. Particle image velocimetry is used to measure the two velocity components in a plane perpendicular to the cylinder where the flow is two-dimensional. To spatially resolve the flow close to the wall, a high-viscosity fluid is used. For a periodic translation, the fixed separation is compared to the theory of \textit{G. Haller} [ibid. 512, 257--311 (2004; Zbl 1066.76054)], while for non-periodic translations, a method is proposed to extract the moving separation point captured by a Lagrangian saddle point, and its finite-time unstable direction (separation profiles). Intermediate cases are also presented where both types of separation, fixed and moving, are either present simultaneously or appear successively. Some results issued from numerical simulations of an impinging jet show that all the cases observed in the rotor-oscillator flow are not restricted to high-viscosity fluid motions but may also occur within any vortical flow.Evolution of a vortex in a strongly stratified shear flow. II: Numerical simulations.https://zbmath.org/1460.763712021-06-15T18:09:00+00:00"Billant, Paul"https://zbmath.org/authors/?q=ai:billant.paul"Bonnici, Julien"https://zbmath.org/authors/?q=ai:bonnici.julienSummary: We conduct direct numerical simulations of an initially vertical Lamb-Oseen vortex in an ambient shear flow varying sinusoidally along the vertical in a stratified fluid. The Froude number \(F_h\) and the Reynolds number \(Re\), based on the circulation \(\Gamma\) and radius \(a_0\) of the vortex, have been varied in the ranges: \(0.1\leqslant F_h\leqslant 0.5\) and \(3000\leqslant Re\leqslant 10\,000\). The shear flow amplitude \(\hat{U}_S\) and vertical wavenumber \(\hat{k}_z\) lie in the ranges: \(0.02\leqslant 2\pi a_0\hat{U}_S/ \Gamma \leqslant 0.4\) and \(0.1\leqslant \hat{k}_za_0\leqslant 2 \pi\). The results are analysed in the light of the asymptotic analyses performed in Part 1 [ibid. 893, Article ID A17, 34 p. (2020; Zbl 1460.76372)]. The vortex is mostly advected in the direction of the shear flow but also in the perpendicular direction owing to the self-induction. The decay of potential vorticity is strongly enhanced in the regions of high shear. The long-wavelength analysis for \(\hat{k}_za_0F_h\ll 1\) predicts very well the deformations of the vortex axis. The evolutions of the vertical shear of the horizontal velocity and of the vertical gradient of the buoyancy at the location of maximum shear are also in good agreement with the asymptotic predictions when \(\hat{k}_za_0F_h\) is sufficiently small. As predicted by the asymptotic analysis, the minimum Richardson number never goes below the critical value \(1/4\) when \(\hat{k}_za_0F_h\ll 1\). The numerical simulations show that the shear instability is triggered only when \(\hat{k}_za_0F_h\gtrsim 1.6\) for sufficiently high buoyancy Reynolds number \(ReF_h^2\). There is also a weak dependence of this threshold on the shear flow amplitude. In agreement with the numerical simulations, the long-wavelength analysis predicts that the minimum Richardson number goes below \(1/4\) when \(\hat{k}_za_0F_h\gtrsim 1.7\) although this is beyond its expected range of validity.Evolution of a vortex in a strongly stratified shear flow. I: Asymptotic analysis.https://zbmath.org/1460.763722021-06-15T18:09:00+00:00"Bonnici, Julien"https://zbmath.org/authors/?q=ai:bonnici.julien"Billant, Paul"https://zbmath.org/authors/?q=ai:billant.paulSummary: In this paper, we investigate the dynamics of an initially vertical vortex embedded in a shear flow in a stratified fluid by means of a long-wavelength analysis. The main goal is to determine, whether or not, the Kelvin-Helmholtz instability can develop unconditionally as speculated by \textit{D. K. Lilly} [``Stratified turbulence and the mesoscale variability of the atmosphere'', J. Atmos. Sci. 40, No. 3, 749--761 (1983; \url{doi:10.1175/1520-0469(1983)040<0749:STATMV>2.0.CO;2})]. The analysis is performed in the case of the Lamb-Oseen vortex profile and a shear flow uniform in the horizontal and varying sinusoidally along the vertical using the assumption \(\hat{k}_za_0F_h\ll 1\), where \(\hat{k}_z\) is the vertical wavenumber, \(a_0\) the vortex radius and \(F_h\) the horizontal Froude number based on the circulation of the vortex. The results show that the vortex axis is advected not only in the direction of the shear flow but also in the perpendicular direction owing to the self-induced motion of the vortex. In addition, internal waves are transiently excited at the beginning, generating an initial non-hydrostatic regime. Their relative effects on the displacements of the vortex axis are weak except initially. The angular velocity of the vortex decays owing to a dynamic effect and viscous effects related to the vertical shear. The former effect is due to the squeezing of isopycnals in the vortex core, which implies a decrease of the vertical vorticity to satisfy potential vorticity conservation. In addition, a horizontal velocity field with an azimuthal wavenumber \(m=2\) is generated, meaning that the shape of the vortex becomes slightly elliptical. We further show that the minimum asymptotic Richardson number is bounded, \(\min (Ri)>3.43\), when \(\hat{k}_za_0F_h\ll 1\) and therefore cannot go below the critical value \(1/4\). This is because the growth of the vertical shear of the horizontal velocity of the vortex saturates owing to the decay of its angular velocity and because the squeezing of isopycnals increases the stratification strength. This suggests that the shear instability cannot always develop in strongly stratified flows, contrary to the conjecture of Lilly (as above). These predictions will be tested against direct numerical simulations in part II [the authors, ibid. 893, Article ID A18, 24 p. (2020; Zbl 1460.76371)].Gravity-capillary waves in reduced models for wave-structure interactions.https://zbmath.org/1460.762592021-06-15T18:09:00+00:00"Jamshidi, Sean"https://zbmath.org/authors/?q=ai:jamshidi.sean"Trinh, Philippe H."https://zbmath.org/authors/?q=ai:trinh.philippe-hSummary: This paper is concerned with steady-state subcritical gravity-capillary waves that are produced by potential flow past a wave-making body. Such flows are characterised by two non-dimensional parameters: the Froude number, \(F\), and the inverse Bond number, \(T\). When the size of the wave-making body is formally small, there are two qualitatively different flow regimes and thus a single bifurcation curve in the \((F,T)\) plane. If, however, the size of the obstruction is of order one, then, in the limit \(F\), \(T\rightarrow 0\), the second author and \textit{S. J. Chapman} [ibid. 724, 392--424 (2013; Zbl 1287.76069)] have shown that the bifurcation curve widens into a band, within which there are four new flow regimes. Here, we use results from exponential asymptotics to show how, in this low-speed limit, the water-wave equations can be asymptotically reduced to a single differential equation, which we solve numerically to confirm one of the new classes of waves. The issue of numerically solving the full set of gravity-capillary equations for potential flow is also discussed.Turbulent boundary-layer flow beneath a vortex. II: Power-law swirl.https://zbmath.org/1460.764802021-06-15T18:09:00+00:00"Loper, David E."https://zbmath.org/authors/?q=ai:loper.david-eSummary: The problem formulated in Part 1 [the author, ibid. 892, Article ID A16, 40 p. (2020; Zbl 1460.76479)] for flow in the turbulent boundary layer beneath a vortex is solved for a power-law swirl: \(v_\infty (r)\sim r^{2 \theta -1}\), where \(r\) is cylindrical radius and \(\theta\) is a constant parameter, with turbulent diffusivity parameterized as \(\nu =v_\infty L\) and the diffusivity function \(L\) either independent of axial distance \(z\) from a stationary plane (model A) or constant within a rough layer of thickness \(z_0\) adjoining the plane and linear in \(z\) outside (model B). Model A is not a useful model of vortical flow, whereas model B produces realistic results. As found in Part 1 for \(\theta =1.0\), radial flow consists of a sequence jets having thicknesses that vary nearly linearly with \(r\). A novel structural feature is the turning point \((r_t,z_t)\), where the primary jet has a minimum height. The radius \(r_t\) is a proxy for the eye radius of a vortex and \(z_t\) is a proxy for the size of the corner region. As \(r\) decreases from \(r_t\), the primary jet thickens, axial outflow from the layer increases and axial oscillations become larger, presaging a breakdown of the boundary layer. For small \(\theta\), \(r_t\sim z_0/\epsilon\theta\) and \(z_t\sim z_0/ \theta^{3/2}\). The lack of existence of the turning point for \(\theta \gtrsim 0.42\) and the acceleration of the turning point away from the origin of the meridional plane as \(\theta \rightarrow 0\) provide partial explanations why weakly swirling flows do not have eyes, why strongly swirling flows have eyes and why a boundary layer cannot exist beneath a potential vortex.Turbulent boundary-layer flow beneath a vortex. I: Turbulent Bödewadt flow.https://zbmath.org/1460.764792021-06-15T18:09:00+00:00"Loper, David E."https://zbmath.org/authors/?q=ai:loper.david-eSummary: The equations governing the mean fluid motions within a turbulent boundary layer adjoining a stationary plane beneath an axisymmetric circumferential flow \(v_\infty (r)\), where \(r\) is cylindrical radius, are solved by assuming the eddy diffusivity is proportional to \(v_\infty\) times a diffusivity function \(L(r,z)\), where \(z\) is axial distance from the plane. The boundary-layer shape and structure depend on the dimensionless vorticity \(\theta =\text{d}(rv_\infty)/2 v_\infty\,\text{d}r\), but are independent of the strength of the circumferential flow. This problem has been solved using a spectral method in the case of rigid-body motion \(( \theta =1\) and \(v_\infty \sim r)\) for two models of \(L\): \(L\) constant (model A) and \(L\) constant within a rough layer of thickness \(z_0\) adjoining the boundary and increasing linearly with \(z\) outside that layer (model B). The influence of the rough layer is quantified by the dimensionless radial coordinate \(\rho = \varepsilon r/z_0\), where \(\varepsilon \ll 1\). The boundary-layer thickness varies parabolically with \(r\) for model A and nearly linearly with \(r\) for model B. Inertial stability of the outer flow causes the velocity components to decay with axial distance as exponentially damped oscillations, with the radial flow consisting of a sequence of jets. Axial flow is positive (flowing out of the boundary layer). Outflow from the layer, velocity gradients at the bounding plane, meridional-plane circulation and oscillations all increase as radius decreases.Flow state estimation in the presence of discretization errors.https://zbmath.org/1460.762872021-06-15T18:09:00+00:00"da Silva, Andre F. C."https://zbmath.org/authors/?q=ai:da-silva.andre-f-c"Colonius, Tim"https://zbmath.org/authors/?q=ai:colonius.timSummary: Ensemble data assimilation methods integrate measurement data and computational flow models to estimate the state of fluid systems in a robust, scalable way. However, discretization errors in the dynamical and observation models lead to biased forecasts and poor estimator performance. We propose a low-rank representation for this bias, whose dynamics is modelled by data-informed, time-correlated processes. State and bias parameters are simultaneously corrected online with the ensemble Kalman filter. The proposed methodology is then applied to the problem of estimating the state of a two-dimensional flow at modest Reynolds number using an ensemble of coarse-mesh simulations and pressure measurements at the surface of an immersed body in a synthetic experiment framework. Using an ensemble size of 60, the bias-aware estimator is demonstrated to achieve at least 70\% error reduction when compared to its bias-blind counterpart. Strategies to determine the bias statistics and their impact on the estimator performance are discussed.On the trajectory of leading-edge vortices under the influence of Coriolis acceleration.https://zbmath.org/1460.769552021-06-15T18:09:00+00:00"Limacher, Eric"https://zbmath.org/authors/?q=ai:limacher.eric"Morton, Chris"https://zbmath.org/authors/?q=ai:morton.chris"Wood, David"https://zbmath.org/authors/?q=ai:wood.david-harlan|wood.david-c-m|wood.david-ronald|wood.david-a|wood.david-muir|wood.david-r-r|wood.david-jSummary: Leading-edge vortices (LEVs) can form and remain attached to a rotating wing indefinitely, but the mechanisms of stable attachment are not well understood. Taking for granted that such stable structures do form, a practical question arises: what is the trajectory of the LEV core? Noting that span-wise flow exists within the LEV core, it is apparent that a mean streamline aligned with the axis of the stable LEV must exist. The present work uses the Navier-Stokes equations along such a steady, axial streamline in order to consider the accelerations that act in the streamline-normal direction to affect its local curvature. With some simplifying assumptions, a coupled system of ordinary differential equations is derived that describes the trajectory of an axial streamline through the vortex core. The model is compared to previous work, and is found to predict the trajectory of the LEV core well at span-wise locations inboard of the midspan. This result suggests that Coriolis acceleration is responsible for limiting the span-wise extent of a stable LEV by tilting it into the wake within several chord lengths from the centre of rotation. The downwash due to the tip vortex also appears to play a role, as the only significant differences between model-predicted LEV trajectories and previous results are in the plate-normal direction.On the origins of transverse jet shear layer instability transition.https://zbmath.org/1460.763122021-06-15T18:09:00+00:00"Shoji, Takeshi"https://zbmath.org/authors/?q=ai:shoji.takeshi"Harris, Elijah W."https://zbmath.org/authors/?q=ai:harris.elijah-w"Besnard, Andrea"https://zbmath.org/authors/?q=ai:besnard.andrea"Schein, Stephen G."https://zbmath.org/authors/?q=ai:schein.stephen-g"Karagozian, Ann R."https://zbmath.org/authors/?q=ai:karagozian.ann-rSummary: This experimental study explores the physical mechanisms by which a transverse jet's upstream shear layer can transition from being a convective instability to an absolute/global instability as the jet-to-cross-flow momentum flux ratio \(J\) is reduced. As first proposed in computational studies by \textit{P. S. Iyer} and \textit{K. Mahesh} [ibid. 790, 275--307 (2016; Zbl 1382.76138)], the upstream shear layer just beyond the jet injection may be analogous to a local counter-current shear layer, which is known for a planar geometry to become absolutely unstable at a large enough counter-current shear layer velocity ratio, \(R_1\). The present study explores this analogy for a range of transverse jet momentum flux ratios and jet-to-cross-flow density ratios \(S\), for jets containing differing species concentrations (nitrogen, helium and acetone vapour) at several different jet Reynolds numbers. These studies make use of experimental data extracted from stereo particle image velocimetry as well as simultaneous stereo particle image velocimetry and acetone planar laser-induced fluorescence imaging. They provide experimental evidence for the relevance of the counter-current shear layer analogy to upstream shear layer instability transition in a nozzle-generated transverse jet.Settling-driven large-scale instabilities in double-diffusive convection.https://zbmath.org/1460.768532021-06-15T18:09:00+00:00"Ouillon, Raphael"https://zbmath.org/authors/?q=ai:ouillon.raphael"Edel, Philip"https://zbmath.org/authors/?q=ai:edel.philip"Garaud, Pascale"https://zbmath.org/authors/?q=ai:garaud.pascale"Meiburg, Eckart"https://zbmath.org/authors/?q=ai:meiburg.eckart-hSummary: When the density of a gravitationally stable fluid depends on a fast diffusing scalar and a slowly diffusing scalar of opposite contribution to the stability, `double diffusive' instabilities may develop and drive convection. When the slow diffuser settles under gravity, as is for instance the case for small sediment particles in water, settling-driven double-diffusive instabilities can additionally occur. Such instabilities are relevant in a variety of naturally occurring settings, such as particle-laden river discharges, or underground inflows in lakes. Inspired by the dynamics of the more traditional thermohaline double-diffusive instabilities, we ask whether large-scale `mean-field' instabilities can develop as a result of sedimentary double-diffusive convection. We first apply the mean-field instability theory of \textit{A. Traxler} et al. [ibid. 677, 530--553 (2011; Zbl 1241.76229)] to high-Prandtl-number fluids, and find that these are unstable to Radko's layering instability, yet collectively stable. We then extend the theory of Traxler et al. [loc. cit.] to include settling and study its impact on the development of the collective instability. We find that two distinct regimes exist. At low settling velocities, the double-diffusive turbulence in the fingering regime is relatively unaffected by settling and remains stable to the classical collective instability. It is, however, unstable to a new instability in which large-scale gravity waves are excited by the phase shift between the salinity and particle concentration fields. At higher settling velocities, the double-diffusive turbulence is substantially affected by settling, and becomes unstable to the classic collective instability. Our findings, validated by direct numerical simulations, reveal new opportunities to observe settling-driven layering in laboratory and field experiments.Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. I: Unbounded domain.https://zbmath.org/1460.762582021-06-15T18:09:00+00:00"Gururaj, Saranraj"https://zbmath.org/authors/?q=ai:gururaj.saranraj"Guha, Anirban"https://zbmath.org/authors/?q=ai:guha.anirbanSummary: In this paper, using multiple-scale analysis, we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal gravity wavepackets in weakly non-uniform density stratifications in an unbounded domain in the presence of viscous and rotational effects. Such triad interactions are one of the mechanisms by which high-wavenumber internal waves lead to ocean turbulence and mixing via parametric subharmonic instability. Non-uniform stratification introduces detuning -- mismatch in the vertical wavenumber triad condition, which may strongly affect the energy transfer process. We investigate in detail how factors like wavepacket width, group speeds, nonlinear coupling coefficients, detuning and viscosity affect energy transfer in weakly varying stratification. We also investigate the effect of detuning on energy transfer in varying stratification for different daughter wave combinations of a fixed parent wave. We find limitations of the well-known `pump-wave approximation' and derive a non-dimensional number, which can be evaluated from initial conditions, that can predict the maximum energy transferred from the parent wave during the later stages. Two additional non-dimensional numbers, based on various factors affecting energy transfer between near-resonant wavepackets, have also been defined. Moreover, we identify the optimal background stratification in a medium of varying stratification for the parent wave to form a triad with no detuning so that the energy transfer is maximum.Impact of centrifugal buoyancy on strato-rotational instability.https://zbmath.org/1460.762792021-06-15T18:09:00+00:00"Lopez, Juan M."https://zbmath.org/authors/?q=ai:lopez.juan-manuel"Marques, Francisco"https://zbmath.org/authors/?q=ai:marques.franciscoSummary: In a recent experiment on the flow between two concentric cylinders with the inner cylinder rotating and the fluid being stably stratified, \textit{J. B. Flór} et al. [``Onset of centrifugal instability at a rotating cylinder in a stratified fluid'', Phys. Fluids 30, Paper No. 084103 (2018; \url{doi:10.1063/1.5033550})] found helical wave structures confined to the inner cylinder in an annulus with small inner-to-outer radius ratio (very large gap) in regimes where the Froude number (ratio of cylinder rotation frequency to buoyancy frequency) is less than one. These helical waves were reported to originate at the corners where the inner cylinder meets the top and bottom boundaries, and were found to be asymmetric with the lower helical wave being more intense. These observations are in marked contrast with other stratified Taylor-Couette experiments that employed much larger inner-to-outer radius ratios and much larger annulus height-to-gap ratios. Here, we present direct numerical simulations of the Navier-Stokes equations, with a Boussinesq approximation that accounts for centrifugal buoyancy effects which are normally neglected. Fixing the stratification and increasing the rotation rate of the inner cylinder (quantified by a Reynolds number), we find a sequence of bifurcations, each one introducing a new frequency, from the steady base state to a three-torus state. The instabilities are generated at the corners where the inner cylinder meets the endwalls, and the first instability is localized at the lower corner as a consequence of centrifugal buoyancy effects. We have also conducted simulations without centrifugal buoyancy and find that centrifugal buoyancy plays a crucial role in breaking the up-down reflection symmetry of the problem, capturing the most salient features of the experimental observations.A regularised slender-body theory of non-uniform filaments.https://zbmath.org/1460.762502021-06-15T18:09:00+00:00"Walker, Benjamin J."https://zbmath.org/authors/?q=ai:walker.benjamin-j"Curtis, M. P."https://zbmath.org/authors/?q=ai:curtis.m-p"Ishimoto, K."https://zbmath.org/authors/?q=ai:ishimoto.kenta"Gaffney, E. A."https://zbmath.org/authors/?q=ai:gaffney.eamonn-aSummary: Resolving the detailed hydrodynamics of a slender body immersed in highly viscous Newtonian fluid has been the subject of extensive research, applicable to a broad range of biological and physical scenarios. In this work, we expand upon classical theories developed over the past fifty years, deriving an algebraically accurate slender-body theory that may be applied to a wide variety of body shapes, ranging from biologically inspired tapering flagella to highly oscillatory body geometries with only weak constraints, most significantly requiring that cross-sections be circular. Inspired by well known analytic results for the flow around a prolate ellipsoid, we pose an ansatz for the velocity field in terms of a regular integral of regularised Stokes-flow singularities with prescribed, spatially varying regularisation parameters. A detailed asymptotic analysis is presented, seeking a uniformly valid expansion of the ansatz integral, accurate at leading algebraic order in the geometry aspect ratio, to enforce no-slip boundary conditions and thus analytically justify the slender-body theory developed in this framework. The regularisation within the ansatz additionally affords significant computational simplicity for the subsequent slender-body theory, with no specialised quadrature or numerical techniques required to evaluate the regular integral. Furthermore, in the special case of slender bodies with a straight centreline in uniform flow, we derive a slender-body theory that is particularly straightforward via use of the analytic solution for a prolate ellipsoid. We evidence the validity of our simple theory with explicit numerical examples for a wide variety of slender bodies, and highlight a potential robustness of our methodology beyond its rigorously justified scope.Collision of vortex rings upon V-walls.https://zbmath.org/1460.762182021-06-15T18:09:00+00:00"New, T. H."https://zbmath.org/authors/?q=ai:new.t-h"Long, J."https://zbmath.org/authors/?q=ai:long.jianceng|long.jianhui|long.jiang|long.jing|long.jiaping|long.jeff|long.jianyu|long.jianwu|long.jun|long.jiancheng|long.jianmin|long.jinling|long.junyan|long.jianzhong|long.jinghua|long.junsheng|long.junyun|long.junbo|long.jason|long.jiangqi|long.jancis|long.jingfan|long.jihao|long.jane|long.jianjun"Zang, B."https://zbmath.org/authors/?q=ai:zang.bilian|zang.binyu"Shi, Shengxian"https://zbmath.org/authors/?q=ai:shi.shengxianSummary: A study on \({Re} =2000\) and 4000 vortex rings colliding with V-walls with included angles of \(\theta =30^\circ\) to \(120^\circ\) has been conducted. Along the valley plane, higher Reynolds numbers and/or included angles of \(\theta \leqslant 60^\circ\) lead to secondary/tertiary vortex-ring cores leapfrogging past the primary vortex-ring cores. The boundary layers upstream of the latter separate and the secondary/tertiary vortex-ring cores pair up with these wall-separated vortices to form small daisy-chained vortex dipoles. Along the orthogonal plane, primary vortex-ring cores grow bulbous and incoherent after collisions, especially as the included angle reduces. Secondary and tertiary vortex-ring core formations along this plane also lag those along the valley plane, indicating that they form by propagating from the wall surfaces to the orthogonal plane as the primary vortex ring gradually comes into contact with the entire V-wall. Circulation results show significant variations between the valley and orthogonal plane, and reinforce the notion that the collision behaviour for \(\theta \leqslant 60^\circ\) is distinctively different from those at larger included angles. Vortex-core trajectories are compared to those for inclined-wall collisions, and secondary vortex-ring cores are found to initiate earlier for the V-walls, postulated to be a result of the opposing circumferential flows caused by the simultaneous collisions of both primary vortex-ring cores with the V-wall surfaces. These circumferential flows produce a bi-helical flow mode [\textit{T. T. Lim}, ``An experimental study of a vortex ring interacting with an inclined wall'', Exp. Fluids 7, No. 7, 453--463 (1989; \url{doi:10.1007/BF00187063})] that sees higher vortex compression levels along the orthogonal plane, which limit vortex stretching along the wall surfaces and produce secondary vortex rings earlier. Lastly, vortex structures and behaviour of the present collisions are compared to those associated with flat/inclined walls and round-cylinder-based collisions for a more systematic understanding of their differences.Fingering instability of a viscous liquid bridge stretched by an accelerating substrate.https://zbmath.org/1460.762612021-06-15T18:09:00+00:00"Brulin, Sebastian"https://zbmath.org/authors/?q=ai:brulin.sebastian"Roisman, Ilia V."https://zbmath.org/authors/?q=ai:roisman.ilia-v"Tropea, Cameron"https://zbmath.org/authors/?q=ai:tropea.cameronSummary: When a viscous liquid bridge between two parallel substrates is stretched by accelerating one substrate, its interface on the plates recedes in the radial direction. In some cases the interface becomes unstable. Such instability leads to the emergence of a network of fingers. In this study, the mechanisms of such fingering are studied experimentally and analysed theoretically. The experimental set-up allows a constant acceleration of a movable substrate at up to 180 m \(s^{-2}\). The phenomena are observed using two high-speed video systems. The number of fingers is measured for different liquid viscosities, liquid bridge sizes and wetting conditions. Linear stability analysis of the bridge interface takes into account the inertial, viscous and capillary effects in the liquid flow. The theoretically predicted maximum number of fingers, corresponding to an instability mode with the maximum amplitude, and a threshold for the onset of finger formation are proposed. Both models agree well with the experimental data up to the start of emerging cavitation bubbles.Contact line motion in axial thermocapillary outward flow.https://zbmath.org/1460.761892021-06-15T18:09:00+00:00"Dominguez Torres, A."https://zbmath.org/authors/?q=ai:dominguez-torres.a"Mac Intyre, J. R."https://zbmath.org/authors/?q=ai:mac-intyre.j-r"Gomba, J. M."https://zbmath.org/authors/?q=ai:gomba.j-m"Perazzo, C. A."https://zbmath.org/authors/?q=ai:perazzo.carlos-alberto"Correa, P. G."https://zbmath.org/authors/?q=ai:correa.p-g"Lopez-Villa, A."https://zbmath.org/authors/?q=ai:lopez-villa.a"Medina, A."https://zbmath.org/authors/?q=ai:medina.alberto-p|medina.arcesio-castaneda|medina.albert|medina.agustin|medina.abudulhekim|medina.aurelio|medina.abraham|medina.anibal-dSummary: We study the contact line dynamics of a viscous droplet deposited at the centre of a substrate subject to an axial thermal gradient. The temperature of the substrate decreases with distance from the centre, so the Marangoni stress induced at the liquid-air interface displaces the liquid radially outward. The flow experiences two stages. In the first stage, the droplet evolves towards an axially symmetric ring whose radius increases with time as \(t^{1/3}\). Using the lubrication approximation, we perform numerical simulations that confirm this law for the motion of the front and show that the maximum thickness of the profile decreases as \(t^{-0.374}\). We explain the evolution law of the contact line by balancing Marangoni and viscous stresses. In the second stage, the contact line becomes unstable and develops smooth corrugations whose amplitude increases with time and that eventually become long fingers. The temporal evolution of the Fourier spectra of the contour shows a shift of the most unstable mode from smaller to larger azimuthal wavenumbers.Stochastic Lagrangian dynamics of vorticity. II: Application to near-wall channel-flow turbulence.https://zbmath.org/1460.762102021-06-15T18:09:00+00:00"Eyink, Gregory L."https://zbmath.org/authors/?q=ai:eyink.gregory-l"Gupta, Akshat"https://zbmath.org/authors/?q=ai:gupta.akshat"Zaki, Tamer A."https://zbmath.org/authors/?q=ai:zaki.tamer-aSummary: We use an online database of a turbulent channel-flow simulation at \(Re_\tau =1000\) [\textit{J. Graham} et al., ``A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES'', J. Turbul. 17, No. 2, 181--215 (2016; \url{doi:10.1080/14685248.2015.1088656})] to determine the origin of vorticity in the near-wall buffer layer. Following an experimental study of \textit{J. Sheng} et al. [J. Fluid Mech. 633, 17--60 (2009; Zbl 1183.76047)], we identify typical `ejection' and `sweep' events in the buffer layer by local minima/maxima of the wall stress. In contrast to their conjecture, however, we find that vortex lifting from the wall is not a discrete event requiring \(\sim 1\) viscous time and \(\sim 10\) wall units, but is instead a distributed process over a space-time region at least \(1\sim 2\) orders of magnitude larger in extent. To reach this conclusion, we exploit a rigorous mathematical theory of vorticity dynamics for Navier-Stokes solutions, in terms of stochastic Lagrangian flows and stochastic Cauchy invariants, conserved on average backward in time. This theory yields exact expressions for vorticity inside the flow domain in terms of vorticity at the wall, as transported by viscous diffusion and by nonlinear advection, stretching and rotation. We show that Lagrangian chaos observed in the buffer layer can be reconciled with saturated vorticity magnitude by `virtual reconnection': although the Eulerian vorticity field in the viscous sublayer has a single sign of spanwise component, opposite signs of Lagrangian vorticity evolve by rotation and cancel by viscous destruction. Our analysis reveals many unifying features of classical fluids and quantum superfluids. We argue that `bundles' of quantized vortices in superfluid turbulence will also exhibit stochastic Lagrangian dynamics and satisfy stochastic conservation laws resulting from particle relabelling symmetry.Stochastic Lagrangian dynamics of vorticity. I: General theory for viscous, incompressible fluids.https://zbmath.org/1460.762092021-06-15T18:09:00+00:00"Eyink, Gregory L."https://zbmath.org/authors/?q=ai:eyink.gregory-l"Gupta, Akshat"https://zbmath.org/authors/?q=ai:gupta.akshat"Zaki, Tamer A."https://zbmath.org/authors/?q=ai:zaki.tamer-aSummary: Prior mathematical work of \textit{P. Constantin} and \textit{G. Iyer} [Commun. Pure Appl. Math. 61, No. 3, 330--345 (2008; Zbl 1156.60048); Ann. Appl. Probab. 21, No. 4, 1466--1492 (2011; Zbl 1246.76018)] has shown that incompressible Navier-Stokes solutions possess infinitely many stochastic Lagrangian conservation laws for vorticity, backward in time, which generalize the invariants of \textit{A. L. Cauchy} [``Sur l'état du fluide. à une époque quelconque du mouvement. Mémoires extraits des recueils de l'Académie des sciences de l'Institut de France, Théorie de la propagation des ondes à la surface d'un fluide pesant d'une profondeur indéfinie. (Extraits des Mémoires présentés par divers savants à l'Académie royale des Sciences de l'Institut de France et imprimés par son ordre)'', Sci. Math. Phys. I, 1827 Seconde Partie, 33--73 (1815)] for smooth Euler solutions. We reformulate this theory for the case of wall-bounded flows by appealing to the \textit{G. A. Kuz'min} [``Ideal incompressible hydrodynamics in terms of the vortex momentum density'', Phys. Lett. A 96, No. 2, 88--90 (1983; \url{doi:10.1016/0375-9601(83)90597-2})]-\textit{V. I. Oseledets} [Russ. Math. Surv. 44, No. 3, 210--211 (1989; Zbl 0850.76130); translation from Usp. Mat. Nauk 44, No. 3 (267), 169--170 (1989)] representation of Navier-Stokes dynamics, in terms of the vortex-momentum density associated to a continuous distribution of infinitesimal vortex rings. The Constantin-Iyer theory provides an exact representation for vorticity at any interior point as an average over stochastic vorticity contributions transported from the wall. We point out relations of this Lagrangian formulation with the Eulerian theory of \textit{M. J. Lighthill} [``Boundary layer theory'', in: Laminar Boundary Layers. Oxford: Oxford University Press. 46--113 (1963)]-\textit{B. R. Morton} [Geophys. Astrophys. Fluid Dyn. 28, 277--308 (1984; Zbl 0551.76019)] for vorticity generation at solid walls, and also with a statistical result of \textit{G. I. Taylor} [Proc. R. Soc. Lond., Ser. A 135, 685--702 (1932; Zbl 0004.17306)]-\textit{E. R. Huggins} [``Vortex currents in turbulent superfluid and classical fluid channel flow, the Magnus effect, and Goldstone boson fields-2'', J. Low Temp. Phys. 96, No. 5--6, 317--346 (1994; \url{doi:10.1007/BF00754743})], which connects dissipative drag with organized cross-stream motion of vorticity and which is closely analogous to the `Josephson-Anderson relation' for quantum superfluids. We elaborate a Monte Carlo numerical Lagrangian scheme to calculate the stochastic Cauchy invariants and their statistics, given the Eulerian space-time velocity field. The method is validated using an online database of a turbulent channel-flow simulation [\textit{J. Graham} et al., ``A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES'', J. Turbul. 17, No. 2, 181--215 (2016; \url{doi:10.1080/14685248.2015.1088656})], where conservation of the mean Cauchy invariant is verified for two selected buffer-layer events corresponding to an `ejection' and a `sweep'. The variances of the stochastic Cauchy invariants grow exponentially backward in time, however, revealing Lagrangian chaos of the stochastic trajectories undergoing both fluid advection and viscous diffusion.The Crouzeix-Raviart element for the Stokes equations with the slip boundary condition on a curved boundary.https://zbmath.org/1460.766362021-06-15T18:09:00+00:00"Zhou, Guanyu"https://zbmath.org/authors/?q=ai:zhou.guanyu"Oikawa, Issei"https://zbmath.org/authors/?q=ai:oikawa.issei"Kashiwabara, Takahito"https://zbmath.org/authors/?q=ai:kashiwabara.takahitoAuthor's abstract: When the curved boundary is approximated by a polygon/polyhedron's surface, using a continuous discrete velocity to implement the slip boundary condition (SBC) of the Stokes problem may cause the variational crime. To avoid the variational crime, we apply the Crouzeix-Raviart (CR) element to discretize SBC. In error analysis, we modify the classical interpolation to satisfy the discrete SBC and obtain the interpolation error. Taking the domain perturbation into account, we derive the consistency error, and then investigate the relationship between the convergence order and the outer normal approximation for both 2D and 3D cases, where we obtain the optimal convergence for 2D cases. However, for 3D cases, our analysis elucidates that the outer normal approximation may yield a loss of the convergence rate, which is confirmed by two specific interpolation examples. The theoretical results are validated by numerical experiments.
Reviewer: J. Manimaran (Ponda)Effects of twist on the evolution of knotted magnetic flux tubes.https://zbmath.org/1460.769482021-06-15T18:09:00+00:00"Xiong, Shiying"https://zbmath.org/authors/?q=ai:xiong.shiying"Yang, Yue"https://zbmath.org/authors/?q=ai:yang.yue|yang.yue.1Summary: We develop a general method for constructing knotted flux tubes with finite thickness, arbitrary shape and tunable twist. The central axis of the knotted tube is specified by a smooth and non-degenerate parametric equation. The helicity of the corresponding solenoidal knotted field can be explicitly decomposed into writhe, normalized total torsion and intrinsic twist. We construct several knotted magnetic flux tubes with various twisting degrees, and investigate the effect of twist on their evolution in resistive magnetohydrodynamic flows using direct numerical simulation. For large twist, the magnetic knot gradually shrinks to a tight stable state, similar to the relaxation process in ideal magnetohydrodynamic flows. For small twist, the knotted flux tube splits at early times, accompanied by a rising magnetic dissipation rate. We elucidate the mechanism of the tube splitting using the phase portrait of the Lorentz force projected onto divergence-free space. For finite twist, the Hopf bifurcation from an unstable spiral point to a limit cycle occurs on the phase plane. In the evolution, field lines inside the limit cycle form invariant tori, whereas they become chaotic outside the limit cycle.The linear stability of an acceleration-skewed oscillatory Stokes layer.https://zbmath.org/1460.761872021-06-15T18:09:00+00:00"Thomas, Christian"https://zbmath.org/authors/?q=ai:thomas.christian.1|thomas.christianSummary: The linear stability of the family of flows generated by an acceleration-skewed oscillating planar wall is investigated using Floquet theory. Neutral stability curves and critical conditions for linear instability are determined for an extensive range of acceleration-skewed oscillating flows. Results indicate that acceleration skewness is destabilising and reduces the critical Reynolds number for the onset of linearly unstable behaviour. The structure of the eigenfunctions is discussed and solutions suggest that disturbances grow in the direction of highest acceleration.Liquid plug formation from heated binary mixtures in capillary tubes.https://zbmath.org/1460.760572021-06-15T18:09:00+00:00"Lv, Cunjing"https://zbmath.org/authors/?q=ai:lv.cunjing"Varanakkottu, Subramanyan N."https://zbmath.org/authors/?q=ai:varanakkottu.subramanyan-n"Hardt, Steffen"https://zbmath.org/authors/?q=ai:hardt.steffenSummary: We study the formation of liquid plugs in a vertical heated tube in contact with a reservoir filled with a binary liquid mixture. Various morphologies, such as liquid films, rings and plugs, are observed. A key phenomenon is the transition between a liquid ring and a plug, which is described using the concept of a quasi-static minimal energy surface that becomes unstable when the liquid volume exceeds a specific value. The critical diameter of the liquid ring and the volume and the position of the formed plug are obtained from an analytical model. The inner diameter of the liquid ring obeys a \(d_l\sim (t_0-t)^{0.57\pm 0.02}\) scaling law shortly before forming a plug at time \(t_0\). The height of the liquid column created develops according to \(X\sim (t-t_0)^{0.5\pm 0.01}\) in the first moments. The subsequent time evolution is described by a damped harmonic oscillator based on a scaling analysis. The discoveries presented in this work could be of great importance for our understanding of thermally induced interfacial phenomena in confined space.Heat and momentum transfer to a particle in a laminar boundary layer.https://zbmath.org/1460.768182021-06-15T18:09:00+00:00"Lattanzi, Aaron M."https://zbmath.org/authors/?q=ai:lattanzi.aaron-m"Yin, Xiaolong"https://zbmath.org/authors/?q=ai:yin.xiaolong"Hrenya, Christine M."https://zbmath.org/authors/?q=ai:hrenya.christine-mSummary: Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas-solids mixture. Previous efforts to resolve the solids' heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle-wall separation distance and asymptotically decays to zero for large particle-wall separation distances, seaming together the unbounded and near-wall regions.Vortex force maps for three-dimensional unsteady flows with application to a delta wing.https://zbmath.org/1460.761992021-06-15T18:09:00+00:00"Li, Juan"https://zbmath.org/authors/?q=ai:li.juan.1|li.juan"Zhao, Xiaowei"https://zbmath.org/authors/?q=ai:zhao.xiaowei"Graham, Michael"https://zbmath.org/authors/?q=ai:graham.michael-d|graham.michael-kSummary: The unsteady forces acting on a body depend strongly on the local flow structures such as vortices. A quantitative understanding of the contribution of these structures to the instantaneous overall force is of fundamental significance. In the present study, a three-dimensional (3-D) vortex force map (VFM) method, extended from a two-dimensional (2-D) one, is used to provide better insight into the complex 3-D flow dynamics. The VFM vectors are obtained from solutions of potential equations and used to build the 3-D VFMs where the critical regions and directions associated with significant positive or negative contributions to the forces are identified. Using the existing velocity/vorticity field near the body, these VFMs can be used to obtain the body forces. A decomposed form of the force formula is also derived to separate the correction term contributed from the uncaptured vortices (close to or far away from the body). The present method is applied to the starting flow of a delta wing at high angle of attack, where LEVs are enhanced and stabilized by an axial flow effect. The analogy between the normal force of a slender delta wing and that of a 2-D flat plate with a steadily growing span is demonstrated via the VFM analysis. We find, for this application, that the force evolution exhibits some similar behaviour to a 2-D airfoil starting flow and, surprisingly, the force contribution mainly comes from the conical vortex sheet rather than the central core. Moreover, a quantitative understanding of the influence of LEVs in different evolution regimes on the body force is demonstrated.Homogenization of hydrodynamic transport in Dirac fluids.https://zbmath.org/1460.820262021-06-15T18:09:00+00:00"Bal, Guillaume"https://zbmath.org/authors/?q=ai:bal.guillaume"Lucas, Andrew"https://zbmath.org/authors/?q=ai:lucas.andrew"Luskin, Mitchell"https://zbmath.org/authors/?q=ai:luskin.mitchellSummary: Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including the Dirac fluid of nearly charge neutral graphene, microscopic transport is not governed by diffusion, but by a more complicated set of linearized hydrodynamic equations, which form a system of degenerate elliptic equations coupled with the Stokes equation for fluid velocity. In sufficiently inhomogeneous media, these hydrodynamic equations reduce to homogenized diffusion equations. We recast the hydrodynamic transport equations as the infimum of a functional over conserved currents and present a functional framework to model and compute the homogenized diffusion tensor relating electrical and thermal currents to charge and temperature gradients. We generalize to this system to the well-known results in homogenization theory: Tartar's proof of local convergence to the homogenized theory in periodic and highly oscillatory media and sub-additivity of the above functional in random media with highly oscillatory, stationary, and ergodic coefficients.
{\copyright 2021 American Institute of Physics}On the stagnation point position of the flow impinging obliquely on a moving flat plate.https://zbmath.org/1460.761642021-06-15T18:09:00+00:00"Cheng, Sheng-Yin"https://zbmath.org/authors/?q=ai:cheng.sheng-yin"Chen, Falin"https://zbmath.org/authors/?q=ai:chen.falinSummary: To study the variation of the stagnation point position of the flow impinging obliquely on a moving flat plate, we follow the mathematical approach of \textit{J. M. Dorrepaal} [ibid. 163, 141--147 (1986; Zbl 0605.76033)] and obtain the analytical solution of the flow. Based on the solution, we derive an equation governing the variation of stagnation point position with both the plate velocity as well as the impinging angle. Results show that, when the plate is stationary, the stagnation point will stay in upstream if the flow is non-orthogonal, as concluded by previous studies. As soon as the plate starts to move, the stagnation point will move from upstream to downstream when the plate velocity increases beyond a small critical value, no matter whether the flow is orthogonal or non-orthogonal.Mammatus cloud formation by settling and evaporation.https://zbmath.org/1460.860282021-06-15T18:09:00+00:00"Ravichandran, S."https://zbmath.org/authors/?q=ai:ravichandran.s"Meiburg, Eckart"https://zbmath.org/authors/?q=ai:meiburg.eckart-h"Govindarajan, Rama"https://zbmath.org/authors/?q=ai:govindarajan.ramaSummary: We show how settling and phase change can combine to drive an instability, as a simple model for the formation of mammatus clouds. Our idealised system consists of a layer (an `anvil') of air mixed with saturated water vapour and monodisperse water droplets, sitting atop dry air. The water droplets in the anvil settle under gravity due to their finite size, evaporating as they enter dry air and cooling the layer of air just below the anvil. The colder air just below the anvil thus becomes denser than the dry air below it, forming a density `overhang', which is unstable. The strength of the instability depends on the density difference between the density overhang and the dry ambient, and the depth of the overhang. Using linear stability analysis and nonlinear simulations in one, two and three dimensions, we study how the amplitude and depth of the density layer depend on the initial conditions, finding that their variations can be explained in terms only of the size of the droplets making up the liquid content of the anvil and by the total amount of liquid water contained in the anvil. We find that the size of the water droplets is the controlling factor in the structure of the clouds: mammatus-like lobes form for large droplet sizes; and small droplet sizes lead to a `leaky' instability resulting in a stringy cloud structure resembling the newly designated \textit{asperitas}.The force on a slender particle under oscillatory translational motion in unsteady Stokes flow.https://zbmath.org/1460.761832021-06-15T18:09:00+00:00"Kabarowski, Jason K."https://zbmath.org/authors/?q=ai:kabarowski.jason-k"Khair, Aditya S."https://zbmath.org/authors/?q=ai:khair.aditya-sSummary: Asymptotic approximations are derived for the hydrodynamic force on a rigid, axisymmetric slender particle executing longitudinal or transverse oscillation in unsteady Stokes flow. The slender particle has an aspect ratio \(\epsilon =a/\ell \ll 1\), where \(\ell\) is the half-length of the particle, and \(a\) is its characteristic cross-sectional width. It is assumed that the particle has zero thickness at its ends. The frequency of oscillation is parameterized by the complex quantity \(\lambda^2=- \text{i}\ell^2\omega/\nu\), where \(\nu\) is the kinematic viscosity, \(\omega\) is the particle angular oscillation frequency (units of radians per second) and \(\text{i}=\sqrt{-1}\). Asymptotic approximations for the force are obtained in three distinguished limits for longitudinal oscillations: (i) a `low-frequency' regime with \(\epsilon \rightarrow 0\) and \(|\lambda|\) fixed; (ii) a `moderate-frequency' regime with \(\epsilon \rightarrow 0\) and \(\epsilon |\lambda |=O(1)\); and (iii) a `high-frequency' regime with \(\epsilon \rightarrow 0\) and \(\epsilon |\lambda|=O(1/ \epsilon^2)\). The acceleration reaction is a leading-order contributor to the force in this last regime, whereas it is subdominant at moderate frequency. For transverse oscillation we construct asymptotic approximations in the low and moderate-frequency regimes. Here, the acceleration reaction here plays a leading-order role at moderate frequency; hence, a `high frequency' regime in this case simply corresponds to the limiting behaviour for \(\epsilon |\lambda |\gg 1\). Our asymptotic predictions are in good agreement with the numerically computed frequency-dependent force on a prolate spheroid \((\epsilon =0.1)\) for longitudinal and transverse oscillations by \textit{C. J. Lawrence} and \textit{S. Weinbaum} [ibid. 189, 463--489 (1988; Zbl 0658.76031)] and \textit{C. Pozrikidis} [Phys. Fluids, A 1, No. 9, 1508--1520 (1989; Zbl 0692.76037)], respectively.Bistability of bubble and conical forms of vortex breakdown in laminar swirling jets.https://zbmath.org/1460.762162021-06-15T18:09:00+00:00"Moise, Pradeep"https://zbmath.org/authors/?q=ai:moise.pradeepSummary: Vortex breakdown (VB) in swirling jets can be classified as either a bubble (BVB) or a conical (CVB) form based on the shape of its recirculation zone. The present study investigates the hysteresis features of these forms in laminar swirling jets using direct numerical simulations. It is established here that BVB and CVB are bistable forms in a large swirl range and for a Reynolds number of 200 (based on jet radius and centreline velocity). Considerable differences were observed in the length scales associated with the two, with the approximate recirculation zone diameters of the BVB and CVB being 1 and 15 jet diameters, respectively. Additionally, two types of BVB were observed, identified as a two-celled BVB with spiral tail and an asymmetric BVB. The former is characterized by an almost steady bubble with a two-celled structure. By contrast, the entire bubble envelope oscillated in a non-axisymmetric fashion for the latter. These two types of BVB themselves were found to coexist in a small swirl range. A global linear stability analysis was used to show that two different unstable single helical modes are associated with these two types. In comparison to using the base flow, a stability analysis performed on the mean flow was found to predict the coherent features of asymmetric BVB observed in the simulations more precisely. This study highlights the rich variety of VB flow states that coexist in various ranges of swirl strengths and the significance of hysteresis effects in laminar swirling jets.Feedback control of flow-induced vibration of a sphere.https://zbmath.org/1460.762422021-06-15T18:09:00+00:00"McQueen, Thomas"https://zbmath.org/authors/?q=ai:mcqueen.thomas"Zhao, J."https://zbmath.org/authors/?q=ai:zhao.jincheng|zhao.jinsong|zhao.juanxia|zhao.jianmin|zhao.junhe|zhao.junning|zhao.jianlin|zhao.jintao|zhao.jingxian|zhao.junxiu|zhao.jianbin|zhao.jinhu|zhao.jiakui|zhao.jinling|zhao.jisheng|zhao.juanping|zhao.jieliang|zhao.jingya|zhao.jikun|zhao.jiafeng|zhao.jinghai|zhao.jichang|zhao.ji|zhao.jing.1|zhao.jinhua|zhao.jun.1|zhao.jihai|zhao.jinshuai|zhao.jianzhe|zhao.jinshi|zhao.jiantao|zhao.jiuhua|zhao.junsong|zhao.jingshan|zhao.jiefeng|zhao.jianye|zhao.jiyin|zhao.jiuli|zhao.jiantang|zhao.jianzhong|zhao.jianyuan|zhao.junyilang|zhao.jianying|zhao.jingtao|zhao.jinman|zhao.jiemei|zhao.justin|zhao.jianhua|zhao.junxi|zhao.jingjun|zhao.jingyi|zhao.jane|zhao.jiyong|zhao.junkun|zhao.jinping|zhao.jixiang|zhao.junhua|zhao.jingtong|zhao.jinbin|zhao.jinglan|zhao.jiaheng|zhao.jingfu|zhao.jianbang|zhao.jiongzhi|zhao.jie|zhao.jinqing|zhao.jing.3|zhao.jiaolian|zhao.jinxing|zhao.jiang|zhao.jinxu|zhao.jinxi|zhao.junping|zhao.jiakun|zhao.jianxin|zhao.jia.1|zhao.jun|zhao.junxiao|zhao.jingsheng|zhao.jiamin|zhao.jiexiu|zhao.jianghai|zhao.jinzhou|zhao.junsan|zhao.junshui|zhao.jianshe|zhao.jinxian|zhao.jianxi|zhao.jingyu|zhao.junfa|zhao.judong|zhao.jiayin|zhao.jingang|zhao.junguang|zhao.junchan|zhao.jingdong|zhao.jizhong|zhao.jize|zhao.jiansheng|zhao.jiaxin|zhao.jialiang|zhao.jingyuan|zhao.jizhen|zhao.junhang|zhao.jidong|zhao.junfeng|zhao.jiman|zhao.junlong|zhao.jiandong|zhao.jianlian|zhao.jianwei|zhao.jiali|zhao.junyong|zhao.ju|zhao.jihong|zhao.jiansen|zhao.jiemin|zhao.jiahong|zhao.jin|zhao.jieling|zhao.junqing|zhao.jisong|zhao.junfang|zhao.jinye|zhao.jiejue|zhao.junkai|zhao.jifeng|zhao.jiaozhi|zhao.jiashu|zhao.jinchao|zhao.jixian|zhao.jingbao|zhao.juanjuan|zhao.jianli|zhao.junhai|zhao.jihui|zhao.jiajia|zhao.jianxing|zhao.jianqing|zhao.jinglin|zhao.jingyue|zhao.jinwei|zhao.jianhui|zhao.jinlou|zhao.junwei|zhao.jianrong|zhao.jiong|zhao.jiangang|zhao.jiaqi|zhao.junli|zhao.jingrui|zhao.junhui|zhao.junpeng|zhao.jinkai|zhao.junyan|zhao.jiaqiang|zhao.jinyan|zhao.junbo|zhao.jianchang|zhao.junzhou|zhao.jinsuo|zhao.jianjun|zhao.jiacheng|zhao.jianyong|zhao.jiancong|zhao.jiao|zhao.jianyu|zhao.jutao|zhao.jiying|zhao.jichao|zhao.jinxin|zhao.jitai|zhao.jianxun|zhao.jiaquan|zhao.jinghui|zhao.jianglin|zhao.juan|zhao.jine|zhao.jiashi|zhao.jiangnan|zhao.junwu|zhao.jinqiu|zhao.jining|zhao.jiaxiang|zhao.jiapei|zhao.jiwei|zhao.jibin|zhao.jing.2|zhao.junling|zhao.junjie|zhao.jiayi|zhao.jianfeng|zhao.jinwen|zhao.jinjun|zhao.jian|zhao.juning|zhao.jianyin|zhao.jijun|zhao.junyin|zhao.jinglei|zhao.junying|zhao.jinbao|zhao.jiangfu|zhao.jianhong|zhao.jing|zhao.jingxin|zhao.jianping|zhao.jiping|zhao.jiabao|zhao.jianguo|zhao.junsheng|zhao.juntao|zhao.junyang|zhao.jiawei|zhao.jinfeng|zhao.junyu|zhao.jinli|zhao.jinghuan|zhao.jinlong|zhao.jinjing|zhao.jianming|zhao.jidi|zhao.jieyu|zhao.jia|zhao.jianzhou|zhao.jiajing|zhao.jianfu|zhao.jinhui|zhao.jingxiang|zhao.jiabin|zhao.jianjie|zhao.junjian|zhao.jiayu|zhao.jun.2|zhao.jiangbo|zhao.jianqiang.1|zhao.jiagui|zhao.jieqiong|zhao.jishen|zhao.jiafei|zhao.jingjing|zhao.jiangming|zhao.jiyun|zhao.junhong"Sheridan, J."https://zbmath.org/authors/?q=ai:sheridan.j-d|sheridan.john-t"Thompson, M. C."https://zbmath.org/authors/?q=ai:thompson.mary-clair|thompson.mark-christopherSummary: The flow-induced vibration of a sphere elastically mounted in the cross-flow direction with imposed feedback rotation was investigated experimentally. The application of rotation provides a means to exercise control over the vibration response of axisymmetric three-dimensional objects. Both the rotational amplitude, which was imposed in proportion to sphere transverse displacement, and the phase of the control signal were varied over a broad parameter space comprising: a non-dimensionalised proportional gain \((0.5\leqslant K_p^* \leqslant 2)\); rotation phase \((0^\circ \leqslant \varphi_{rot}\leqslant 360^\circ)\), which is the phase between the applied sphere rotation and the transverse displacement; and reduced velocity \((3\leqslant U^* \leqslant 20)\). The corresponding Reynolds number range was \((3900\lesssim Re\lesssim 25\,800)\). The structural vibration, fluid forces and wake structure were examined to characterise the effect of the imposed rotation. It was found that the rotation not only altered the magnitude of the vibration response, either amplifying or attenuating the response depending on operating conditions, but it also altered the reduced velocity at which vibrations commenced, the vibration frequency and periodicity and significantly altered the phase between the transverse fluid force and displacement. It was possible to almost completely suppress the vibration in the mode I, mode II and mode III transition regimes for imposed rotation over the ranges \(90^\circ \lesssim \varphi_{rot}\lesssim 180^\circ\), \(15^\circ \lesssim \varphi_{rot}\lesssim 135^\circ\) and \(0^\circ \lesssim \varphi_{rot}\lesssim 120^\circ\), respectively. In particular, this could be achieved at effective rotation rates well below those required by using open-loop control [\textit{A. Sareen} et al., ibid. 837, 258--292 (2018; Zbl 1419.76167)]. Past the peak of mode II, a `galloping-like' response, similar to that reported by \textit{D. Vicente-Ludlam} et al. [ibid. 847, 93--118 (2018; Zbl 1404.76153)] for the circular cylinder, was observed with an increase in vibration amplitude of up to 368 \% at the highest reduced velocity tested \((U^* =20)\). Particle image velocimetry measurements revealed a change in the timing and spatial position of the streamwise vortex structures with imposed rotation. Contrary to what has been observed for the circular cylinder, however, no de-synchronisation between vortex shedding and sphere motion was observed.Low-order model for successive bifurcations of the fluidic pinball.https://zbmath.org/1460.762362021-06-15T18:09:00+00:00"Deng, Nan"https://zbmath.org/authors/?q=ai:deng.nan"Noack, Bernd R."https://zbmath.org/authors/?q=ai:noack.bernd-r"Morzyński, Marek"https://zbmath.org/authors/?q=ai:morzynski.marek"Pastur, Luc R."https://zbmath.org/authors/?q=ai:pastur.luc-rSummary: We propose the first least-order Galerkin model of an incompressible flow undergoing two successive supercritical bifurcations of Hopf and pitchfork type. A key enabler is a mean-field consideration exploiting the symmetry of the mean flow and the asymmetry of the fluctuation. These symmetries generalize mean-field theory, e.g. no assumption of slow growth rate is needed. The resulting five-dimensional Galerkin model successfully describes the phenomenogram of the fluidic pinball, a two-dimensional wake flow around a cluster of three equidistantly spaced cylinders. The corresponding transition scenario is shown to undergo two successive supercritical bifurcations, namely a Hopf and a pitchfork bifurcation on the way to chaos. The generalized mean-field Galerkin methodology may be employed to describe other transition scenarios.Vortex-induced vibration prediction via an impedance criterion.https://zbmath.org/1460.762212021-06-15T18:09:00+00:00"Sabino, D."https://zbmath.org/authors/?q=ai:sabino.d"Fabre, D."https://zbmath.org/authors/?q=ai:fabre.david"Leontini, J. S."https://zbmath.org/authors/?q=ai:leontini.justin-s"Jacono, D. Lo"https://zbmath.org/authors/?q=ai:jacono.d-loSummary: The vortex-induced vibration of a spring-mounted, damped, rigid circular cylinder, immersed in a Newtonian viscous flow and capable of moving in the direction orthogonal to the unperturbed flow is investigated for Reynolds numbers \(Re\) in the vicinity of the onset of unsteadiness \((15\leqslant Re\leqslant 60)\) using the incompressible linearised Navier-Stokes equations. In a first step, we solve the linear problem considering an imposed harmonic motion of the cylinder. Results are interpreted in terms of the mechanical impedance, i.e. the ratio between the vertical force coefficient and the cylinder velocity, which is represented as function of the Reynolds number and the driving frequency. Considering the energy transfer between the cylinder and the fluid, we show that impedance results provide a simple criterion allowing the prediction of the onset of instability of the coupled fluid-elastic structure case. A global stability analysis of the fully coupled fluid/cylinder system is then performed. The instability thresholds obtained by this second approach are found to be in perfect agreement with the predictions of the impedance-based criterion. A theoretical argument, based on asymptotic developments, is then provided to give a prediction of eigenvalues of the coupled problem, as well as to characterise the region of instability beyond the threshold as function of the reduced velocity \(U^*\), the dimensionless mass \(m^*\) and the Reynolds number. The influence of the damping parameter \(\gamma\) on the instability region is also explored.Lagrangian description of three-dimensional viscous flows at large Reynolds numbers.https://zbmath.org/1460.761782021-06-15T18:09:00+00:00"Setukha, A. V."https://zbmath.org/authors/?q=ai:setukha.alexey-vSummary: Boundary layer theory is used to show that, at large Reynolds numbers, the three-dimensional Navier-Stokes equations can be rewritten in a form with diffusion velocity that was previously known for the cases of two-dimensional and axisymmetric flows. Relying on this hypothesis, a closed system of equations that is a development of a similar model for the indicated special cases is derived to describe fluid flows in the Lagrangian approach. Simultaneously, a number of mathematical issues are investigated. The existence of an integral representation for the velocity field with integrals with respect to Lagrangian coordinates is proved by analyzing the equations of motion of selected Lagrangian particles and applying the theory of ordinary differential equations with parameters. An equation describing the vorticity flux from the body surface is derived.Thermodynamically consistent phase-field modelling of contact angle hysteresis.https://zbmath.org/1460.762732021-06-15T18:09:00+00:00"Yue, Pengtao"https://zbmath.org/authors/?q=ai:yue.pengtaoSummary: In the phase-field description of moving contact line problems, the two-phase system can be described by free energies, and the constitutive relations can be derived based on the assumption of energy dissipation. In this work we propose a novel boundary condition for contact angle hysteresis by exploring wall energy relaxation, which allows the system to be in non-equilibrium at the contact line. Our method captures pinning, advancing and receding automatically without the explicit knowledge of contact line velocity and contact angle. The microscopic dynamic contact angle is computed as part of the solution instead of being imposed. Furthermore, the formulation satisfies a dissipative energy law, where the dissipation terms all have their physical origin. Based on the energy law, we develop an implicit finite element method that is second order in time. The numerical scheme is proven to be unconditionally energy stable for matched density and zero contact angle hysteresis, and is numerically verified to be energy dissipative for a broader range of parameters. We benchmark our method by computing pinned drops and moving interfaces in the plane Poiseuille flow. When the contact line moves, its dynamics agrees with the Cox theory. In the test case of oscillating drops, the contact line transitions smoothly between pinning, advancing and receding. Our method can be directly applied to three-dimensional problems as demonstrated by the test case of sliding drops on an inclined wall.A weakly nonlinear analysis of the precessing vortex core oscillation in a variable swirl turbulent round jet.https://zbmath.org/1460.762152021-06-15T18:09:00+00:00"Manoharan, Kiran"https://zbmath.org/authors/?q=ai:manoharan.kiran"Frederick, Mark"https://zbmath.org/authors/?q=ai:frederick.mark"Clees, Sean"https://zbmath.org/authors/?q=ai:clees.sean"O'Connor, Jacqueline"https://zbmath.org/authors/?q=ai:oconnor.jacqueline"Hemchandra, Santosh"https://zbmath.org/authors/?q=ai:hemchandra.santoshSummary: We study the emergence of precessing vortex core (PVC) oscillations in a swirling jet experiment. We vary the swirl intensity while keeping the net mass flow rate fixed using a radial-entry swirler with movable blades upstream of the jet exit. The swirl intensity is quantified in terms of a swirl number \(S\). Time-resolved velocity measurements in a radial-axial plane anchored at the jet exit for various \(S\) values are obtained using stereoscopic particle image velocimetry. Spectral proper orthogonal decomposition and spatial cross-spectral analysis reveal the simultaneous emergence of a bubble-type vortex breakdown and a strong helical limit-cycle oscillation in the flow for \(S>S_c\) where \(S_c=0.61\). The oscillation frequency, \(f_{PVC}\), and the square of the flow oscillation amplitudes vary linearly with \(S-S_c\). A solution for the coherent unsteady field accurate up to \(O( \varepsilon^3) (\varepsilon \sim O((S-S_c)^{1/2}))\) is determined from the nonlinear Navier-Stokes equations, using the method of multiple scales. We show that onset of bubble type vortex breakdown at \(S_c\), results in a marginally stable, helical linear global hydrodynamic mode. This results in the stable limit-cycle precession of the breakdown bubble. The variation of \(f_{LC}\) with \(S-S_c\) is determined from the Stuart-Landau equation associated with the PVC. Reasonable agreement with the corresponding experimental result is observed, despite the highly turbulent nature of the flow in the present experiment. Further, amplitude saturation results from the time-averaged distortion imposed on the flow by the PVC, suggesting that linear stability analysis may predict PVC characteristics for \(S>S_c\).Description of the transitional wake behind a strongly streamwise rotating sphere.https://zbmath.org/1460.762412021-06-15T18:09:00+00:00"Lorite-Díez, M."https://zbmath.org/authors/?q=ai:lorite-diez.m"Jiménez-González, J. I."https://zbmath.org/authors/?q=ai:jimenez-gonzalez.j-iSummary: Direct numerical simulations are performed to study the flow regimes at the wake behind a strongly streamwise rotating sphere, covering the range of rotation parameters \(0\leqslant \Omega \leqslant 3\) and laminar and transitional Reynolds numbers \(Re=250, 500\) and 1000. The wake dynamics is investigated in terms of flow topology, dominant modes and force coefficients. A higher wake complexity is found for growing values of the rotation parameter \(\Omega\) for all the Reynolds numbers investigated. In particular, at low and intermediate \(Re\), successive bifurcations entail the development of periodic, quasi-periodic and irregular regimes, constituting a classical scenario of route to chaos, through the destabilization of different structures associated to incommensurate frequencies, which have been analysed by means of flow decomposition techniques. At low \(Re\) and high rotation rates, the flow is governed by double-threaded structures due to the destabilization of helical symmetries of azimuthal wavenumber \(m=2\), which are not dominant at larger \(Re\). Interestingly, at intermediate values of \(\Omega\) and \(Re=500\), a bistable dynamics is observed whereby the wake undergoes a random switching between a modulated quasi-periodic regime and an irregular regime, which is associated to a sudden increase of the drag coefficient, on account of the development of a double-celled recirculating bubble. Finally, for \(Re=1000\), the flow is already chaotic at \(\Omega =0\), and the evolution with the rotation rate of the flow dynamics is simpler, with wake regimes being characterized by the rotation and massive shedding of vortex loops, that are a continuous deformation through axial rotation of the irregular wake behind the static sphere.Unsuitability of the Beavers-Joseph interface condition for filtration problems.https://zbmath.org/1460.767462021-06-15T18:09:00+00:00"Eggenweiler, Elissa"https://zbmath.org/authors/?q=ai:eggenweiler.elissa"Rybak, Iryna"https://zbmath.org/authors/?q=ai:rybak.i-vSummary: Coupled free-flow and porous-medium systems appear in a variety of industrial and environmental applications. Fluid flow in the free-flow domain is typically described by the (Navier-)Stokes equations while Darcy's law is applied in the porous medium. The correct choice of coupling conditions on the fluid-porous interface is crucial for accurate numerical simulations of coupled problems. We found out that the Beavers-Joseph interface condition, which is widely used not only for fluid flow parallel to the porous layer but also for filtration problems, is unsuitable for arbitrary flow directions. To validate our statement, we provide several examples and compare numerical simulation results for the coupled Stokes-Darcy problems to the pore-scale resolved models. We show also that the Beavers-Joseph parameter cannot be fitted for arbitrary flow directions.The viscous Holmboe instability for smooth shear and density profiles.https://zbmath.org/1460.762832021-06-15T18:09:00+00:00"Parker, Jeremy P."https://zbmath.org/authors/?q=ai:parker.jeremy-p"Caulfield, C. P."https://zbmath.org/authors/?q=ai:caulfield.c-p"Kerswell, R. R."https://zbmath.org/authors/?q=ai:kerswell.richard-rSummary: The Holmboe wave instability is one of the classic examples of a stratified shear instability, usually explained as the result of a resonance between a gravity wave and a vorticity wave. Historically, it has been studied by linear stability analyses at infinite Reynolds number, \(Re\), and by direct numerical simulations at relatively low \(Re\) in the regions known to be unstable from the inviscid linear stability results. In this paper, we perform linear stability analyses of the classical `Hazel model' of a stratified shear layer (where the background velocity and density distributions are assumed to take the functional form of hyperbolic tangents with different characteristic vertical scales) over a range of different parameters at finite \(Re\), finding new unstable regions of parameter space. In particular, we find instability when the Richardson number is everywhere greater than \(1/4\), where the flow would be stable at infinite \(Re\) by the Miles-Howard theorem. We find unstable modes with no critical layer, and show that, despite the necessity of viscosity for the new instability, the growth rate relative to diffusion of the background profile is maximised at large \(Re\). We use these results to shed new light on the wave-resonance and over-reflection interpretations of stratified shear instability. We argue for a definition of Holmboe instability as being characterised by propagating vortices above or below the shear layer, as opposed to any reference to sharp density interfaces.The wake structure of a propeller operating upstream of a hydrofoil.https://zbmath.org/1460.762202021-06-15T18:09:00+00:00"Posa, Antonio"https://zbmath.org/authors/?q=ai:posa.antonio"Broglia, Riccardo"https://zbmath.org/authors/?q=ai:broglia.riccardo"Balaras, Elias"https://zbmath.org/authors/?q=ai:balaras.eliasSummary: Large eddy simulations are presented on the wake flow of a notional propeller (the INSEAN E1658), upstream of a NACA0020 hydrofoil of infinite spanwise extent, mimicking propeller-rudder interaction. Results show that the flow physics is dominated by the interaction between the coherent structures populating the wake of the propeller and the surface of the hydrofoil. The suction and pressure side branches of the tip vortices move towards inner and outer radii, respectively. The hub vortex is split into two branches at the leading edge of the hydrofoil. The two branches of the hub vortex shift in the opposite direction, compared to the tip vortices, towards the rudder suction sides. As a result, a contraction of the propeller wake on the suction sides occurs, leading to increased levels of shear stress and turbulence. At downstream locations along the hydrofoil the spanwise deflection of the suction side branches of the tip vortices affects the trajectory of the overall propeller wake, including also the smaller helical vortices across the span of the wake of each blade and the two branches of the hub vortex on the two sides of the hydrofoil. This cross-stream shift persists, producing a strong anti-symmetry of the overall wake.A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics.https://zbmath.org/1460.761822021-06-15T18:09:00+00:00"Modin, Klas"https://zbmath.org/authors/?q=ai:modin.klas"Viviani, Milo"https://zbmath.org/authors/?q=ai:viviani.miloSummary: The incompressible two-dimensional Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical mechanics predicts a steady vorticity configuration, but detailed numerical results in the literature contradict this theory, yielding instead persistent unsteadiness. Such numerical results were obtained using artificial hyperviscosity to account for the cascade of enstrophy into smaller scales. Hyperviscosity, however, destroys the underlying geometry of the phase flow (such as conservation of Casimir functions), and therefore might affect the qualitative long-time behaviour. Here, we develop an efficient numerical method for long-time simulations that preserve the geometric features of the exact flow, in particular conservation of Casimirs. Long-time simulations on a non-rotating sphere then reveal three possible outcomes for generic initial conditions: the formation of either 2, 3 or 4 coherent vortex structures. These numerical results contradict the statistical mechanics theory and show that previous numerical results, suggesting 4 coherent vortex structures as the generic behaviour, display only a special case. Through integrability theory for point vortex dynamics on the sphere we present a theoretical model which describes the mechanism by which the three observed regimes appear. We show that there is a correlation between a first integral \(\gamma \) (the ratio of total angular momentum and the square root of enstrophy) and the long-time behaviour: \( \gamma\) small, intermediate and large yields most likely 4, 3 or 2 coherent vortex formations. Our findings thus suggest that the likely long-time behaviour can be predicted from the first integral \(\gamma \).Settling disks in a linearly stratified fluid.https://zbmath.org/1460.762802021-06-15T18:09:00+00:00"Mercier, Matthieu J."https://zbmath.org/authors/?q=ai:mercier.matthieu-j"Wang, S."https://zbmath.org/authors/?q=ai:wang.saihua|wang.shiye|wang.shurui|wang.sixin|wang.songhao|wang.sulian|wang.sile|wang.shanxia|wang.shuoliang|wang.shuyue|wang.serena|wang.sijia|wang.shenlong|wang.shubiao|wang.shugang|wang.shaobu|wang.shifeng|wang.suhui|wang.shirui|wang.shenyang|wang.shunjiang|wang.shaonan|wang.shiju|wang.shuping.1|wang.suyang|wang.shizhe|wang.shaowei|wang.shanjin|wang.shuzhen|wang.shengquan|wang.shiying|wang.songyou|wang.shourong|wang.shicun|wang.shengjun|wang.sulin|wang.shikung|wang.shuhua|wang.shengxi|wang.shuyi|wang.shijia|wang.shunfang|wang.shengqiang|wang.shengli|wang.shouyin|wang.shichang|wang.songfeng|wang.shiheng|wang.songli|wang.shengming|wang.shengfu|wang.shunmin|wang.sanfu|wang.shijin|wang.shuangyue|wang.suhua|wang.shuyang|wang.shanfeng|wang.sijian|wang.suxia|wang.suning|wang.shoujue|wang.shouqiang|wang.shuyan|wang.shengyong|wang.shouyong|wang.shenpiong|wang.shoucai|wang.shaochang|wang.shaoqin|wang.shaofang|wang.soujin|wang.shue|wang.shuchen|wang.songtao|wang.shuwei|wang.shubing|wang.shan|wang.shuangquan|wang.songling|wang.sanmin|wang.shunan|wang.shenlin|wang.shu|wang.shifen|wang.shun|wang.shouzhang|wang.sunan|wang.shugui|wang.shiyu|wang.shuaikun|wang.shixi|wang.sunpeng|wang.shupei|wang.shouzhu|wang.shuya|wang.shanbiao|wang.shixiong|wang.shuangxin|wang.shaochun|wang.song.2|wang.shian|wang.shiyi|wang.shuheng|wang.shuhe|wang.siqi|wang.shiguang|wang.soushi|wang.shen|wang.shuodao|wang.shi.1|wang.shengkun|wang.simin|wang.shaogang|wang.shengwei|wang.shilong|wang.shiming|wang.shejun|wang.shuaiyu|wang.shui|wang.song.1|wang.shaoqing|wang.shujing|wang.suojin|wang.shengwang|wang.shu.1|wang.souyang|wang.shuzhong|wang.shaochu|wang.shoubin|wang.shuren|wang.siwei|wang.shaoshang|wang.shabo|wang.shangsi|wang.shuaijiao|wang.shengling|wang.shixiang|wang.souren|wang.shanzhu|wang.semyung|wang.shanyuan|wang.sijing|wang.shengqi|wang.siyan|wang.shuangtao|wang.shulan|wang.shangshan|wang.shengxiang|wang.shasha|wang.shuanghu|wang.shengqing|wang.shenglan|wang.suyun|wang.shoshen|wang.shoudao|wang.shouhe|wang.sabrina|wang.shanping|wang.shuangcai|wang.shougen|wang.shifu|wang.shihuan|wang.shoucheng|wang.shuangjin|wang.shouhui|wang.songping|wang.shengqian|wang.shangbo|wang.sanbao|wang.shuai|wang.shichao|wang.shigang|wang.shibing|wang.shili|wang.sai|wang.shilin|wang.shanmin|wang.siyun|wang.sookyun|wang.shihua|wang.siwen|wang.suogang|wang.shuwen|wang.siyang|wang.shaowen|wang.shunlai|wang.shoufeng|wang.shanshe|wang.shidong|wang.shiqin|wang.shaoping|wang.shengbing|wang.shiqing|wang.siyu|wang.shaoqian|wang.shiran|wang.shuran|wang.shaokun|wang.siming|wang.shouyang|wang.shuangfeng|wang.shixin|wang.shuting|wang.simi|wang.sitao|wang.shixiao|wang.shoujun|wang.shaohua|wang.shengwen|wang.shufen|wang.sha|wang.shufan|wang.shuaijie|wang.shishi|wang.sifeng|wang.shoudong|wang.shouguang|wang.shihong|wang.shuying|wang.shaokai|wang.shitie|wang.shengdong|wang.shaoying|wang.shengnan|wang.shizhen|wang.shirou|wang.shuhui|wang.suyi|wang.shaoli|wang.shunqing|wang.siqun|wang.suxin|wang.shitong|wang.shurong|wang.shaoyi|wang.shaohong|wang.shuiting|wang.shaorong|wang.shuli|wang.shengmei|wang.songui|wang.sheng-wang|wang.shouhong.1|wang.shijun|wang.seongmoon|wang.suian|wang.shuquan|wang.shushi|wang.shuxun|wang.shangzhi|wang.shaoxin|wang.shangguang|wang.shiquan|wang.shumei|wang.shaowu|wang.shenwen|wang.shigong|wang.shifang|wang.shiqiang|wang.shaojun|wang.shienyu|wang.shengbo|wang.suzhen|wang.shiku|wang.sharon|wang.suli|wang.shiji|wang.shaofan|wang.sheng|wang.shuqiang|wang.shuji|wang.sichuan|wang.song.3|wang.shunqiang|wang.sainan|wang.shiliang|wang.shunjin|wang.shanquan|wang.shengchun|wang.shifan|wang.shengyin|wang.sishui|wang.shaojie|wang.shuozhong|wang.songhua|wang.shao|wang.shiwen|wang.shouwen|wang.shixuan|wang.shaodi|wang.sigang|wang.shikai|wang.shuaian|wang.shuangli|wang.shuaifa|wang.shimin|wang.songlin|wang.sizhe|wang.shuangming|wang.shipeng|wang.shengda|wang.shengua|wang.shikun|wang.shunfeng|wang.shuhao|wang.sikui|wang.shilian|wang.shixun|wang.sanhu|wang.shouxin|wang.shaoheng|wang.shaoming|wang.shujia|wang.shujun|wang.shengrong|wang.suping|wang.shuiping|wang.sunfu|wang.sicheng|wang.sisi|wang.shouhong|wang.shize|wang.silei|wang.shuangshuang|wang.shifei|wang.sumei|wang.shunkang|wang.shibin|wang.shihyih|wang.shoubai|wang.shenhuai|wang.shumin|wang.shuxia|wang.shaocheng|wang.shiuhjeng|wang.shangjiu|wang.shao-fu|wang.shuangqiang|wang.shuangbu|wang.shengpei|wang.siyuan|wang.shoumei|wang.shousong|wang.shenzhi|wang.shangpeng|wang.shizhao|wang.shance|wang.songyu|wang.shijian|wang.shuning|wang.shunli|wang.shouren|wang.shuo|wang.shuzhou|wang.shuyun|wang.song|wang.shangping|wang.shekuan|wang.shouxiang|wang.shudong|wang.shenghui|wang.shaofeng|wang.sumin|wang.shukuang|wang.shimi|wang.shiguong|wang.shitao|wang.shaozu|wang.shenxing|wang.shiwei|wang.shouzhong|wang.si|wang.shaomin|wang.shutang|wang.shulin|wang.shimo|wang.shige|wang.shuiding|wang.siping|wang.shouyu|wang.shaojiang|wang.shiyun|wang.shunting|wang.shenghai|wang.songbai|wang.shangming|wang.shi-cheng|wang.shuigen|wang.sasa|wang.shusen|wang.suihua|wang.sizhao|wang.shengxian|wang.shengzhang|wang.shuhong|wang.shengbao|wang.shangfei|wang.site|wang.shengyi|wang.shengru|wang.shouchen|wang.shuqin|wang.shulei|wang.suge|wang.simeng|wang.shiqi|wang.shouyi|wang.su|wang.shuoyu|wang.steve|wang.shanwu|wang.siyao|wang.shuoxing|wang.shunxu|wang.shufang|wang.songlai|wang.shengfang|wang.shaozhi|wang.senhua|wang.shilei|wang.shenhua|wang.shujiang|wang.shida|wang.shupeng|wang.shiyuan|wang.sanzhou|wang.shengkui|wang.shaoyu|wang.shubin|wang.shuliang|wang.shengrui|wang.shujuan|wang.sanliang|wang.suyu|wang.shaokang|wang.shiping|wang.shuogui|wang.sufeng|wang.suijie|wang.shufeng|wang.shaodong|wang.shuxiong|wang.sujing|wang.sanwu|wang.songgui|wang.shanghu|wang.susheng|wang.shixue|wang.shigui|wang.shunjun|wang.shengsheng|wang.suna|wang.shuyu|wang.shunqin|wang.suchen|wang.shenling|wang.sara|wang.sichao|wang.shaohui|wang.shuling|wang.sujuan|wang.sichun|wang.shengcou|wang.suojie|wang.shangjin|wang.shuguo|wang.siqing|wang.songran|wang.shuailin|wang.shengjie|wang.shanqin|wang.sen|wang.shouyanc|wang.suhang|wang.shengjin|wang.sheliang|wang.shuaiqing|wang.sugun|wang.shizhong|wang.shenzhong|wang.shuaiqiang|wang.shuchao|wang.shihai|wang.shaochen|wang.shuqiao|wang.shenggang|wang.shanrong|wang.songjing|wang.shengping|wang.shuanglin|wang.shengguo|wang.sufang|wang.shanshan|wang.shuyin|wang.sikan|wang.shunhong|wang.shiru|wang.shuilin|wang.sean|wang.songmin|wang.shengfa|wang.suqin|wang.shuihua|wang.shanbao|wang.songsheng|wang.shangyun|wang.shuangcheng|wang.suling|wang.shengyuan|wang.shuguang|wang.shaobing|wang.shuyong|wang.shuen|wang.songgao|wang.shenquan|wang.shuxin|wang.shingmin|wang.shuhuang|wang.suohong|wang.shuang|wang.shuming|wang.shuangbao|wang.suming|wang.shihu|wang.shenghua|wang.shuailing|wang.shuchun|wang.shengyao|wang.shuqing|wang.sven|wang.shibo|wang.shihui|wang.shengde|wang.shixing|wang.shaopeng|wang.sichen|wang.shaomei|wang.shaoting|wang.shoukun|wang.shaobo|wang.songjian|wang.shuangwei|wang.sunxin|wang.shengzhong|wang.shijie|wang.shaojiu|wang.shanwen|wang.shouyou|wang.shoutian|wang.shuhang|wang.shubo|wang.shaobin|wang.sihai|wang.shengbin|wang.shiyue|wang.sanhua|wang.shoulei|wang.songxin|wang.sinan|wang.sirui|wang.shunzeng|wang.senpeng|wang.shizhang|wang.sanxia|wang.shaoshan|wang.sheldon|wang.shiyan|wang.shuaiwen|wang.shuaihui|wang.shuqi|wang.sanxiu|wang.shukang"Péméja, J."https://zbmath.org/authors/?q=ai:pemeja.j"Ern, P."https://zbmath.org/authors/?q=ai:ern.patricia"Ardekani, A. M."https://zbmath.org/authors/?q=ai:ardekani.arezoo-m|ardekani.aref-mahdaviSummary: We consider the unbounded settling dynamics of a circular disk of diameter \(d\) and finite thickness \(h\) evolving with a vertical speed \(U\) in a linearly stratified fluid of kinematic viscosity \(\nu\) and diffusivity \(\kappa\) of the stratifying agent, at moderate Reynolds numbers \((Re=Ud/ \nu )\). The influence of the disk geometry (diameter \(d\) and aspect ratio \(\chi =d/h\)) and of the stratified environment (buoyancy frequency \(N\), viscosity and diffusivity) are experimentally and numerically investigated. Three regimes for the settling dynamics have been identified for a disk reaching its gravitational equilibrium level. The disk first falls broadside-on, experiencing an enhanced drag force that can be linked to the stratification. A second regime corresponds to a change of stability for the disk orientation, from broadside-on to edgewise settling. This occurs when the non-dimensional velocity \(U/\sqrt{\nu N}\) becomes smaller than some threshold value. Uncertainties in identifying the threshold value is discussed in terms of disk quality. It differs from the same problem in a homogeneous fluid which is associated with a fixed orientation (at its initial value) in the Stokes regime and a broadside-on settling orientation at low, but finite Reynolds numbers. Finally, the third regime corresponds to the disk returning to its broadside orientation after stopping at its neutrally buoyant level.Shape design for stabilizing microparticles in inertial microfluidic flows.https://zbmath.org/1460.766482021-06-15T18:09:00+00:00"Kommajosula, Aditya"https://zbmath.org/authors/?q=ai:kommajosula.aditya"Stoecklein, Daniel"https://zbmath.org/authors/?q=ai:stoecklein.daniel"Di Carlo, Dino"https://zbmath.org/authors/?q=ai:di-carlo.dino"Ganapathysubramanian, Baskar"https://zbmath.org/authors/?q=ai:ganapathysubramanian.baskarSummary: Design of isolated microparticles which stabilize at the centreline of a channel flow is examined numerically, for moderate Reynolds numbers \((10\leqslant Re\leqslant 80)\). This problem is motivated by the need for the design of shaped particle carriers for use in next generation microfluidic cell analysis devices. Stability metrics for particles with arbitrary shapes are formulated based on linear stability theory. Particle shape is parametrized by a compact, non-uniform rational B-spline-based representation. Shape design is posed as an optimization problem and solved using adaptive Bayesian optimization. We focus on designing particles for stability at the channel centreline robust to perturbations. Our results indicate that centreline focusing particles are families of characteristic `fish'/`bottle'/`dumbbell'-like shapes, exhibiting fore-aft asymmetry. A parametric exploration is then performed to identify stable particle designs at different \(k\) values (particle chord-to-channel width ratio) and \(Re\) values (\(0.1\leqslant k\leqslant 0.4\), \(10\leqslant Re\leqslant 80\)). Particles at high \(k\) values and \(Re\) values are highly stabilized when compared to those at low \(k\) values and \(Re\) values. We validate the performance of designed particles to perturbations in flow using detailed fluid-structure interaction simulations over different \(k\) values and \(Re\) values. We identify a basin of attraction around the centreline, within which any arbitrary release results in rotationally stable centreline focusing. We find that this basin spans larger release angle ranges and lateral locations (tending to the channel width) for narrower channels. This effectively standardizes the notion of global focusing using the current stability paradigm in narrow channels, which eliminates the need for an independent design for global focusing in such configurations. The framework detailed in this work is illustrated for two-dimensional cases and is generalizable to stability in three-dimensional flow fields. The current formulation is agnostic to \(Re\) and particle/channel geometry, which indicates substantial potential for integration with imaging flow cytometry tools and microfluidic biosensing assays.Pressure-driven flows in helical pipes: bounds on flow rate and friction factor.https://zbmath.org/1460.761692021-06-15T18:09:00+00:00"Kumar, Anuj"https://zbmath.org/authors/?q=ai:kumar.anujSummary: In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large Reynolds number. As a consequence, we also obtain an equivalent upper bound on the friction factor. These bounds are also valid for toroidal and straight pipes as limiting cases. By considering a two-dimensional background flow with varying boundary layer thickness along the circumference of the pipe, we obtain these bounds as a function of the curvature and torsion of the pipe and therefore capture the geometrical aspects of the problem. In this paper, we also present a sufficient criterion for determining which pressure-driven flow and surface-velocity-driven flow problems can be tackled using the background method.Submersion of impacting spheres at low bond and Weber numbers owing to a confined pool.https://zbmath.org/1460.762642021-06-15T18:09:00+00:00"Chen, Han"https://zbmath.org/authors/?q=ai:chen.han"Liu, Hao-Ran"https://zbmath.org/authors/?q=ai:liu.haoran"Gao, Peng"https://zbmath.org/authors/?q=ai:gao.peng.1"Ding, Hang"https://zbmath.org/authors/?q=ai:ding.hangSummary: We numerically investigate the mechanism resulting in fate change of a hydrophobic sphere impacting onto a confined pool, that is, at the same impact speed, it does not submerge in a wide pool but does in a narrow pool. We find that the reflection of the impact-induced gravity-capillary waves from the pool boundary is responsible for this phenomenon. In particular, the return of the wave to the symmetry axis may coincide with the rising of the impacting sphere to the water surface, which corresponds to the critical conditions of the fate change. Moreover, for the spheres at the onset of submersion in a wide pool, our analysis suggests that this scenario also accounts for an interesting observation in the numerical simulations. That is, the effective pool size \(S_c\), beyond which the submersion of impacting spheres is no longer affected by the pool size \(S\), is mainly dependent on the sphere diameter, no matter whether the surface waves are the capillary or gravity waves. For \(S<S_c\), two important pool sizes \((S_{w,1}\) and \(S_{w,2}\), and \(S_{w,2}\geqslant S_{w,1})\) are identified at the same impact speed, and the sphere submersion takes place at \(S_{w,1}\leqslant S\leqslant S_{w,2}\). Based on the flow features identified in simulations, a scaling law is proposed to correlate the Weber number and Bond number with \(S_w\). The theoretical prediction is shown to agree well with the numerical results.The mode B structure of streamwise vortices in the wake of a two-dimensional blunt trailing edge.https://zbmath.org/1460.762372021-06-15T18:09:00+00:00"Gibeau, Bradley"https://zbmath.org/authors/?q=ai:gibeau.bradley"Ghaemi, Sina"https://zbmath.org/authors/?q=ai:ghaemi.sinaSummary: The structure of streamwise vortices that arise due to secondary instabilities in the wake of a two-dimensional blunt body with a chord-to-thickness ratio of 12.5 was investigated using high-speed stereoscopic particle image velocimetry. Reynolds numbers spanning an order of magnitude from \(Re(h)=2600\) to \(25\, 800\) were considered, where \(h\) is the height of the blunt trailing edge. A modified two-dimensional \(Q\)-criterion \((Q' =\omega_x Q/|\omega_x|)\) was applied to identify the streamwise vortices. The wavelength of the streamwise vortices, defined as the spanwise distance between adjacent streamwise vortex pairs in the wake, was investigated by applying an autocorrelation algorithm to snapshots of \(Q'\). The most probable wavelength was found to range from \(0.67h\) to \(0.85h\) with increasing \(Re\), and the mean wavelengths increased from \(0.77h\) to \(0.96h\). These wavelength values appeared to increase asymptotically. Visual inspection and cross-correlation analyses based on \(Q'\) showed that the streamwise vortices maintain their directions of rotation during primary shedding cycles. The latter analysis was carried out at low \(Re\) because of a large amount of wake distortion and the absence of time-resolved data at high \(Re\). The characteristics of the streamwise vortex structure found here match those of mode B, which, at similar \(Re\), dominates the wakes of circular and square cylinders and has also recently been shown to exist in the wake of an elongated blunt body with a larger chord-to-thickness ratio of 46.5 [\textit{B. Gibeau} et al., ibid. 846, 578--604 (2018; Zbl 1404.76084)].Slippery bounces.https://zbmath.org/1460.762662021-06-15T18:09:00+00:00"Gauthier, Anaïs"https://zbmath.org/authors/?q=ai:gauthier.anaisSummary: The complex hierarchical texture covering the lotus leaf is at the source of two of its extraordinary properties. While its water-repellent properties are now emblematic, the lotus is much less known for its extreme slipperiness. And for good reason: until the recent work of \textit{G. Martouzet} et al. [ibid. 892, Article ID R2, 12 p. (2020; Zbl 1460.76271)], the effect of slippage on drop impact dynamics had never been demonstrated. This remarkable study unveils a complex interplay between wetting and friction, with counter-intuitive consequences. Hierarchical structures, which minimize the contact between the substrate and the droplets, are less efficient at repelling viscous liquids than simpler systems, because of the slip! A clever and original approach, based on a scaling analysis of the spreading time, is used to disentangle the different physical phenomena occurring during drop impact. This is an important step towards a better understanding of the crucial problem of drop impact dynamics on both wetting and non-wetting substrates.Phase-synchronization properties of laminar cylinder wake for periodic external forcings.https://zbmath.org/1460.762902021-06-15T18:09:00+00:00"Khodkar, M. A."https://zbmath.org/authors/?q=ai:khodkar.m-a"Taira, Kunihiko"https://zbmath.org/authors/?q=ai:taira.kunihikoSummary: We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, together with the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.Free-stream coherent structures in the unsteady Rayleigh boundary layer.https://zbmath.org/1460.762952021-06-15T18:09:00+00:00"Johnstone, Eleanor C."https://zbmath.org/authors/?q=ai:johnstone.eleanor-c"Hall, Philip"https://zbmath.org/authors/?q=ai:hall.philipSummary: Results are presented for nonlinear equilibrium solutions of the Navier-Stokes equations in the boundary layer set up by a flat plate started impulsively from rest. The solutions take the form of a wave-roll-streak interaction, which takes place in a layer located at the edge of the boundary layer. This extends previous results for similar nonlinear equilibrium solutions in steady 2D boundary layers. The results are derived asymptotically and then compared to numerical results obtained by marching the reduced boundary-region disturbance equations forward in time. It is concluded that the previously found canonical free-stream coherent structures in steady boundary layers can be embedded in unbounded, unsteady shear flows.Stokes drift: theory and experiments.https://zbmath.org/1460.761842021-06-15T18:09:00+00:00"Monismith, Stephen G."https://zbmath.org/authors/?q=ai:monismith.stephen-gSummary: An important facet of water wave dynamics is the fact that Stokes' 1847 approximate theory of water waves predicts mean Lagrangian velocities even when mean Eulerian velocities are zero. This motion, known as Stokes drift, is important to a wide variety of oceanic processes. Reflecting the difficulty of avoiding effects associated with the boundaries in wave tanks, the first convincing experimental evidence confirming this behaviour has only recently been given in [\textit{T. S. van den Bremer} et al., ibid. 879, 168--186 (2019; Zbl 1430.76007)]. This is an important result given prior evidence that the exact rotational waves first studied by Gerstner in 1802 may exist. Nonetheless, despite more than 200 years of work on the theory of water waves, much remains to be discovered.Linear inviscid damping for Couette flow in stratified fluid.https://zbmath.org/1460.762982021-06-15T18:09:00+00:00"Yang, Jincheng"https://zbmath.org/authors/?q=ai:yang.jincheng"Lin, Zhiwu"https://zbmath.org/authors/?q=ai:lin.zhiwuSummary: We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full Euler equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the dispersive decay due to the exponential stratification when there is no shear.A general definition of formation time for starting jets and forced plumes at low Richardson number.https://zbmath.org/1460.762122021-06-15T18:09:00+00:00"Gao, Lei"https://zbmath.org/authors/?q=ai:gao.lei"Guo, Hui-Fen"https://zbmath.org/authors/?q=ai:guo.huifen"Yu, Simon C. M."https://zbmath.org/authors/?q=ai:yu.simon-c-mSummary: As an important dimensionless parameter for the vortex formation process, the general form of the formation time defined by \textit{J. O. Dabiri} [Annu. Rev. Fluid Mech. 41, 17--33 (2009; Zbl 1157.76062)] is refined so as to provide better normalization for various vortex generator configurations. Our proposed definition utilizes the total circulation over the entire flow domain rather than that of the forming vortex ring alone. It adopts an integral form by considering the instantaneous infinitesimal increment in the formation time so that the effect of temporally varying properties of the flow configuration can be accounted for properly. By including the effect of buoyancy, the specific form of the general formation time for the starting forced plumes with negative and positive buoyancy is derived. A theoretical prediction based on the Kelvin-Benjamin variational principle shows that the general formation time manifests the invariance of the critical time scale, i.e. the formation number, under the influence of a source-ambient density difference. It demonstrates that the general formation time, based on the circulation production over the entire flow field, could take into account the effect of various vorticity production mechanisms, such as from a flux term or in a baroclinic fluid, on the critical formation number. The proposed definition may, therefore, serve as a guideline for deriving the specific form of the formation time in other types of starting/pulsatile flows.Optimal feedback control problem for inhomogeneous Voigt fluid motion model.https://zbmath.org/1460.762922021-06-15T18:09:00+00:00"Zvyagin, Victor"https://zbmath.org/authors/?q=ai:zvyagin.victor-g"Turbin, Mikhail"https://zbmath.org/authors/?q=ai:turbin.mikhail-vSummary: In the present paper, we study weak solvability of the optimal feedback control problem for the inhomogeneous Voigt fluid motion model. The proof is based on the approximation-topological approach. This approach involves the approximation of the original problem by regularized operator inclusion with the consequent application of topological degree theory. Then, we show the convergence of the sequence of solutions for the approximation problem to the solution for the original problem. For this, we use independent on approximation parameter a priori estimates. Finally, we prove that the cost functional achieves its minimum on the weak solution set.Oscillatory spontaneous dimpling in evaporating curved thin films.https://zbmath.org/1460.760682021-06-15T18:09:00+00:00"Shi, Xingyi"https://zbmath.org/authors/?q=ai:shi.xingyi"Fuller, Gerald G."https://zbmath.org/authors/?q=ai:fuller.gerald-g"Shaqfeh, Eric S. G."https://zbmath.org/authors/?q=ai:shaqfeh.eric-s-gSummary: We examine the dynamics of a thin film composed of a non-evaporative silicone oil (high surface tension) with trace amounts of an evaporative silicone oil (low surface tension) over an air bubble. An evaporating thin liquid film is formed atop a capillary-pinned air bubble by squeezing then holding the bubble against the air-silicone oil interface. Despite the simplicity of the system, complex oscillatory dynamical behaviour has been observed. Through interferometric experiments and numerical simulations, we show that as the bubble is moved towards the opposite interface, a dimple forms and during the subsequent holding period the dimple spontaneously oscillates. The evaporation-driven solutal-thermal Marangoni flow thickens the film and capillarity subsequently discharges the dimple. Solutal and thermal Marangoni flows both contribute to film thickening and as the local concentration of the non-evaporative species increases, the strength of the Marangoni flows increases. The oscillation frequency and waveform depend on initial composition and the maximum dimple volume. We suggest that these oscillatory solutions and the associated mechanism are a partial explanation for the film stabilization in multicomponent oils, reported experimentally in a recent publication [\textit{V. Chandran Suja} et al., ``Evaporation-induced foam stabilization in lubricating oils'', Proc. Natl. Acad. Sci. 115, No. 31, 7919--7924 (2018; \url{doi:10.1073/pnas.1805645115})].Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness.https://zbmath.org/1460.760282021-06-15T18:09:00+00:00"Liu, Lin"https://zbmath.org/authors/?q=ai:liu.lin"Liu, Fawang"https://zbmath.org/authors/?q=ai:liu.fawangSummary: A novel investigation about the boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness is presented. By introducing new variables, the irregular boundary changes as a regular one. Solutions of the governing equations are obtained numerically where the L1-scheme is applied. Dynamic characteristics with the effects of different parameters are shown by graphical illustrations. Three kinds of distributions versus power law parameter are presented, including monotonically increasing in nearly linear form at \(y =1\), increasing at first and then decreasing at \(y =1.4\) and monotonically decreasing in nearly linear form at \(y =2\).Slickwater hydraulic fracturing of shales.https://zbmath.org/1460.740752021-06-15T18:09:00+00:00"Detournay, Emmanuel"https://zbmath.org/authors/?q=ai:detournay.emmanuelSummary: Stimulation of gas or oil shales by hydraulic fracturing requires injecting water at a very high rate into kilometre-long boreholes, in order to induce sufficient fracture width to place the proppant. Since such high rate of injection implies flow in the turbulent regime, heavy-molecular-weight polymers are added to water to reduce drag and thus drastically lessen the energy required for pumping. \textit{B. Lecampion} and \textit{H. Zia} [ibid. 880, 514--550 (2019; Zbl 1430.76445)] explore via modelling how the rheology of slickwater -- water with a small amount of drag-reducing agents -- affects the propagation of a hydraulic fracture. Theoretical models in combination with scaling arguments and numerical simulations indicate that flow in a radial fracture is inherently laminar, with the turbulent regime restricted at most to the first few minutes of injection, for plausible values of rock and fluid parameters and the injection rate.Three-dimensional surfactant-covered flows of thin liquid films on rotating cylinders.https://zbmath.org/1460.760562021-06-15T18:09:00+00:00"Li, Weihua"https://zbmath.org/authors/?q=ai:li.weihua"Kumar, Satish"https://zbmath.org/authors/?q=ai:kumar.satishSummary: The coating of discrete objects is an important but poorly understood step in the manufacturing of a broad variety of products. An important model problem is the flow of a thin liquid film on a rotating cylinder, where instabilities can arise and compromise coating uniformity. In this work, we use lubrication theory and flow visualization experiments to study the influence of surfactant on these flows. Two coupled evolution equations describing the variation of film thickness and concentration of insoluble surfactant as a function of time, the angular coordinate and the axial coordinate are solved numerically. The results show that surface-tension forces arising from both axial and angular variations in the angular curvature drive flows in the axial direction that tend to smooth out free-surface perturbations and lead to a stable speed window in which axial perturbations do not grow. The presence of surfactant leads to Marangoni stresses that can cause the stable speed window to disappear by driving flow that opposes the stabilizing flow. In addition, Marangoni stresses tend to reduce the spacing between droplets that form at low rotation rates, and reduce the growth rate of rings that form at high rotation rates. Flow visualization experiments yield observations that are qualitatively consistent with predictions from linear stability analysis and the simulation results. The visualizations also indicate that surfactants tend to suppress dripping, slow the development of free-surface perturbations, and reduce the shifting and merging of rings and droplets, allowing more time for solidifying coatings in practical applications.Weak solutions to the Muskat problem with surface tension via optimal transport.https://zbmath.org/1460.651142021-06-15T18:09:00+00:00"Jacobs, Matt"https://zbmath.org/authors/?q=ai:jacobs.matthew"Kim, Inwon"https://zbmath.org/authors/?q=ai:kim.inwon-christina"Mészáros, Alpár R."https://zbmath.org/authors/?q=ai:meszaros.alpar-richardThe global existence of weak solutions for the Muskat problem with surface tension, based on its gradient flow structure is obtained. The paper is organized as follows. Section 1 is an introduction. In the same section, the statement of the problem and its variational formulation are given. The main theorem of the paper is also formulated in Section 1. In Section 2, the basic properties of the minimizing movements scheme are derived and discrete-time quantities are constructed. The existence of pressure as a Lagrange multiplier for the incompressibility constraint is derived and the Euler-Lagrange equation for the minimization problem is obtained. In Section 3, weak solutions to the Muskat problem are obtained, under the assumption that the internal energy of the discrete solutions converges to the internal energy of the limiting solutions. The main task in Section 3 amounts to showing that one can pass to the limit in the Euler-Lagrange equation obtained in Section 2. In Section 4, several numerical examples with illustrations are given and discussed. Finally, in Appendix A, the results that are used when passing to the limit the weak curvature equation are recalled from the following paper [\textit{T. Laux} and \textit{F. Otto}, Calc. Var. Partial Differ. Equ. 55, No. 5, Paper No. 129, 74 p. (2016; Zbl 1388.35121)].
Reviewer: Temur A. Jangveladze (Tbilisi)The mechanics of cilium beating: quantifying the relationship between metachronal wavelength and fluid flow rate.https://zbmath.org/1460.769532021-06-15T18:09:00+00:00"Hall, Jon"https://zbmath.org/authors/?q=ai:hall.jon-g"Clarke, Nigel"https://zbmath.org/authors/?q=ai:clarke.nigelSummary: We investigate the relationship between the metachronal wavelength of an array of beating cilia and the resulting fluid flow rate through numerical simulations. Our model is based on a hybrid immersed boundary lattice Boltzmann algorithm. Our results suggest that varying the metachronal wavelength of the cilium array affects the fluid flow rate by increasing or decreasing the spread of cilia during their active strokes. We quantify this behaviour by constructing an analytical model of the system and deriving an equation for free area within the cilium array that depends on the metachronal wavelength. We show that there is a strong correlation between free area and fluid flow rate that holds for different values of cilium spacing.Wake dynamics and flow-induced vibration of a freely rolling cylinder.https://zbmath.org/1460.762382021-06-15T18:09:00+00:00"Houdroge, F. Y."https://zbmath.org/authors/?q=ai:houdroge.f-y"Leweke, T."https://zbmath.org/authors/?q=ai:leweke.thomas"Hourigan, K."https://zbmath.org/authors/?q=ai:hourigan.kerry"Thompson, Mark C."https://zbmath.org/authors/?q=ai:thompson.mark-christopherSummary: This article examines numerically the two-dimensional fluid-structure interaction problem of a circular cylinder rolling under gravity along an inclined surface under the assumption of a fixed but small gap. The motion of the cylinder is governed by the ratio of cylinder and fluid densities and the Reynolds number based on a velocity scale derived from the momentum balance in the asymptotic regime. For increasing Reynolds number, the cylinder wake undergoes a transition from steady to periodic flow, causing oscillations of the cylinder motion. The critical Reynolds number increases for light cylinders. Whereas the time-averaged characteristics of the asymptotic rolling states depend only on the Reynolds number, the density ratio has an additional influence on the vibration amplitude and on the cylinder motion during a start-up transient from rest. Light cylinders reach their final state quickly after the initial acceleration; heavier cylinders traverse a series of quasi-steady states, including a temporary velocity overshoot, before settling in the asymptotic regime. The amplitudes of the flow-induced vibrations remain small over the entire parameter range, which can be attributed to the value of the added-mass force associated with a rolling cylinder. Special attention is paid to the influence of the small but finite gap between cylinder and wall, since lubrication theory predicts a diverging pressure drag for a vanishing gap. The variations with gap size of the forces, torque and added mass are explored. The gap also influences the characteristics of the cylinder vibrations in the unsteady wake regime, in particular their amplitude.Bidensity particle-laden exchange flows in a vertical duct.https://zbmath.org/1460.768472021-06-15T18:09:00+00:00"Mirzaeian, N."https://zbmath.org/authors/?q=ai:mirzaeian.n"Testik, F. Y."https://zbmath.org/authors/?q=ai:testik.f-y"Alba, K."https://zbmath.org/authors/?q=ai:alba.kSummary: Buoyancy-driven exchange flow in a vertical duct is studied theoretically for a light pure fluid and a heavy fluid. The latter is a suspension composed of a Newtonian fluid and two populations of negatively buoyant particles of the same size but different densities (bidensity). In a previous study [the first author and the third author, ibid. 847, 134--160 (2018; Zbl 1404.76274)], the authors developed a lubrication model for monodensity suspension of particles of uniform size. The main observation of the monodensity study was the discovery of particle-enriched zones near heavy and light fluid fronts due to the relative motion of particles and the fluid. Distinct from the previous work, here, mismatched densities instigate a relative motion of lighter and heavier particles in addition to the movement of fluids. Other than the previously observed enrichment case, the bidensity case gives rise to a novel flow regime where there is enrichment of heavy particles but depletion of light particles near the interface. The transition to this regime is governed by a balance between the densities of heavy and light particles as well as those of light and carrying fluids for a given choice of initial volume fractions of particles. Such density balance is characterized by two dimensionless parameters comprising light and heavy particle-to-carrying-fluid density ratios. The transition mechanism is studied through additional simulations, revealing that the former increases with initial volume fraction of particles of either type, while the latter contrarily decreases. The effect of other parameters on the flow are discussed within the context of the paper.Mixed baroclinic convection in a cavity.https://zbmath.org/1460.767212021-06-15T18:09:00+00:00"Kumar, Abhishek"https://zbmath.org/authors/?q=ai:kumar.abhishek"Pothérat, Alban"https://zbmath.org/authors/?q=ai:potherat.albanSummary: We study the convective patterns that arise in a nearly semicylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semicircular boundary at the bottom, and infinitely extended in the third direction. While this configuration is relevant to continuous casting processes that are significantly more complex, we focus on the flow patterns associated with the particular form of mixed convection that arises in it. Linear stability analysis (LSA) and direct numerical simulations (DNS) are conducted, using the spectral-element method to identify observable states. The nature of the bifurcations is determined through Stuart-Landau analysis for completeness. The base flow consists of two counter-rotating rolls driven by the baroclinic imbalance due to the curved isothermal boundary. These are, however, suppressed by the through-flow, which is found to have a stabilising influence as soon as the Reynolds number \(Re\) based on the through-flow exceeds 25. For a sufficiently high Rayleigh number, this base flow is linearly unstable to three different modes, depending on \(Re\). For \(Re\leqslant 75\), the rolls destabilise through a supercritical bifurcation into a travelling wave. For \(100\leqslant Re\leqslant 110\), a subcritical bifurcation leads to a standing oscillatory mode, whereas for \(Re\geqslant 150\), the unstable mode is non-oscillatory and grows out of a supercritical bifurcation. The DNS confirm that in all cases the dominant mode returned by the LSA precisely matches the topology and evolution of the flow patterns that arise out of the fully nonlinear dynamics.A numerical study of mass transfer from laminar liquid films.https://zbmath.org/1460.760722021-06-15T18:09:00+00:00"Zhou, Guangzhao"https://zbmath.org/authors/?q=ai:zhou.guangzhao"Prosperetti, Andrea"https://zbmath.org/authors/?q=ai:prosperetti.andreaSummary: The paper presents results of numerical simulations of a dissolved substance diffusing out of a liquid film in a two-dimensional, gravity-driven laminar flow down a vertical solid plane. The fluid mechanic problem is solved separately subject to periodicity conditions in the flow direction. After steady-state is reached, up to a hundred copies of the calculated wave and associated flow fields are efficiently `glued' together to generate a long computational domain for the diffusion process which is solved as an initial-value problem. This approach renders it possible to follow the diffusion process over a long distance and to elucidate its various stages. It is found that large and small waves, with a maximum liquid velocity larger or smaller than the wave speed, respectively, behave differently. For the latter, the Sherwood number reaches an asymptotic value by the time the film still contains a significant amount of solute. From this point on, the mass transfer is very similar to that of a flat film with a smaller thickness (quantified in this paper). For large waves, the contributions of the various parts of the wave -- main crest, capillary waves, nearly flat substrate -- evolve differently with time and conditions and may negatively affect the mass transfer process if they get out of balance. Thus, the presence of recirculation is, in and by itself, insufficient to judge the mass transfer performance of a falling film.Vortex flows of moist air with non-equilibrium and homogeneous condensation.https://zbmath.org/1460.766682021-06-15T18:09:00+00:00"Rusak, Zvi"https://zbmath.org/authors/?q=ai:rusak.zvi"Rawcliffe, Gerald A."https://zbmath.org/authors/?q=ai:rawcliffe.gerald-a"Zhang, Yuxin"https://zbmath.org/authors/?q=ai:zhang.yuxinSummary: A small-disturbance model is presented for the complex dynamics of vortex flows of moist air in a straight, circular pipe with non-equilibrium and homogeneous condensation. The model explores the nonlinear interactions among the vortex near-critical swirl ratio and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. These are the flow inlet swirl ratio \(\omega\), the inlet Mach number \(Ma_0\), the initial humidity \(\tilde{\omega}_0 \), the number of water molecules in a characteristic fluid element \(n_C\), the inlet centreline super-saturation ratio \(S_0\) and the ratio of characteristic condensation and flow time scales \(K\). Also, the flow field may be described by an ordinary first-order nonlinear differential equation for the flow evolution coupled with a set of four first-order ordinary differential equations along the pipe for the calculation of the condensate mass fraction. An iterative numerical scheme which combines the Runge-Kutta integration technique for the flow dynamics with Simpson's integration rule for the calculation of the condensation variables is developed. Specifically, equilibrium states are determined, including the possibility of the appearance of multiple states under the same boundary conditions, and the stability characteristics of these states are described. The model is used to study the effects of humidity and of energy supply from nanoscale condensation processes on the large-scale dynamics of vortex flows as well as the effect of flow swirl on condensation processes in swirling flows.Numerical simulations of flow past three circular cylinders in equilateral-triangular arrangements.https://zbmath.org/1460.762342021-06-15T18:09:00+00:00"Chen, Weilin"https://zbmath.org/authors/?q=ai:chen.weilin"Ji, Chunning"https://zbmath.org/authors/?q=ai:ji.chunning"Alam, Md. Mahbub"https://zbmath.org/authors/?q=ai:alam.muhammad-mahbub"Williams, John"https://zbmath.org/authors/?q=ai:williams.john-j-r"Xu, Dong"https://zbmath.org/authors/?q=ai:xu.dongSummary: Flow past three identical circular cylinders is numerically investigated using the immersed boundary method. The cylinders are arranged in an equilateral-triangle configuration with one cylinder placed upstream and the other two side-by-side downstream. The focus is on the effect of the spacing ratio \(L/D(=1.0-6.0)\), Reynolds number \(Re(=50-300)\) and three-dimensionality on the flow structures, hydrodynamic forces and Strouhal numbers, where \(L\) is the cylinder centre-to-centre spacing and \(D\) is the cylinder diameter. The fluid dynamics involved is highly sensitive to both \(Re\) and \(L/D\), leading to nine distinct flow structures, namely single bluff-body flow, deflected flow, flip-flopping flow, steady symmetric flow, steady asymmetric flow, hybrid flow, anti-phase flow, in-phase flow and fully developed in-phase co-shedding flow. The time-mean drag and lift of each cylinder are more sensitive to \(L/D\) than \(Re\) while fluctuating forces are less sensitive to \(L/D\) than \(Re\). The three-dimensionality of the flow affects the development of the wake patterns, changing the \(L/D\) ranges of different flow structures. A diagram of flow regimes, together with the contours of hydrodynamic forces, in the \(Re-L/D\) space, is given, providing physical insights into the complex interactions of the three cylinders.A model for the propagation of inertial gravity currents released from a two-layer stratified lock.https://zbmath.org/1460.762862021-06-15T18:09:00+00:00"Zemach, T."https://zbmath.org/authors/?q=ai:zemach.tamar"Ungarish, M."https://zbmath.org/authors/?q=ai:ungarish.mariusSummary: Consider the propagation of a gravity current (GC) released from a lock of length \(x_0\) and height \(h_0\) into an ambient fluid of height \(H h_0\) and density \(\rho_o\). The lock contains a layer of thickness \(H_L h_0\) of density \(\rho_L\) overlaid by a layer of thickness \((1-H_L)h_0\) and density \(\rho_U\), where \(\rho_o < \rho_U < \rho_L\) and \(H_L \in (0, 1)\). Assume Boussinesq and large Reynolds-number flow. The internal stratification parameter is \(\sigma = (\rho_L - \rho_U)/(\rho_L - \rho_o)\), in the range \((0,1)\); the classical GC is \(\sigma =0\). Such GCs were investigated experimentally [\textit{C. Gladstone} et al., ``An experimental investigation of density-stratified inertial gravity currents'', Sedimentology 51, No. 4, 767--789 (2004; \url{doi:10.1111/j.1365-3091.2004.00650.x}); \textit{A. Dai}, ``Experiments on two-layer density-stratified inertial gravity currents'', Phys. Rev. Fluids 2, No. 7, Article ID 073802, 24 p. (2017; \url{doi:10.1103/PhysRevFluids.2.073802}); \textit{C.-S. Wu} and \textit{A. Dai}, ``Experiments on two-layer stratified gravity currents in the slumping phase'', J. Hydraul. Res. 58, No. 5, 831--844 (2019; \url{doi:10.1080/00221686.2019.1671517})]; we present a new self-contained model for the prediction of the thickness \(h\) and depth-averaged velocity \(u\) as functions of distance \(x\) and time \(t\); the position and speed of the nose \(x_N(t)\) and \(u_N(t)\) follow. We derive a compact scaling upon which, for a given \(H\) (height ratio of ambient to lock), the flows differ in only one parameter: \( \Psi = \{ [1 -\sigma (1-H_L)]/[1 - \sigma (1-H_L^2)] \}^{1/2}\). The parameter \(\Psi\) equals \(1\) for the classical GC and is larger in the presence of stratification; a larger \(\Psi\) means a faster and a thinner GC. The solution reveals an initial slumping phase with constant \(u_N\), a self-similar phase \(x_N \sim t^{2/3}\), and the transition at \(x_V\) to the viscous regime. Comparisons with published experiments show good data collapse with the present scaling \(\Psi\), and fair-to-good quantitative agreement (the discrepancy and the stability conditions are discussed).Effective permeability tensor of confined flows with wall grooves of arbitrary shape.https://zbmath.org/1460.762532021-06-15T18:09:00+00:00"Dewangan, Mainendra Kumar"https://zbmath.org/authors/?q=ai:dewangan.mainendra-kumar"Datta, Subhra"https://zbmath.org/authors/?q=ai:datta.subhraSummary: Pressure and shear-driven flows of a confined film of fluid overlying a periodic one-dimensional topography of arbitrary shape are considered for prediction of the effective hydraulic permeability in the Stokes flow regime. The other surface confining the fluid may be a planar no-slip wall, an identically patterned wall, a free surface or a surface with prescribed shear. Analytical predictions are obtained using spectral analysis and the domain perturbation method under the assumption of small pattern size to pitch ratio. Using a novel decomposition of the channel height effects into exponentially and algebraically decaying components, a simple surface-metrology-dependent relationship which connects the eigenvalues of the effective permeability tensor is obtained. Two representative topographies are assessed numerically: the infinitely differentiable topography of a phase-modulated sinusoid which has multiple local extrema and zero crossings and the non-differentiable triangular-wave topography. Non-differentiability in the form of corners of triangular patterns and the cusps of scalloped patterns are not found to be an impediment to meaningful and numerically accurate asymptotic predictions of effective permeability and effective slip, contradicting an earlier suggestion from the literature. Several distinct applications of the theory to the friction-reduction and shear-stability performance of the recently developed lubricant impregnated patterned surfaces as well as to scalloped and trapezoidal drag-reduction riblets are discussed, with comparison to experimental data from the literature for the last application. Analytical approximations which have an extended domain of numerical accuracy are also proposed.Inertial focusing of non-neutrally buoyant spherical particles in curved microfluidic ducts.https://zbmath.org/1460.768372021-06-15T18:09:00+00:00"Harding, Brendan"https://zbmath.org/authors/?q=ai:harding.brendan"Stokes, Yvonne M."https://zbmath.org/authors/?q=ai:stokes.yvonne-marieSummary: We examine the effect of gravity and (rotational) inertia on the inertial focusing of spherical non-neutrally buoyant particles suspended in flow through curved microfluidic ducts. In the neutrally buoyant case, examined in [\textit{B. Harding} et al., ibid. 875, 1--43 (2019; Zbl 1419.76129)], the gravitational contribution to the force on the particle is exactly zero and the net effect of centrifugal and centripetal forces (due to the motion around the curved duct) is negligible. Inertial lift force and drag from the secondary fluid flow vortices interact and lead to focusing behaviour which is sensitive to the bend radius of the device and the particle size (each measured relative to the height of the cross-section). In the case of non-neutrally buoyant particles the behaviour becomes more complex with the two additional perturbing forces. The gravitational force, relative to the inertial lift force, scales with the inverse square of the flow velocity, making it a potentially important factor for devices operating at low flow rates with a suspension of non-neutrally buoyant particles. In contrast, the net centripetal/centrifugal force scales with the inverse of the bend radius, similar to the drag force from the secondary flow. We examine how these forces perturb the stable equilibria within the cross-sectional plane to which neutrally buoyant particles ultimately migrate.Capillary plugs in horizontal rectangular tubes with non-uniform contact angles.https://zbmath.org/1460.768162021-06-15T18:09:00+00:00"Zhu, Chengwei"https://zbmath.org/authors/?q=ai:zhu.chengwei"Zhou, Xinping"https://zbmath.org/authors/?q=ai:zhou.xinping"Zhang, Gang"https://zbmath.org/authors/?q=ai:zhang.gangSummary: The aim of this paper is to make the formation of liquid plugs as difficult as possible in liquid partially filling a horizontal rectangular tube in a downward gravity field by setting the walls to have differing contact angles. \textit{R. Manning} et al.'s method [ibid. 682, 397--414 (2011; Zbl 1241.76381)], extended from Concus-Finn theory, is applied to the existence of capillary plugs in rectangular tubes. The critical Bond numbers \((B_c)\) determining the existence of capillary plugs in a rectangular tube are studied for different settings of the non-uniform contact angles, and the influence of the aspect ratio (defined as the width-to-height ratio) of the rectangular cross-section on \(B_c\) is examined. Compared to the maximum and minimum of \(B_c\) reached for uniform contact angles, the maximum of \(B_c\) is higher, which is attained for the bottom contact angle \(\gamma_2=135^\circ\), the top contact angle \(\gamma_4=45^\circ\), and the side contact angles \(\gamma_1=\gamma_3=90^\circ\); while the minimum is considerably lowered to zero, which is reached for \(\gamma_1=\gamma_2=45^\circ\) and \(\gamma_3=\gamma_4=135^\circ\). The aspect ratio of the rectangle has no influence on the maximum and minimum \(B_c\) for a tube with walls of differing contact angles. There is only one non-occluded liquid topology in a square, while two topologies may occur in a rectangle with aspect ratio 2, and the transition between the two topologies is accompanied by a kink of the curve of \(B_c\). Optimization of the non-uniform contact angles can facilitate or effectively block the capillary plugs in rectangular tubes regardless of the aspect ratios.Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent.https://zbmath.org/1460.761762021-06-15T18:09:00+00:00"Padovan, Alberto"https://zbmath.org/authors/?q=ai:padovan.alberto"Otto, Samuel E."https://zbmath.org/authors/?q=ai:otto.samuel-e"Rowley, Clarence W."https://zbmath.org/authors/?q=ai:rowley.clarence-wSummary: We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More specifically, we consider a periodically time-varying base flow, and perform a frequency-domain analysis of periodic perturbations about this base flow. The response of these perturbations is governed by the harmonic resolvent, which is a linear operator similar to the harmonic transfer function introduced by \textit{N. M. Wereley} [Analysis and control of linear periodically time varying systems. Massachusetts: Massachusetts Institute of Technology (PhD Thesis) (1991)]. This approach makes it possible to explicitly capture the triadic interactions that are responsible for the energy transfer between different time scales in the flow. For instance, perturbations at frequency \(\omega\) are coupled with perturbations at frequency \(\alpha\) through the base flow at frequency \(\omega -\alpha\). We draw a connection with resolvent analysis, which is a special case of the harmonic resolvent when evaluated about a steady base flow. We show that the left and right singular vectors of the harmonic resolvent are the optimal response and forcing modes, which can be understood as full spatio-temporal signals that reveal space-time amplification characteristics of the flow. Finally, we illustrate the method on examples, including a three-dimensional system of ordinary differential equations and the flow over an airfoil at near-stall angle of attack.Kinetic equations. Volume 1: Boltzmann equation, Maxwell models, and hydrodynamics beyond Navier-Stokes.https://zbmath.org/1460.350012021-06-15T18:09:00+00:00"Bobylev, Alexander V."https://zbmath.org/authors/?q=ai:bobylev.alexandre-vasiljevitchThe methods of kinetic theory of gases are used in many different fields of science and technology. They are closely connected with particle methods of numerical modeling of various processes on modern computers.
We give a brief summary of the contents of the present book The chapters 1 and 2 of the book contain the standard material with all necessary material for beginners. The notion of \(N\)-particle distribution function and the Liouville equation follows. The Hamiltonian form of the Navier equations attached to the \(N\)-particle system. Then the two-body problem and pair collisions are discussed in details. At the end of Chapter 2 the Boltzmann equation for mixtures is introduced and discussed. The second part of the book (Chapters 3--6) is devoted to the general theory of kinetic Maxwell models. The theory of spatially homogenous Boltzmann equation for Maxwell molecules based on Fourier transform in the velocity space-an approach due to the author of this book [Sov. Phys., Dokl. 20 (1975), 820--822 (1976; Zbl 0361.76077); translation from Dokl. Akad. Nauk SSSR 225, 1041--1044 (1975)] represents the core of this chapter. The last part of this book (Chapter 7) is about the status of ``higher'' equations of hydrodynamics obtained by the famous Chapman-Enskog expansion. The Burnett equations which appeared in 1930 as a next step after the Navier-Stokes level being ill-posed are replaced by the so called ``generalized Burnett equations'' which are derived and discussed in detail.
This book will be a very important work-tool for both physicists and mathematicians working in kinetic theory and applications.
Reviewer: Titus Petrila (Cluj-Napoca)On the formation of three-dimensional separated flows over wings under tip effects.https://zbmath.org/1460.765942021-06-15T18:09:00+00:00"Zhang, Kai"https://zbmath.org/authors/?q=ai:zhang.kai"Hayostek, Shelby"https://zbmath.org/authors/?q=ai:hayostek.shelby"Amitay, Michael"https://zbmath.org/authors/?q=ai:amitay.michael"He, Wei"https://zbmath.org/authors/?q=ai:he.wei.1|he.wei|he.wei.2|he.wei.3"Theofilis, Vassilios"https://zbmath.org/authors/?q=ai:theofilis.vassilios"Taira, Kunihiko"https://zbmath.org/authors/?q=ai:taira.kunihikoSummary: We perform direct numerical simulations of flows over unswept finite-aspect-ratio NACA 0015 wings at \(Re=400\) over a range of angles of attack (from \(0^\circ\) to \(30^\circ)\) and (semi) aspect ratios (from 1 to 6) to characterize the tip effects on separation and wake dynamics. This study focuses on the development of three-dimensional separated flow over the wing. We discuss the flow structures formed on the wing surface as well as in the far-field wake. Vorticity is introduced from the wing surface into the flow in a predominantly two-dimensional manner. The vortex sheet from the wing tip rolls up around the free end to form the tip vortex. At its inception, the tip vortex is weak and its effect is spatially confined. As the flow around the tip separates, the tip effects extend farther in the spanwise direction, generating noticeable three dimensionality in the wake. For low-aspect-ratio wings \((sAR\approx 1)\), the wake remains stable due to the strong tip-vortex induced downwash over the entire span. Increasing the aspect ratio allows unsteady vortical flow to emerge away from the tip at sufficiently high angles of attack. These unsteady vortices shed and form closed vortical loops. For higher-aspect-ratio wings \((sAR\gtrsim 4)\), the tip effects retard the near-tip shedding process, which desynchronizes from the two-dimensional shedding over the midspan region, yielding vortex dislocation. At high angles of attack, the tip vortex exhibits noticeable undulations due to the strong interaction with the unsteady shedding vortices. The spanwise distribution of force coefficients is found to be related to the three-dimensional wake dynamics and the tip effects. Vortical elements in the wake that are responsible for the generation of lift and drag forces are identified through the force element analysis. We note that at high angles of attack, a stationary vortical structure forms at the leading edge near the tip, giving rise to locally high lift and drag forces. The analysis performed in this paper reveals how the vortical flow around the tip influences the separation physics, the global wake dynamics, and the spanwise force distributions.Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy-Weisbach equation and the issue of friction factor.https://zbmath.org/1460.762912021-06-15T18:09:00+00:00"Kowalczuk, Zdzisław"https://zbmath.org/authors/?q=ai:kowalczuk.zdzislaw"Tatara, Marek S."https://zbmath.org/authors/?q=ai:tatara.marek-sSummary: In this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy-Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated by integrating the pressure along the pipeline. Through appropriate transformation, we show the difference between the Darcy-Weisbach equation and the improved model that should be treated as a Darcy-Weisbach model error, in multiplicative and additive form. This error increases when the overall pressure drop increases. This symptomatic phenomenon is discussed in detail. In addition, we also consider four methods of estimating the coefficient of friction, assess the impact of pressure difference on the estimated average flow velocity and, based on experimental data, we show the usefulness of new proposals in various applications.Faraday pilot-wave dynamics in a circular corral.https://zbmath.org/1460.762572021-06-15T18:09:00+00:00"Durey, Matthew"https://zbmath.org/authors/?q=ai:durey.matthew"Milewski, Paul A."https://zbmath.org/authors/?q=ai:milewski.paul-a"Wang, Zhan"https://zbmath.org/authors/?q=ai:wang.zhanSummary: A millimetric droplet of silicone oil may bounce and self-propel on the free surface of a vertically vibrating fluid bath due to the droplet's interaction with its accompanying Faraday wave field. This hydrodynamic pilot-wave system exhibits many dynamics that were previously thought to be peculiar to the quantum realm. When the droplet is confined to a circular cavity, referred to as a `corral', a range of dynamics may occur depending on the details of the geometry and the decay time of the subcritical Faraday waves. We herein present a theoretical investigation into the behaviour of subcritical Faraday waves in this geometry and explore the accompanying pilot-wave dynamics. By computing the Dirichlet-to-Neumann map for the velocity potential in the corral geometry, we can evolve the quasi-potential flow between successive droplet impacts, which, when coupled with a simplified model for the droplet's vertical motion, allows us to derive and implement a highly efficient discrete-time iterative map for the pilot-wave system. We study the onset of the Faraday instability, the emergence and quantisation of circular orbits and simulate the exotic dynamics that arises in smaller corrals.Lubrication of soft viscoelastic solids.https://zbmath.org/1460.761922021-06-15T18:09:00+00:00"Pandey, Anupam"https://zbmath.org/authors/?q=ai:pandey.anupam"Karpitschka, Stefan"https://zbmath.org/authors/?q=ai:karpitschka.stefan"Venner, Cornelis H."https://zbmath.org/authors/?q=ai:venner.cornelis-h"Snoeijer, Jacco H."https://zbmath.org/authors/?q=ai:snoeijer.jacco-hSummary: Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.Thermocapillary stress and meniscus curvature effects on slip lengths in ridged microchannels.https://zbmath.org/1460.762692021-06-15T18:09:00+00:00"Kirk, Toby L."https://zbmath.org/authors/?q=ai:kirk.toby-l"Karamanis, Georgios"https://zbmath.org/authors/?q=ai:karamanis.georgios"Crowdy, Darren G."https://zbmath.org/authors/?q=ai:crowdy.darren-g"Hodes, Marc"https://zbmath.org/authors/?q=ai:hodes.marcSummary: Pressure-driven flow in the presence of heat transfer through a microchannel patterned with parallel ridges is considered. The coupled effects of curvature and thermocapillary stress along the menisci are captured. Streamwise and transverse thermocapillary stresses along menisci cause the flow to be three-dimensional, but when the Reynolds number based on the transverse flow is small the streamwise and transverse flows decouple. In this limit, we solve the streamwise flow problem, i.e. that in the direction parallel to the ridges, using a suite of asymptotic limits and techniques -- each previously shown to have wide ranges of validity thereby extending results by \textit{M. Hodes} et al. [ibid. 814, 301--324 (2017; Zbl 1383.76079)] for a flat meniscus. First, we take the small-ridge-period limit, and then we account for the curvature of the menisci with two further complementary limits: (i) small meniscus curvature using boundary perturbation; (ii) arbitrary meniscus curvature but for small slip (or cavity) fractions using conformal mapping and the Poisson integral formula. Heating and cooling the liquid always degrade and enhance (apparent) slip, respectively, but their effect is greatest for large meniscus protrusions, with positive protrusion (into the liquid) being the most sensitive. For strong enough heating the solutions become complex, suggesting instability, with large positive protrusions transitioning first.Tri-periodic fully three-dimensional analytic solutions for the Navier-Stokes equations.https://zbmath.org/1460.761632021-06-15T18:09:00+00:00"Antuono, Matteo"https://zbmath.org/authors/?q=ai:antuono.matteoSummary: In this paper we derive unsteady tri-periodic laminar solutions of the Navier-Stokes equations. In particular, these represent fully three-dimensional (3-D) flows, since all the velocity components depend non-trivially on all three coordinate directions. We show that they belong to the class of Beltrami flows and can be gathered in two distinct solutions characterized by positive and negative helicity. These can be regarded as an extension in three dimensions of the bi-periodic vortex solution by \textit{G. I. Taylor} [Phil. Mag. (6) 46, 671--674 (1923; JFM 49.0607.02)]. Their use as benchmarks for checking the accuracy of 3-D numerical codes and/or studying the onset of turbulence is suggested.Pulsating spiral Poiseuille flow.https://zbmath.org/1460.761712021-06-15T18:09:00+00:00"Manna, M."https://zbmath.org/authors/?q=ai:manna.marcello"Vacca, A."https://zbmath.org/authors/?q=ai:vacca.andrea"Verzicco, R."https://zbmath.org/authors/?q=ai:verzicco.robertoSummary: Direct numerical simulation of the Navier-Stokes equations has been used to investigate the Taylor-Couette flow with an imposed pulsatile axial pressure gradient resulting in a spiral Poiseuille flow modulated by an oscillating forcing. Keeping the Reynolds and Taylor numbers constant, both the amplitude and frequency of the oscillating component are varied to span a small region of the phase space. In the narrow-gap geometry considered in this study, the base flow (spiral Poiseuille flow) is in the turbulent regime whereas the oscillating component is laminar. It has been found that the effect of the oscillation is to induce a global flow laminarization provided the frequency is sufficiently small (at constant amplitude) or the amplitude is sufficiently large (at constant frequency). The coupling between steady and oscillating components has been analysed with the help of long-time and phase-averaged statistics. The reverse transition mechanism has been associated to an anisotropic modification of the Reynolds stress tensor components, which has been shown to be caused by an alteration of the pressure-strain interaction.Erratum to: ``Modelling film flows down a fibre''.https://zbmath.org/1460.761862021-06-15T18:09:00+00:00"Ruyer-Quil, C."https://zbmath.org/authors/?q=ai:ruyer-quil.christian"Trevelyan, P."https://zbmath.org/authors/?q=ai:trevelyan.philip-m-j"Giorgiutti-Dauphiné, F."https://zbmath.org/authors/?q=ai:giorgiutti-dauphine.frederique"Duprat, C."https://zbmath.org/authors/?q=ai:duprat.camille|duprat.cedric"Kalliadasis, S."https://zbmath.org/authors/?q=ai:kalliadasis.serafimCorrects the name of the second author in [the authors, ibid. 603, 431--462 (2008; Zbl 1151.76378)].The dynamics of a subglacial salt wedge.https://zbmath.org/1460.860492021-06-15T18:09:00+00:00"Wilson, Earle A."https://zbmath.org/authors/?q=ai:wilson.earle-a"Wells, Andrew J."https://zbmath.org/authors/?q=ai:wells.andrew-j"Hewitt, Ian J."https://zbmath.org/authors/?q=ai:hewitt.ian-j"Cenedese, Claudia"https://zbmath.org/authors/?q=ai:cenedese.claudiaSummary: Marine-terminating glaciers, such as those along the coastline of Greenland, often release meltwater into the ocean in the form of subglacial discharge plumes. Though these plumes can dramatically alter the mass loss along the front of a glacier, the conditions surrounding their genesis remain poorly constrained. In particular, little is known about the geometry of subglacial outlets and the extent to which seawater may intrude into them. Here, the latter is addressed by exploring the dynamics of an arrested salt wedge -- a steady-state, two-layer flow system where salty water partially intrudes a channel carrying fresh water. Building on existing theory, we formulate a model that predicts the length of a non-entraining salt wedge as a function of the Froude number, the slope of the channel and coefficients for interfacial and wall drag. In conjunction, a series of laboratory experiments were conducted to observe a salt wedge within a rectangular channel. For experiments conducted with laminar flow (Reynolds number \(Re<800)\), good agreement with theoretical predictions are obtained when the drag coefficients are modelled as being inversely proportional to \(Re\). However, for fully turbulent flows on geophysical scales, these drag coefficients are expected to asymptote toward finite values. Adopting reasonable drag coefficient estimates for this flow regime, our theoretical model suggests that typical subglacial channels may permit seawater intrusions of the order of several kilometres. While crude, these results indicate that the ocean has a strong tendency to penetrate subglacial channels and potentially undercut the face of marine-terminating glaciers.Swimming sheet in a viscosity-stratified fluid.https://zbmath.org/1460.762762021-06-15T18:09:00+00:00"Dandekar, Rajat"https://zbmath.org/authors/?q=ai:dandekar.rajat"Ardekani, Arezoo M."https://zbmath.org/authors/?q=ai:ardekani.arezoo-mSummary: In this work, we theoretically investigate the motion of a Taylor swimming sheet immersed in a viscosity-stratified fluid. The propulsion of the swimmer disturbs the surrounding fluid, which influences the transport of the stratifying agent described by the advection-diffusion equation. We employ a regular perturbation scheme to solve the coupled differential equations of motion up to the second order with the small parameter given by the ratio of the wave amplitude and the wavelength. The expression for the swimming velocity is linear in the magnitude of the viscosity gradient, while depending on the Péclet number in a non-monotonic way. Interestingly, we find that the Péclet number governs the propensity of the sheet to propel towards regions of favourable viscosities. In particular, for small Péclet numbers \((0<Pe<3)\), the swimmer prefers regions of low viscosity, while for high Péclet numbers \((Pe>3)\), the swimmer prefers regions of high viscosity. Our analysis shows that purely hydrodynamic effects might be responsible for the experimentally observed accumulation of swimmers near favourable viscosity regions. We find that viscosity gradients influence other motility characteristics of the swimmer, such as power expenditure and hydrodynamic efficiency, and provide analytical expressions for both.Levitation by thin viscous layers.https://zbmath.org/1460.761912021-06-15T18:09:00+00:00"Mullin, Tom"https://zbmath.org/authors/?q=ai:mullin.tom"Ockendon, H."https://zbmath.org/authors/?q=ai:ockendon.hilary"Ockendon, J. R."https://zbmath.org/authors/?q=ai:ockendon.john-rSummary: We consider the levitation of cuboidal blocks by means of the viscous stresses that are generated when the block adheres to a vertically moving wall that is coated with oil. We first describe an experimental procedure that reveals the parameter regimes in which long-time levitation can occur. Then a simple model for the relevant lubrication flows is used to explain the theoretical basis for these observations.Droplet breakup in a stagnation-point flow.https://zbmath.org/1460.767892021-06-15T18:09:00+00:00"Hooshanginejad, Alireza"https://zbmath.org/authors/?q=ai:hooshanginejad.alireza"Dutcher, Cari"https://zbmath.org/authors/?q=ai:dutcher.cari-s"Shelley, Michael J."https://zbmath.org/authors/?q=ai:shelley.michael-j"Lee, Sungyon"https://zbmath.org/authors/?q=ai:lee.sungyonSummary: We experimentally and theoretically investigate the dynamics of a partially wetting water droplet subject to a two-dimensional high-speed jet of air blowing perpendicularly to the substrate. When the jet velocity is above a critical value, the droplet evolves under wind and splits into two secondary drops. In addition to droplet splitting, we observe depinning of the droplet on one side when the jet is applied at a small distance from the initial centre of the droplet. In parallel with systematic experiments, we develop a mathematical model to compute the coupled evolution of the droplet and an idealised stagnation-point flow. Our simplified lubrication model yields a criterion for the critical jet velocity, as well as the time scale of the droplet breakup, in qualitative agreement with the experiments.Helicity effects on inviscid instability in Batchelor vortices.https://zbmath.org/1460.761372021-06-15T18:09:00+00:00"Hiejima, Toshihiko"https://zbmath.org/authors/?q=ai:hiejima.toshihikoSummary: In this paper we investigate the instability properties of Batchelor vortices with a large swirl number and a fixed axial velocity deficit. In particular, it elucidates the effect of the helicity profile on the instability of the vortices as swirling wakes. In a linear stability analysis, a negative helicity profile destabilised a vortex with a large swirl number; the name given to this instability is `helicity instability'. Note that helicity instability is qualified for the case of axial flow with wake. In contrast, a conventional Batchelor vortex was stable at swirl numbers above a value of circulation, which is determined by the axial velocity deficit. The instability was related to a parameter \(D\) proportional to the square of the inverse azimuthal vorticity thickness. Decreasing this helicity-profile parameter increased the growth property of the vortex. Such unstable features (helicity effects) were also studied in direct numerical simulations of vortices subjected to small random disturbances at Mach numbers 2.5 and 5.0. The instability based on the vorticity thickness originally grew at the outer edge of the vortex, whereas the instability waves in a conventional Batchelor vortex originate inside the vortex core. The simulation results support the results of the linear stability analysis on the helicity profile when the parameter \(D\) is small. Because of the helicity instability, the nonlinear developments yielded a large fluctuation field with many small scales and high radial spreading rates. Even at the Mach number of 5.0, negative helicity exerted a much greater destabilisation effect than a zero entropy gradient. Therefore, the investigated novel effect established a reasonably powerful instability in compressible fluids, which is favourable for supersonic mixing.Frequency selection in a gravitationally stretched capillary jet in the jetting regime.https://zbmath.org/1460.763132021-06-15T18:09:00+00:00"Shukla, Isha"https://zbmath.org/authors/?q=ai:shukla.isha"Gallaire, François"https://zbmath.org/authors/?q=ai:gallaire.francoisSummary: A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional \textit{J. Eggers} and \textit{T. F. Dupont} [ibid. 262, 205--221 (1994; Zbl 0804.76027)] equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework, the WKBJ (Wentzel-Kramers-Brillouin-Jeffreys) formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However, in the global framework, the resolvent analysis, supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.Receptivity of the turbulent precessing vortex core: synchronization experiments and global adjoint linear stability analysis.https://zbmath.org/1460.765702021-06-15T18:09:00+00:00"Müller, Jens S."https://zbmath.org/authors/?q=ai:muller.jens-s"Lückoff, F."https://zbmath.org/authors/?q=ai:luckoff.f"Paredes, P."https://zbmath.org/authors/?q=ai:paredes.pedro"Theofilis, V."https://zbmath.org/authors/?q=ai:theofilis.vassilis"Oberleithner, K."https://zbmath.org/authors/?q=ai:oberleithner.kilianSummary: The precessing vortex core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical prediction by global linear stability analysis (LSA) is found. By employing an adjoint LSA, it is found that the PVC is particularly receptive inside the duct upstream of the swirling jet. Open-loop zero-net-mass-flux actuation is applied at different axial positions inside the duct with the goal of frequency synchronization of the PVC. The actuation is shown to have the strongest effect close to the exit of the duct. There, frequency synchronization is reached primarily through direct mode-to-mode interaction. Applying the actuation farther upstream, synchronization is only achieved by a modification of the mean flow that manipulates the swirl number. These experimental observations match qualitatively well with the theoretical receptivity derived from adjoint LSA. Although the process of synchronization is very complex, it is concluded that adjoint LSA based on mean-field theory sufficiently predicts regions of high and low receptivity. Furthermore, the adjoint framework promises to be a valuable tool for finding ideal locations for flow control applications.On singularity formation via viscous vortex reconnection.https://zbmath.org/1460.762282021-06-15T18:09:00+00:00"Yao, Jie"https://zbmath.org/authors/?q=ai:yao.jie"Hussain, Fazle"https://zbmath.org/authors/?q=ai:hussain.fazleSummary: Recognizing the fact that the finite-time singularity of the Navier-Stokes equations is widely accepted as a key issue in fundamental fluid mechanics, and motivated by the recent model of \textit{H. K. Moffatt} and \textit{Y. Kimura} [ibid. 861, 930--967 (2019; Zbl 1415.76131);
ibid. 870, R1, 11 p. (2019; Zbl 1429.76042)] on this issue, we have performed direct numerical simulation (DNS) for two colliding slender vortex rings of radius \(R\). The separation between the two tipping points \(2s_0\) and the scale of the core cross-section \(\delta_0\) are chosen as \(\delta_0=0.1 s_0=0.01R\); the vortex Reynolds number \((Re=\text{circulation/viscosity} )\) ranges from 1000 to 4000. In contrast to the claim that the core remains compact and circular, there is notable core flattening and stripping, which further increases with \(Re\) -- akin to our previous finding in the standard anti-parallel vortex reconnection. Furthermore, the induced motion of bridges arrests the curvature growth and vortex stretching at the tipping points; consequently, the maximum vorticity grows with \(Re\) substantially slower than the exponential scaling predicted by the model -- implying that, for this configuration, even physical singularity is unlikely. Our simulations not only shed light on the longstanding question of finite-time singularities, but also further delineate the detailed mechanisms of reconnection. In particular, we show for the first time that the separation distance \(s ( \tau )\) before reconnection follows 1/2 scaling exactly -- a significant DNS result.Vortex dislocation mechanisms in the near wake of a step cylinder.https://zbmath.org/1460.762492021-06-15T18:09:00+00:00"Tian, Cai"https://zbmath.org/authors/?q=ai:tian.cai"Jiang, Fengjian"https://zbmath.org/authors/?q=ai:jiang.fengjian"Pettersen, Bjørnar"https://zbmath.org/authors/?q=ai:pettersen.bjornar"Andersson, Helge I."https://zbmath.org/authors/?q=ai:andersson.helge-iSummary: Vortex interactions behind step cylinders with diameter ratio \(D/d=2\) and 2.4 at Reynolds number \((Re_D) 150\) were investigated by directly solving the three-dimensional Navier-Stokes equations. In accordance with previous studies, three spanwise vortex cells were captured: S-, N- and L-cell vortices. In this paper, we focused on vortex interactions between the N- and L-cell vortices, especially the vortex dislocations and subsequent formations of vortex loop structures. The phase difference accumulation process of every pair of corresponding N- and L-cell vortices and its effects on the vortex dislocations were investigated. We revealed that the total phase difference between N- and L-cell vortices was accumulated by two physically independent mechanisms, namely different shedding frequencies and different convective velocities of these two cells. The second mechanism has never been reported before. The relative importance of these two mechanisms varied periodically in the phase difference accumulation process of every pair of corresponding N- and L-cell vortices. This variation caused the vortex dislocation process and the subsequent formation of the loop structures to change from one N-cell cycle to another. Our long-time observations also revealed an interruption of the conventional antisymmetric vortex interactions between two subsequent N-cell cycles in this wake. Moreover, the trigger value and the threshold value in the phase difference accumulation processes were identified and discussed. Both values contribute to better understanding of the vortex dislocations in this kind of wake flow. Finally, the universality of our discussions and conclusions was investigated.Viscous flow under an elastic sheet.https://zbmath.org/1460.761932021-06-15T18:09:00+00:00"Peng, Gunnar G."https://zbmath.org/authors/?q=ai:peng.gunnar-g"Lister, John R."https://zbmath.org/authors/?q=ai:lister.john-rSummary: We study the spreading of viscous fluid injected under an elastic sheet, which is driven by gravity and by elastic bending and tension forces and resisted by viscous forces. The injected fluid forms a large blister and spreads outwards analogously to a viscous gravity current or a capillary droplet. The relative strengths of the three driving forces are determined by how the horizontal length scales of the system compare with three key transition length scales. Bending is dominant on small length scales, tension is dominant on intermediate length scales and gravity is dominant on large length scales. We show how to use the method of matched asymptotic expansions to predict the spreading rate and thickness profile of the blister of fluid in the seven possible asymptotic regimes, for both two-dimensional and axisymmetric geometries. Consideration of different physical effects at the fluid front increases the number of regimes yet further.Emergence of superwalking droplets.https://zbmath.org/1460.761952021-06-15T18:09:00+00:00"Valani, Rahil N."https://zbmath.org/authors/?q=ai:valani.rahil-n"Dring, Jack"https://zbmath.org/authors/?q=ai:dring.jack"Simula, Tapio P."https://zbmath.org/authors/?q=ai:simula.tapio-p"Slim, Anja C."https://zbmath.org/authors/?q=ai:slim.anja-cSummary: A new class of self-propelled droplets, coined superwalkers, has been shown to emerge when a bath of silicone oil is vibrated simultaneously at a given frequency and its subharmonic tone with a relative phase difference between them \textit{R. N. Valani} et al. [``Superwalking droplets'', Phys. Rev. Lett. 123, No. 2, Article ID 024503, 5 p. (2019; \url{doi:10.1103/PhysRevLett.123.024503})]. To understand the emergence of superwalking droplets, we explore their vertical and horizontal dynamics by extending previously established theoretical models for walkers driven by a single frequency to superwalkers driven by two frequencies. Here, we show that driving the bath at two frequencies with an appropriate phase difference raises every second peak and lowers the intermediate peaks in the vertical periodic motion of the fluid surface. This allows large droplets that could otherwise not walk to leap over the intermediate peaks, resulting in superwalking droplets whose vertical dynamics is qualitatively similar to normal walkers. We find that the droplet's vertical and horizontal dynamics are strongly influenced by the relative height difference between successive peaks of the bath motion, a parameter that is controlled by the phase difference. Comparison of our simulated superwalkers with the experiments of Valani et al. [loc. cit.] shows good agreement for small- to moderate-sized superwalkers.The organizing centre for the flow around rapidly spinning cylinders.https://zbmath.org/1460.763032021-06-15T18:09:00+00:00"Brøns, Morten"https://zbmath.org/authors/?q=ai:brons.mortenSummary: The flow around a rotating circular cylinder has a parameter regime with a complex pattern of periodic solutions and multiple steady states. \textit{J. Sierra} et al. [ibid. 905, Article ID A2, 25 p. (2020; Zbl 1460.76248)] provide a complete bifurcation analysis of this regime. The numerical computations are guided by a qualitative analysis of the bifurcations stemming from a highly degenerate singular dynamical system. Surprisingly, the dynamics of the singular system itself cannot be realized as a specific flow, but acts mathematically as an organizer of the physical bifurcation diagram.Destratification of thermally stratified turbulent open-channel flow by surface cooling.https://zbmath.org/1460.765072021-06-15T18:09:00+00:00"Kirkpatrick, Michael P."https://zbmath.org/authors/?q=ai:kirkpatrick.michael-philip"Williamson, N."https://zbmath.org/authors/?q=ai:williamson.nicholas-john"Armfield, S. W."https://zbmath.org/authors/?q=ai:armfield.steve-w|armfield.steven-william"Zecevic, V."https://zbmath.org/authors/?q=ai:zecevic.vanjaSummary: Destratification of thermally stratified open-channel flow by surface cooling is investigated using direct numerical simulation. The initial states are the equilibrium states resulting from radiative heating. Using these states as initial conditions, a series of direct numerical simulations was run with radiative heating removed and a constant, uniform cooling flux applied at the upper surface. The flow evolves until the initial stable stratification is broken down and replaced by unstable stratification driven by surface cooling. The destratification process is described with reference to the evolution of the internal structure of the turbulent flow field. Based on these observations, we conclude that the dominant time scales in the flow from the perspective of destratification are the time scales associated with shear \(t_\tau\), convection \(t_*\) and stable density stratification \(t_N\). Scaling arguments are then used to derive a scaling relationship for destratification rate as a function of a friction Richardson number \(Ri_\tau =(t_\tau/t_N)^2\) and a convection Richardson number \(Ri_* = (t_*/ t_N)^2\). The relationship takes the form \(\mathcal{D}_N = C_1Ri_\tau^{-1} + C_2Ri_*^{-1}\), where \({\mathcal{D}}_N\) is the destratification rate non-dimensionalised with respect to \(t_N\) and \(C_1\) and \(C_2\) are model coefficients. The relationship is compared with simulation results and is shown to accurately predict the destratification rate in the simulations across a range of parameters. This relationship is then integrated to give a formula for the time taken for the flow to destratify.Corrigendum to: ``Towards a finite-time singularity of the Navier-Stokes equations. Part 2. Vortex reconnection and singularity evasion''.https://zbmath.org/1460.761722021-06-15T18:09:00+00:00"Moffatt, H. K."https://zbmath.org/authors/?q=ai:moffatt.henry-keith"Kimura, Yoshifumi"https://zbmath.org/authors/?q=ai:kimura.yoshifumiSummary: Corrects reference [5] in [the authors, ibid. 870, R1, 11 p. (2019; Zbl 1429.76042)].New exotic capillary free-surface flows.https://zbmath.org/1460.762652021-06-15T18:09:00+00:00"Doak, A."https://zbmath.org/authors/?q=ai:doak.alex|doak.alexander"Vanden-Broeck, J.-M."https://zbmath.org/authors/?q=ai:vanden-broeck.jean-marcSummary: In this paper, we consider two-dimensional steady free-surface flows where gravity is ignored, but the effects of surface tension are included. It is found that the existence of an additional solid boundary can allow for previously unseen limiting configurations as the surface tension tends to infinity. The free surface of these new solutions is formed of straight lines, arcs of circles and a point where the flow turns at a wall. These limiting configurations form endpoints of solution branches of capillary free-surface flows. Other endpoints of these branches include the surface tension free (i.e. free streamline) solution, and a solution whose free surface is composed simply of a straight line. The model we explore is flow incoming along a channel of constant width. One of the walls terminates, where the fluid is forcibly separated from the wall and a free boundary is formed. The other wall meets a second straight boundary with interior angle \(\beta\). Far downstream the solution approaches a uniform stream. Making use of Cauchy's integral formula, the unknowns are expressed in terms of values on the boundary. The integral equations are then solved numerically. The solution space relative to the parameter values of the model is discussed.Viscous and electro-osmotic effects upon motion of an oil droplet through a capillary.https://zbmath.org/1460.762672021-06-15T18:09:00+00:00"Grassia, Paul"https://zbmath.org/authors/?q=ai:grassia.paulSummary: In the context of waterflooding in oil recovery, the motion of an oil droplet through a capillary pore initially filled with aqueous liquid is considered. The droplet is affected by capillary and viscous forces, with a thin aqueous film being formed between the droplet and capillary wall. Moreover, the droplet surface and capillary wall surface have opposite and equal electrical charge. Attractive electro-osmotic interactions then tend to thin the film. A case is considered in which electro-osmotic interactions are strong and capillary forces are inherently weak, leading, in the first instance, to a viscous, electro-osmotic balance. Solutions are obtained for the droplet shape close to its front end. Whilst visco-electro-osmotic dominated solutions can indeed be found, additional solution classes are identified for which the film thickness oscillates with longitudinal position, and capillary forces regain importance. A parametric study is presented indicating that oscillation length scales along the film can be selected such that capillary effects never become negligible. Moreover gradients of electro-osmotic conjoining pressures are small in thinner parts of the film, even though electro-osmotic conjoining pressures themselves are not. Thus, rather than a visco-electro-osmotic balance being the norm, a capillary, viscous balance results in thinner parts of the film, giving way to a capillary, electro-osmotic balance in thicker parts. However, solutions are non-unique, and a given system can admit multiple solutions with films of various different thicknesses. Some of these solutions have films that increase monotonically in thickness with position, while others fall into the oscillatory class.Objective barriers to the transport of dynamically active vector fields.https://zbmath.org/1460.764212021-06-15T18:09:00+00:00"Haller, George"https://zbmath.org/authors/?q=ai:haller.george"Katsanoulis, Stergios"https://zbmath.org/authors/?q=ai:katsanoulis.stergios"Holzner, Markus"https://zbmath.org/authors/?q=ai:holzner.markus"Frohnapfel, Bettina"https://zbmath.org/authors/?q=ai:frohnapfel.bettina"Gatti, Davide"https://zbmath.org/authors/?q=ai:gatti.davideSummary: We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the vorticity, in general fluid flows. These special material surfaces (Lagrangian active barriers) provide physics-based, observer-independent boundaries of dynamically active coherent structures. We find that Lagrangian active barriers evolve from invariant surfaces of an associated steady and incompressible barrier equation, whose right-hand side is the time-averaged pullback of the viscous stress terms in the evolution equation for the dynamically active vector field. Instantaneous limits of these barriers mark objective Eulerian active barriers to the short-term diffusive transport of the dynamically active vector field. We obtain that in unsteady Beltrami flows, Lagrangian and Eulerian active barriers coincide exactly with purely advective transport barriers bounding observed coherent structures. In more general flows, active barriers can be identified by applying Lagrangian coherent structure (LCS) diagnostics, such as the finite-time Lyapunov exponent and the polar rotation angle, to the appropriate active barrier equation. In comparison to their passive counterparts, these active LCS diagnostics require no significant fluid particle separation and hence provide substantially higher-resolved LCS and Eulerian coherent structure boundaries from temporally shorter velocity data sets. We illustrate these results and their physical interpretation on two-dimensional, homogeneous, isotropic turbulence and on a three-dimensional turbulent channel flow.Surfactant-driven escape from endpinching during contraction of nearly inviscid filaments.https://zbmath.org/1460.762682021-06-15T18:09:00+00:00"Kamat, Pritish M."https://zbmath.org/authors/?q=ai:kamat.pritish-m"Wagoner, Brayden W."https://zbmath.org/authors/?q=ai:wagoner.brayden-w"Castrejón-Pita, Alfonso A."https://zbmath.org/authors/?q=ai:castrejon-pita.alfonso-a"Castrejón-Pita, José R."https://zbmath.org/authors/?q=ai:castrejon-pita.jose-r"Anthony, Christopher R."https://zbmath.org/authors/?q=ai:anthony.christopher-r"Basaran, Osman A."https://zbmath.org/authors/?q=ai:basaran.osman-aSummary: Highly stretched liquid drops, or filaments, surrounded by a gas are routinely encountered in nature and industry. Such filaments can exhibit complex and unexpected dynamics as they contract under the action of surface tension. Instead of simply retracting to a sphere of the same volume, low-viscosity filaments exceeding a critical aspect ratio undergo localized pinch-off at their two ends resulting in a sequence of daughter droplets -- a phenomenon called endpinching -- which is an archetype breakup mode that is distinct from the classical Rayleigh-Plateau instability seen in jet breakup. It has been shown that endpinching can be precluded in filaments of intermediate viscosity, with the so-called escape from endpinching being understood heretofore only qualitatively as being caused by a viscous mechanism. Here, we show that a similar escape can also occur in nearly inviscid filaments when surfactants are present at the free surface of a recoiling filament. The fluid dynamics of the escape phenomenon is probed by numerical simulations. The computational results are used to show that the escape is driven by the action of Marangoni stress. Despite the apparently distinct physical origins of escape in moderately viscous surfactant-free filaments and that in nearly inviscid but surfactant-covered filaments, it is demonstrated that the genesis of all escape events can be attributed to a single cause -- the generation of vorticity at curved interfaces. By analysing vorticity dynamics and the balance of vorticity in recoiling filaments, the manner in which surface tension gradients and concomitant Marangoni stresses can lead to escape from endpinching is clarified.The \(l_1\)-based sparsification of energy interactions in unsteady lid-driven cavity flow.https://zbmath.org/1460.762942021-06-15T18:09:00+00:00"Rubini, Riccardo"https://zbmath.org/authors/?q=ai:rubini.riccardo"Lasagna, Davide"https://zbmath.org/authors/?q=ai:lasagna.davide"Da Ronch, Andrea"https://zbmath.org/authors/?q=ai:da-ronch.andreaSummary: In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach produces interpretable, sparsely connected models that reproduce the original dynamical behaviour at a much lower computational cost, as fewer triadic interactions need to be evaluated. The key feature of the approach is that dominant interactions are selected systematically from the solution of a convex optimisation problem, with a unique solution, and no \textit{a priori} assumptions on the structure of scale interactions are required. We demonstrate this approach on models of two-dimensional lid-driven cavity flow at Reynolds number \(Re = 2 \times 10^4 \), where fluid motion is chaotic. To understand the role of the subspace utilised for the Galerkin projection in the sparsity characteristics, we consider two families of models obtained from two different modal decomposition techniques. The first uses energy-optimal proper orthogonal decomposition modes, while the second uses modes oscillating at a single frequency obtained from discrete Fourier transform of the flow snapshots. We show that, in both cases, and despite no \textit{a priori} physical knowledge being incorporated into the approach, relevant interactions across the hierarchy of modes are identified in agreement with the expected picture of scale interactions in two-dimensional turbulence. Yet, substantial structural changes in the interaction pattern and a quantitatively different sparsity are observed. Finally, although not directly enforced in the procedure, the sparsified models have excellent long-term stability properties and correctly reproduce the spatio-temporal evolution of dominant flow structures in the cavity.Local well-posedness for 2D incompressible magneto-micropolar boundary layer system.https://zbmath.org/1460.769332021-06-15T18:09:00+00:00"Lin, Xueyun"https://zbmath.org/authors/?q=ai:lin.xueyun"Zhang, Ting"https://zbmath.org/authors/?q=ai:zhang.tingThe authors consider a two-dimensional incompressible magneto-micropolar boundary layer system. Using suitable variables and analytic energy estimates, they obtain the local well-posedness for the two-dimensional incompressible magneto-micropolar boundary layer system when the initial data is analytic in the \(x\) variable.
Reviewer: Panagiotis Koumantos (Athína)Motion of an inertial squirmer in a density stratified fluid.https://zbmath.org/1460.769842021-06-15T18:09:00+00:00"More, Rishabh V."https://zbmath.org/authors/?q=ai:more.rishabh-v"Ardekani, Arezoo M."https://zbmath.org/authors/?q=ai:ardekani.arezoo-mSummary: We investigate the self-propulsion of an inertial swimmer in a linearly density stratified fluid using the archetypal squirmer model which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution of the Navier-Stokes equations using the finite volume method for solving the fluid flow and the distributed Lagrange multiplier method for modelling the swimmer. The simulations are performed for Reynolds numbers \((Re)\) between 5 and 100 and Froude numbers \((Fr)\) between 1 and 10. We find that increasing the fluid stratification strength reduces the swimming speeds of both pushers and pullers relative to their speeds in a homogeneous fluid. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. With increasing the stratification, the isopycnals tend to deform less, which offers resistance to the flow generated by the squirmers around them to propel themselves. This resistance increases with stratification, thus, reducing the squirmer swimming velocity. Stratification also stabilizes the flow around a puller keeping it axisymmetric even at high \(Re\), thus, leading to stability which is otherwise absent in a homogeneous fluid for \(Re\) greater than \(O(10)\). On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady and three-dimensional, which is otherwise steady and axisymmetric in a homogeneous fluid. A pusher is a more efficient swimmer than a puller owing to efficient convection of vorticity along its surface and downstream. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers.On the linear global stability analysis of rigid-body motion fluid-structure-interaction problems.https://zbmath.org/1460.761752021-06-15T18:09:00+00:00"Negi, P. S."https://zbmath.org/authors/?q=ai:negi.pooran-singh"Hanifi, A."https://zbmath.org/authors/?q=ai:hanifi.ardeshir"Henningson, D. S."https://zbmath.org/authors/?q=ai:henningson.dan-sSummary: A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body motion problem is performed in an Eulerian framework. We show that the `added stiffness' terms arising in the formulation of \textit{T. Fanion} et al. [Rev. Eur. Élém. Finis 9, No. 6--7, 681--708 (2000; Zbl 1010.74080)] vanish at the FSI interface in a first-order approximation and can be neglected when considering the growth of infinitesimal disturbances. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and nonlinear equations when the base flow is perturbed by identical small-amplitud+e perturbations. In all cases both the growth rate and angular frequency of the instability matches within 0.1\% accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero frequency linearly unstable mode of the coupled FSI system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.Leveraging reduced-order models for state estimation using deep learning.https://zbmath.org/1460.761742021-06-15T18:09:00+00:00"Nair, Nirmal J."https://zbmath.org/authors/?q=ai:nair.nirmal-j"Goza, Andres"https://zbmath.org/authors/?q=ai:goza.andresSummary: State estimation is key to both analysing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When desired, the full state can be recovered via the ROM.) Current methods in this category nearly always use a linear model to relate the sensor data to the reduced state, which often leads to restrictions on sensor locations and has inherent limitations in representing the generally nonlinear relationship between the measurements and reduced state. We propose an alternative methodology whereby a neural network architecture is used to learn this nonlinear relationship. A neural network is a natural choice for this estimation problem, as a physical interpretation of the reduced state-sensor measurement relationship is rarely obvious. The proposed estimation framework is agnostic to the ROM employed, and can be incorporated into any choice of ROMs derived on a linear subspace (e.g. proper orthogonal decomposition) or a nonlinear manifold. The proposed approach is demonstrated on a two-dimensional model problem of separated flow around a flat plate, and is found to outperform common linear estimation alternatives.Existence of a stationary Navier-Stokes flow past a rigid body, with application to starting problem in higher dimensions.https://zbmath.org/1460.352652021-06-15T18:09:00+00:00"Takahashi, Tomoki"https://zbmath.org/authors/?q=ai:takahashi.tomokiSummary: We consider the large time behavior of the Navier-Stokes flow past a rigid body in \(\mathbb{R}^n\) with \(n\geq 3\). We first construct a small stationary solution possessing the optimal summability at spatial infinity, which is the same as that of the Oseen fundamental solution. When the translational velocity of the body gradually increases and is maintained after a certain finite time, we then show that the nonstationary fluid motion converges to the stationary solution corresponding to a small terminal velocity of the body as time \(t\rightarrow \infty\) in \(L^q\) with \(q\in [n,\infty]\). This is called Finn's starting problem and the three-dimensional case was affirmatively solved by \textit{G. P. Galdi} et al. [Arch. Ration. Mech. Anal. 138, No. 4, 307--318 (1997; Zbl 0898.35071)]. The present paper extends the latter cited paper to the case of higher dimensions. Even for the three-dimensional case, our theorem provides new convergence rate, that is determined by the summability of the stationary solution at infinity and seems to be sharp.The effect of a strong density step on blocked stratified flow over topography.https://zbmath.org/1460.762782021-06-15T18:09:00+00:00"Jagannathan, Arjun"https://zbmath.org/authors/?q=ai:jagannathan.arjun"Winters, Kraig B."https://zbmath.org/authors/?q=ai:winters.kraig-b"Armi, Laurence"https://zbmath.org/authors/?q=ai:armi.laurenceSummary: The dynamical connection between topographic control and wave excitation aloft is investigated theoretically and numerically in the idealized setting of two-dimensional stratified flow over an isolated ridge. We consider a constant far upstream inflow with uniform stratification except for a sharp density step located above the height of the ridge crest. Below this step, the stratification is sufficiently strong that the low level flow is blocked upstream and a hydraulically controlled flow spills over the crest. Above the density step, the flow supports upward radiating waves. In the inviscid limit, a bifurcating isopycnal separates the hydraulically controlled overflow from the wave field aloft. We show that, depending on the height of the density step, the sharp interface can either remain approximately flat, above the controlled downslope flow, or plunge in the lee of the obstacle as part of the controlled overflow itself. Whether the interface plunges or not is a direct consequence of hydraulic control at the crest. The flow above the crest responds to the top of the sharp density step as if it were a virtual topography. We find that a plunging interface can excite a wave field aloft that is approximately six times as energetic, with 15\% higher pressure drag, than that in a comparable flow in which the interface remains approximately flat.Modified Reynolds equation for steady flow through a curved pipe.https://zbmath.org/1460.761662021-06-15T18:09:00+00:00"Ghosh, A."https://zbmath.org/authors/?q=ai:ghosh.arpan.1"Kozlov, V. A."https://zbmath.org/authors/?q=ai:kozlov.vladimir-a"Nazarov, S. A."https://zbmath.org/authors/?q=ai:nazarov.sergei-aleksandrovichSummary: A Reynolds equation governing the steady flow of a fluid through a curvilinear, narrow tube, with its derivation from Navier-Stokes equations through asymptotic methods is presented. The channel considered may have a rather large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed by artificially imposing appropriate boundary conditions at the inlet and the outlet. A justification for the approximations is provided along with a comparison with a simpler case.Viscous flow around a rigid body performing a time-periodic motion.https://zbmath.org/1460.352552021-06-15T18:09:00+00:00"Eiter, Thomas"https://zbmath.org/authors/?q=ai:eiter.thomas-walter"Kyed, Mads"https://zbmath.org/authors/?q=ai:kyed.madsSummary: The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.Upper-ocean Ekman current dynamics: a new perspective.https://zbmath.org/1460.764022021-06-15T18:09:00+00:00"Shrira, Victor I."https://zbmath.org/authors/?q=ai:shrira.victor-i"Almelah, Rema B."https://zbmath.org/authors/?q=ai:almelah.rema-bSummary: The work examines upper-ocean response to time-varying winds within the Ekman paradigm. Here, in contrast to the earlier works we assume the eddy viscosity to be both time and depth dependent. For self-similar depth and time dependence of eddy viscosity and arbitrary time dependence of wind we find an exact general solution to the Navier-Stokes equations which describes the dynamics of the Ekman boundary layer in terms of the Green's function. Two basic scenarios (a periodic wind and an increase of wind ending up with a plateau) are examined in detail. We show that accounting for the time dependence of eddy viscosity is straightforward and that it substantially changes the ocean response, compared to the predictions of the models with constant-in-time viscosity. We also examine the Stokes-Ekman equations taking into account the Stokes drift created by surface waves with an arbitrary spectrum and derive the general solution for the case of a linearly varying with depth eddy viscosity. Stability of transient Ekman currents to small-scale perturbations has never been examined. We find that the Ekman currents evolving from rest quickly become unstable, which breaks down the assumed horizontal uniformity. These instabilities proved to be sensitive to the model of eddy viscosity, they have small (\(\sim 10^2\text{m}\)) spatial scales and can be very fast compared to the inertial period, which suggests spikes of dramatically enhanced mixing localized in the vicinity of the water surface. This picture is incompatible with the Ekman paradigm and thus prompts radical revision of the Ekman-type models.The local well-posedness to the density-dependent magnetic Bénard system with nonnegative density.https://zbmath.org/1460.353012021-06-15T18:09:00+00:00"Zhong, Xin"https://zbmath.org/authors/?q=ai:zhong.xinSummary: We study the Cauchy problem of density-dependent magnetic Bénard system with zero density at infinity on the whole two-dimensional (2D) space. Despite the degenerate nature of the problem, we show the local existence of a unique strong solution in weighted Sobolev spaces by energy method.Inviscid and viscous global stability of vortex rings.https://zbmath.org/1460.761312021-06-15T18:09:00+00:00"Balakrishna, Naveen"https://zbmath.org/authors/?q=ai:balakrishna.naveen"Mathew, Joseph"https://zbmath.org/authors/?q=ai:mathew.joseph.2|mathew.joseph.3|mathew.joseph.1"Samanta, Arnab"https://zbmath.org/authors/?q=ai:samanta.arnabSummary: We perform inviscid and viscous, global, linear stability analyses of vortex rings which are compared with asymptotic theories and numerical simulations. We find growth rates of rings to be very sensitive to the details of vorticity distribution, in a way not accounted for in asymptotic theories, clearly demonstrated in our analyses of equilibrated rings-ring base flows initially obtained from Gaussian rings evolved to a quasi-steady state before any instabilities set in. Such equilibrated rings with the same \(\epsilon = a/R\), the ratio of core radius \(a\) to ring radius \(R\), but evolved with different viscosities, have inviscid growth rates differing by up to 9 \%, though the differences in vorticity at any point are small. In contrast, the growth rates of rings with a Gaussian vorticity distribution are found to be up to 33 \% smaller than the inviscid asymptotic theories over \(0.4 > \epsilon > 0.05\). We attribute these differences to the nature of velocity fields at \(O(\epsilon^2)\), between equilibrated and Gaussian rings, where the former shows a good quantitative match with the asymptotic theories. Additionally, there are some differences with previous direct numerical simulations (DNS), but in very close quantitative agreement with our DNS results. Our calculations provide a new relation capturing the near-linear dependence of growth rates on the reciprocal of a strain rate-based Reynolds number \(\widehat{R}e\). Importantly, our equilibrated ring calculations do tend to the inviscid limit of asymptotic theories, once corrections for ring radius evolution and equilibrated distribution are imposed, unlike for Gaussian rings.Conditional estimates in three-dimensional chemotaxis-Stokes systems and application to a Keller-Segel-fluid model accounting for gradient-dependent flux limitation.https://zbmath.org/1460.353582021-06-15T18:09:00+00:00"Winkler, Michael"https://zbmath.org/authors/?q=ai:winkler.michaelThe goal of this paper is to study effects of the Stokes flow on the fully parabolic chemotaxis system with suitable flux limitation in the equation for the evolution of the density of population. Results on the absence of blowup of solutions obtained in the three-dimensional case are similar to those for the chemotaxis system without fluid. General estimates derived for fluid motion and taxis gradients have also an independent interest for study of global-in-time existence of bounded solutions in related problems.
Reviewer: Piotr Biler (Wrocław)On some weighted Stokes problems: applications on Smagorinsky models.https://zbmath.org/1460.761852021-06-15T18:09:00+00:00"Rappaz, Jacques"https://zbmath.org/authors/?q=ai:rappaz.jacques"Rochat, Jonathan"https://zbmath.org/authors/?q=ai:rochat.jonathanSummary: In this paper we study existence and uniqueness of weak solutions for some non-linear weighted Stokes problems using convex analysis. The characterization of these equations is the viscosity, which depends on the strain rate of the velocity field and in some cases is related with a weight being the distance to the boundary of the domain. Such non-linear relations can be seen as a first approach of mixing-length eddy viscosity from turbulent modeling. A well known model is von Karman's on which the viscosity depends on the square of the distance to the boundary of the domain. Numerical experiments conclude the work and show properties from the theory.
For the entire collection see [Zbl 1411.35011].Thermocapillary effects during the melting of phase-change materials in microgravity: steady and oscillatory flow regimes.https://zbmath.org/1460.800122021-06-15T18:09:00+00:00"Salgado Sánchez, Pablo"https://zbmath.org/authors/?q=ai:salgado-sanchez.pablo"Ezquerro, J. M."https://zbmath.org/authors/?q=ai:ezquerro.jose-m"Fernández, J."https://zbmath.org/authors/?q=ai:fernandez.jose-jesus"Rodríguez, J."https://zbmath.org/authors/?q=ai:rodriguez.jesus-a|rodriguez.j-p-j|rodriguez.jose-angel|rodriguez.jose-gregorio|rodriguez.juan-carlos-sanchez|rodriguez.jose-miguel|rodriguez.jose-s|rodriguez.jorge-tomas|rodriguez.jose-israel|rodriguez.jose-e|rodriguez.john-david|rodriguez.jose-antonio|rodriguez.jose-ignacio|rodriguez.jaime-e-a|rodriguez.j-fernandez|rodriguez.juan-r|rodriguez.jesus-f|rodriguez.jeronimo|rodriguez.joanna|rodriguez.joel-arturo|rodriguez.jose-felix|rodriguez.jose-victor|rodriguez.jose-luis|rodriguez.jose-manuel|rodriguez.juan-manuel|rodriguez.jorge-luis-garcia|rodriguez.juan-angel|rodriguez.judith-s|rodriguez.jesus-m|rodriguez.joana|rodriguez.jose-maria|rodriguez.j-l-hospido|rodriguez.juan-sebastian|rodriguez.juan-gabriel|rodriguez.j-daza|rodriguez.joaquin|rodriguez.josemar|rodriguez.j-noyola|rodriguez.joseph-m|rodriguez.j-tinguaro|rodriguez.jonnathan|rodriguez.jorge-luis-dominguez|rodriguez.jeremy|rodriguez.jorge-p|rodriguez.javier|rodriguez.juan-j|rodriguez-seijo.jose-m|rodriguez.jhan|rodriguez.jeffrey-j|rodriguez.julio|rodriguez.j-c-rodr|rodriguez.juan-p|rodriguez.juan-i|rodriguez-velazquez.juan-alberto|rodriguez.jorge-eSummary: A detailed numerical investigation of thermocapillary effects during the melting of phase-change materials in microgravity is presented. The phase-change transition is analysed for the high-Prandtl-number material n-octadecane, which is enclosed in a two-dimensional rectangular container subjected to isothermal conditions along the lateral walls. The progression of the solid/liquid front during the melting leaves a free surface, where the thermocapillary effect acts driving convection in the liquid phase. The nature of the flow found during the melting depends on the container aspect ratio, \(\Gamma\), and on the Marangoni number, \(Ma\). For large \(\Gamma\), this flow initially adopts a steady return flow structure characterised by a single large vortex, which splits into a series of smaller vortices to create a steady multicellular structure (SMC) with increasing \(Ma\). At larger values of \(Ma\), this SMC undergoes a transition to oscillatory flow through the appearance of a hydrothermal travelling wave (HTW), characterised by the creation of travelling vortices near the cold boundary. For small \(\Gamma\), the thermocapillary flow at small to moderate \(Ma\) is characterised by an SMC that develops initially within a thin layer near the free surface. At larger times, the SMC evolves into a large-scale steady vortical structure. With increasing applied \(Ma\), a complex oscillatory mode is observed. This state, referred to as an oscillatory standing wave (OSW), is characterised by the pulsation of the vortical structure. Finally, for an intermediate \(\Gamma\) both HTW and OSW modes can be found depending on \(Ma\).A mixed-primal finite element method for the coupling of Brinkman-Darcy flow and nonlinear transport.https://zbmath.org/1460.651382021-06-15T18:09:00+00:00"Alvarez, Mario"https://zbmath.org/authors/?q=ai:alvarez.mario-m"Gatica, Gabriel N."https://zbmath.org/authors/?q=ai:gatica.gabriel-n"Ruiz-Baier, Ricardo"https://zbmath.org/authors/?q=ai:ruiz-baier.ricardoSummary: This paper is devoted to the mathematical and numerical analysis of a model describing the interfacial flow-transport interaction in a porous-fluidic domain. The medium consists of a highly permeable material, where the flow of an incompressible viscous fluid is governed by Brinkman equations (written in terms of vorticity, velocity and pressure), and a porous medium where Darcy's law describes fluid motion using filtration velocity and pressure. Gravity and the local fluctuations of a scalar field (representing for instance, the solids volume fraction or the concentration of a contaminant) are the main drivers of the fluid patterns on the whole domain, and the Brinkman-Darcy equations are coupled to a nonlinear transport equation accounting for mass balance of the scalar concentration. We introduce a mixed-primal variational formulation of the problem and establish existence and uniqueness of solution using fixed-point arguments and small-data assumptions. A family of Galerkin discretizations that produce divergence-free discrete velocities is also presented and analysed using similar tools to those employed in the continuous problem. Convergence of the resulting mixed-primal finite element method is proven, and some numerical examples confirming the theoretical error bounds and illustrating the performance of the proposed discrete scheme are reported.Implicit MAC scheme for compressible Navier-Stokes equations: low Mach asymptotic error estimates.https://zbmath.org/1460.651082021-06-15T18:09:00+00:00"Maltese, David"https://zbmath.org/authors/?q=ai:maltese.david"Novotný, Antonín"https://zbmath.org/authors/?q=ai:novotny.antoninSummary: We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier-Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier-Stokes equations. The main tool is the relative energy method suggested on the continuous level in [\textit{E. Feireisl} et al., J. Math. Fluid Mech. 14, No. 4, 717--730 (2012; Zbl 1256.35054)]. Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space-time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.Periodic solutions to Navier-Stokes equations on non-compact Einstein manifolds with negative curvature.https://zbmath.org/1460.352632021-06-15T18:09:00+00:00"Nguyen, Thieu Huy"https://zbmath.org/authors/?q=ai:nguyen-thieu-huy."Pham, Truong Xuan"https://zbmath.org/authors/?q=ai:pham.truong-xuan"Vu, Thi Ngoc Ha"https://zbmath.org/authors/?q=ai:vu-thi-ngoc-ha."Vu, Thi Mai"https://zbmath.org/authors/?q=ai:vu.thi-maiSummary: Consider the Navier-Stokes Equations (NSE) for viscous incompressible fluid flows on a non-compact, smooth, simply-connected and complete Einstein manifold \((\mathbf{M},g)\) with negative Ricci curvature tensor. We prove the existence and uniqueness of a time-periodic solution to NSE for vector fields on \((\mathbf{M},g)\). Our method is based on the dispersive and smoothing properties of the semigroup generated by the linearized Stokes equations to construct a bounded (in time) solution of the nonhomogeneous Stokes equation and on the ergodic method to obtain the periodic solution to Stokes equation. Then, using the fixed point arguments, we can pass from the Stokes equations to Navier-Stokes equations to obtain periodic solutions to NSE on the Einstein manifold \((\mathbf{M},g)\). We also prove the stability of the periodic solution.Centrifugal/elliptic instabilities in slowly varying channel flows.https://zbmath.org/1460.763072021-06-15T18:09:00+00:00"Gajjar, Jitesh S. B."https://zbmath.org/authors/?q=ai:gajjar.jitesh-s-b"Hall, Philip"https://zbmath.org/authors/?q=ai:hall.philipSummary: The instability of the flow in a two-dimensional meandering channel of slowly varying depth is considered. The flow is characterised by \(\delta\) the typical slope of the channel walls and the modified Reynolds number \(R_m\) which is the usual Reynolds number multiplied by \(\delta\). The modified Reynolds number is shown to be the appropriate parameter controlling the instability of the flow to streamwise vortices periodic in the spanwise direction. In particular, channels periodic in the streamwise direction are considered and it is found that the most unstable mode can correspond to either a subharmonic or synchronous disturbance. The instability problem at finite \(R_m\) is discussed first and then the inviscid and large wavenumber regimes are discussed in detail. The instability is shown to be a hybrid form of centrifugal instability having properties of both Görtler vortices and a parametric resonance usually referred to as an elliptic instability. The limiting case of small wall modulation amplitudes is investigated and the results suggest that at small amplitudes the subharmonic mode is always dominant.Dispersion induced by non-Newtonian gravity flow in a layered fracture or formation.https://zbmath.org/1460.767442021-06-15T18:09:00+00:00"Chiapponi, L."https://zbmath.org/authors/?q=ai:chiapponi.luca"Petrolo, D."https://zbmath.org/authors/?q=ai:petrolo.diana"Lenci, A."https://zbmath.org/authors/?q=ai:lenci.alessandro"Di Federico, V."https://zbmath.org/authors/?q=ai:di-federico.vittorio"Longo, Sandro"https://zbmath.org/authors/?q=ai:longo.sandroSummary: Models are developed to grasp the combined effect of rheology and spatial layering on buoyancy-driven dispersion in geologic media. We consider a power-law (PL) or Herschel-Bulkley (HB) constitutive equation for the fluid, and an array of \(N\) independent layers in a vertical fracture or porous medium subject to the same upstream overpressure. Under these assumptions, analytical solutions are derived in self-similar form (PL) or based on an expansion (HB) for the nose of single-phase gravity currents advancing into the layers ahead of a pressurized body. The position and size of the body and nose and the shape of the latter are significantly influenced by the interplay of model parameters: flow behaviour index \(n\), dimensionless yield stress \(\kappa\) for HB fluids, number of layers \(N\) and upstream overpressure. It is seen that layering produces (i) a relatively modest increase of the total flow rate with respect to the single layer of equal thickness, and (ii) macro-dispersion at the system scale in addition to local dispersion. The second longitudinal spatial moment of the solute cloud scales with time as \(t^{2n/(n+1)}\) for power-law fluids. The macro-dispersion induced by the layering prevails upon local dispersion beyond a threshold time. Theoretical results for the fracture are validated against a set of experiments conducted within a Hele-Shaw cell consisting of six layers. Comparison with experimental results shows that the proposed model is able to capture the propagation of the current and the macro-dispersion due to the velocity difference between layers, typically over-predicting the former and under-predicting the latter.On the distinct drag, reconfiguration and wake of perforated structures.https://zbmath.org/1460.762392021-06-15T18:09:00+00:00"Jin, Yaqing"https://zbmath.org/authors/?q=ai:jin.yaqing"Kim, Jin-Tae"https://zbmath.org/authors/?q=ai:kim.jintae"Cheng, Shyuan"https://zbmath.org/authors/?q=ai:cheng.shyuan"Barry, Oumar"https://zbmath.org/authors/?q=ai:barry.oumar"Chamorro, Leonardo P."https://zbmath.org/authors/?q=ai:chamorro.leonardo-pSummary: Using especially designed laboratory experiments, we demonstrate that the flow-driven deformation of sufficiently porous, wall-mounted, flexible plates can exhibit positive Vogel exponent \(V\), i.e. drag proportional to the \((2+V)\) power of the incoming flow velocity. High-resolution force balance, planar particle image velocimetry and particle tracking velocimetry are used to measure the drag force, flow characteristics and plate bending. For a flexible plate with relatively high porosity given by an array of regularly spaced square openings, we derive a simple analytical argument that accounts for the sub-quadratic trends of the drag in a range of flow velocities spanning one order of magnitude. There, the drag experienced by the structure is modulated by the contributions of the local structure containing an open area. The effective approach velocity for each of these sections appears to increase monotonically with increased structure deformation due to the reduced effect of local wakes produced by adjacent areas. The uncovered aerodynamic behaviour may help to understand the complex flow-structure interaction of perforated structures in nature and engineering.On quasi-steady boundary-layer separation in supersonic flow. II: Downstream moving separation point.https://zbmath.org/1460.762012021-06-15T18:09:00+00:00"Ruban, A. I."https://zbmath.org/authors/?q=ai:ruban.anatoly-i"Djehizian, A."https://zbmath.org/authors/?q=ai:djehizian.a"Kirsten, J."https://zbmath.org/authors/?q=ai:kirsten.jorrit"Kravtsova, M. A."https://zbmath.org/authors/?q=ai:kravtsova.marina-aSummary: In this paper we study the perturbations produced in the boundary layer by an impinging oblique shock wave or Prandtl-Meyer expansion fan. The flow outside the boundary layer is assumed supersonic, and we also assume that the point, where the shock wave/expansion fan impinges on the boundary layer, moves downstream. To study the flow, it is convenient to use the coordinate frame moving with the shock; in this frame, the body surface moves upstream. We first study numerically the case when the shock velocity \(V_{sh} = O (Re^{-1/8})\). In this case the interaction of the boundary layer with the shock can be described by the classical equations of the triple-deck theory. We find that, as \(V_{sh}\) increases, the boundary layer proves to be more prone to separation when exposed to the expansion fan, not the compression shock. Then we assume \(V_{sh}\) to be in the range \(1 \gg V_{sh} \gg Re^{-1/8}\). Under these conditions, the process of the interaction between the boundary layer and the shock/expansion fan can be treated as inviscid and quasi-steady if considered in the reference frame moving with the shock/expansion fan. The inviscid analysis allows us to determine the pressure distribution in the interaction region. We then turn our attention to a thin viscous sublayer that lies closer to the body surface. In this sublayer the flow is described by classical Prandtl's equations. The solution to these equations develops a singularity provided that the expansion fan is strong enough. The flow analysis in a small vicinity of the singular point shows an accelerated `expansion' of the flow similar to the one reported by \textit{Y. V. Neiland} [``Asymptotic theory for calculating heat fluxes near the corner of a body'', Fluid. Dyn. 4, No. 5, 33--37 (1969; \url{doi:10.1007/BF01015952})] in his analysis of supersonic flow separation from a convex corner.
For part I, see [\textit{A. I. Ruban} et al., ibid. 678, 124--155 (2011; Zbl 1241.76339)].Generation and decay of counter-rotating vortices downstream of yawed wind turbines in the atmospheric boundary layer.https://zbmath.org/1460.762222021-06-15T18:09:00+00:00"Shapiro, Carl R."https://zbmath.org/authors/?q=ai:shapiro.carl-r"Gayme, Dennice F."https://zbmath.org/authors/?q=ai:gayme.dennice-f"Meneveau, Charles"https://zbmath.org/authors/?q=ai:meneveau.charlesSummary: A quantitative understanding of the dominant mechanisms that govern the generation and decay of the counter-rotating vortex pair (CVP) produced by yawed wind turbines is needed to fully realize the potential of yawing for wind farm power maximization and regulation. Observations from large eddy simulations (LES) of yawed wind turbines in the turbulent atmospheric boundary layer and concepts from the aircraft trailing vortex literature inform a model for the shed vorticity and circulation. The model is formed through analytical integration of simplified forms of the vorticity transport equation. Based on an eddy viscosity approach, it uses the boundary-layer friction velocity as the velocity scale and the width of the vorticity distribution itself as the length scale. As with the widely used Jensen model for wake deficit evolution in wind farms, our analytical expressions do not require costly numerical integration of differential equations. The predicted downstream decay of maximum vorticity and total circulation agree well with LES results. We also show that the vorticity length scale grows linearly with downstream distance and find several power laws for the decay of maximum vorticity. These results support the notion that the decay of the CVP is dominated by gradual cancellation of the vorticity at the line of symmetry of the wake through cross-diffusion.On the forced surface quasi-geostrophic equation: existence of steady states and sharp relaxation rates.https://zbmath.org/1460.352842021-06-15T18:09:00+00:00"Hadadifard, Fazel"https://zbmath.org/authors/?q=ai:hadadifard.fazel"Stefanov, Atanas G."https://zbmath.org/authors/?q=ai:stefanov.atanas-gSummary: We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori estimates for them. Importantly, to do so, we only impose minimal cancellation conditions on the forcing function. Our main result is that all \(L^1\cap L^\infty\) localized initial data produces global solutions of the forced SQG, which converge to the steady states in \(L^p(\mathbb{R}^2)\), \(1<p\leq 2\) as time goes to infinity. This establishes that the steady states serve as one point attracting set. Moreover, by employing the method of scaling variables, we compute the sharp relaxation rates, by requiring slightly more localized initial data.Well-posedness of a family of degenerate parabolic mixed equations.https://zbmath.org/1460.780262021-06-15T18:09:00+00:00"Acevedo, Ramiro"https://zbmath.org/authors/?q=ai:acevedo.ramiro"Gómez, Christian"https://zbmath.org/authors/?q=ai:gomez.christian"López-Rodríguez, Bibiana"https://zbmath.org/authors/?q=ai:lopez-rodriguez.bibianaSummary: In this study, we present an abstract framework for analyzing a family of linear degenerate parabolic mixed equations. We combine the theory of degenerate parabolic equations with the classical Babuška-Brezzi theory for linear mixed stationary equations to deduce sufficient conditions to prove the well-posedness of the problem. Finally, we illustrate the application of the abstract framework based on examples from physical science applications, including fluid dynamics models and electromagnetic problems.An existence and uniqueness theorem for the Navier-Stokes equations in dimension four.https://zbmath.org/1460.761622021-06-15T18:09:00+00:00"Coscia, Vincenzo"https://zbmath.org/authors/?q=ai:coscia.vincenzoSummary: We prove that the steady state Navier-Stokes equations have a solution in an exterior Lipschitz domain of \(\mathbb{R}^4\), vanishing at infinity, provided the boundary datum belongs to \(L^3(\partial\Omega)\).A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes.https://zbmath.org/1460.651502021-06-15T18:09:00+00:00"Xu, Shipeng"https://zbmath.org/authors/?q=ai:xu.shipengSummary: In this paper, a posteriori error estimates for the Weak Galerkin finite element methods (WG-FEMs) for second order elliptic problems are derived in terms of an \(H^1\)-equivalent energy norm. Corresponding estimators based on the Helmholtz decomposition yield globally upper and locally lower bounds for the approximation errors of the WG-FEMs. Especially, the error analysis of our methods is proved to be valid for polygonal meshes (e.g., hybrid, polytopal non-convex meshes and those with hanging nodes) under general assumptions. In addition, the work can make adaptive WG-FEMs solving partial differential equations such as Stokes equations and biharmonic equations on polygonal meshes possible. Finally, we verify the theoretical findings by a few numerical examples.Viscous dissipation in the collision between a sphere and a textured wall.https://zbmath.org/1460.768492021-06-15T18:09:00+00:00"Mongruel, Anne"https://zbmath.org/authors/?q=ai:mongruel.anne"Gondret, Philippe"https://zbmath.org/authors/?q=ai:gondret.philippeSummary: A model is presented for the bouncing dynamics of a fluid-immersed sphere impacting normally a textured wall with micropillars. By taking into account the hydrodynamic and contact interactions between the smooth sphere and the textured wall, the complete motion of the sphere is recovered when approaching, colliding with and bouncing off the wall. We demonstrate that the critical Stokes number for the bouncing transition, \(St_c\), is the sum of two contributions corresponding to dissipation prior to and during the collision, both contributions being critically influenced by the geometrical parameters of the model roughness. The experimental data obtained from interferometric measurements are found to be in agreement with the theoretical predictions. In the bouncing regime, the coefficient of restitution is also derived analytically and shows a linear evolution with the Stokes number, \(St\), just above the bouncing transition, in agreement with the experimental data obtained very close to \(St_c\).Liouville theorem of the 3D stationary MHD system: for D-solutions converging to non-zero constant vectors.https://zbmath.org/1460.352612021-06-15T18:09:00+00:00"Li, Zijin"https://zbmath.org/authors/?q=ai:li.zijin"Pan, Xinghong"https://zbmath.org/authors/?q=ai:pan.xinghongSummary: In this paper, we derive the Liouville theorem of D-solutions to the stationary MHD system under the asymptotic assumption: one of the velocity field and the magnetic field approaches zero and the other approaches a non zero constant vector at infinity. Our result extends the corresponding one of D-solutions to the Navier-Stokes equations when the velocity approaches a non zero constant vector at infinity.Global-in-time existence for liquid mixtures subject to a generalised incompressibility constraint.https://zbmath.org/1460.352802021-06-15T18:09:00+00:00"Druet, Pierre-Etienne"https://zbmath.org/authors/?q=ai:druet.pierre-etienneSummary: We consider a system of partial differential equations describing diffusive and convective mass transport in a fluid mixture of \(N > 1\) chemical species. A weighted sum of the partial mass densities of the chemical species is assumed to be constant, which expresses the incompressibility of the fluid, while accounting for different reference sizes of the involved molecules. This condition is different from the usual assumption of a constant total mass density, and it leads in particular to a non-solenoidal velocity field in the Navier-Stokes equations. In turn, the pressure gradient occurs in the diffusion fluxes, so that the PDE-system of mass transport equations and momentum balance is fully coupled. Another striking feature of such incompressible \textit{mixtures} is the algebraic formula connecting the pressure and the densities, which can be exploited to prove a pressure bound in \(L^1\). In this paper, we consider incompressible initial states with bounded energy and show the global existence of weak solutions with defect measure.Small data global regularity for the 3-D Ericksen-Leslie hyperbolic liquid crystal model without kinematic transport.https://zbmath.org/1460.352872021-06-15T18:09:00+00:00"Huang, Jiaxi"https://zbmath.org/authors/?q=ai:huang.jiaxi"Jiang, Ning"https://zbmath.org/authors/?q=ai:jiang.ning"Luo, Yi-Long"https://zbmath.org/authors/?q=ai:luo.yi-long"Zhao, Lifeng"https://zbmath.org/authors/?q=ai:zhao.lifengThis work considers the hyperbolic Ericksen-Leslie system, which combined the hydrodynamical equation of motion with a constitutive equation for the orientation field that, in complex, models the motion of liquid crystals. The main result reported in prooving the existence of a unique global solution for such a system satisfying the energy bounds, which are provided.
Reviewer: Eugene Postnikov (Kursk)Vortex moment map for unsteady incompressible viscous flows.https://zbmath.org/1460.762142021-06-15T18:09:00+00:00"Li, Juan"https://zbmath.org/authors/?q=ai:li.juan|li.juan.1"Wang, Yinan"https://zbmath.org/authors/?q=ai:wang.yinan"Graham, Michael"https://zbmath.org/authors/?q=ai:graham.michael-k|graham.michael-d"Zhao, Xiaowei"https://zbmath.org/authors/?q=ai:zhao.xiaoweiSummary: In this paper, a vortex moment map (VMM) method is proposed to predict the pitching moment on a body from the vorticity field. VMM is designed to identify the moment contribution of each given vortex in the flow field. Implementing this VMM approach in starting flows of a NACA0012 airfoil, it is found that, due to the rolling up of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs), the unsteady nose-down moment about the quarter chord is higher than the steady-state value. The time variation of the unsteady moment is closely related to the LEVs and TEVs near the body and the VMM gives an intuitive understanding of how each part of the vorticity field contributes to the pitching moment on the body.The von Kármán street behind a circular cylinder: flow control through synthetic jet placed at the rear stagnation point.https://zbmath.org/1460.762882021-06-15T18:09:00+00:00"Greco, Carlo Salvatore"https://zbmath.org/authors/?q=ai:greco.carlo-salvatore"Paolillo, Gerardo"https://zbmath.org/authors/?q=ai:paolillo.gerardo"Astarita, Tommaso"https://zbmath.org/authors/?q=ai:astarita.tommaso"Cardone, Gennaro"https://zbmath.org/authors/?q=ai:cardone.gennaroSummary: The present paper aims at establishing the synthetic jet technology capabilities in controlling the von Kármán street behind a circular cylinder. The circular cylinder, placed in an open-circuit wind tunnel, presents a slot in its rear position, through which the synthetic jet is issued. The Reynolds number, based on the circular cylinder diameter and the free-stream velocity, is equal to 4600 and the von Kármán street is characterized, in the baseline configuration (i.e. without synthetic jet), by a shedding frequency of 16.2 Hz. Several synthetic jet operating conditions are tested. Therefore, the effects of the momentum coefficient \((C_\mu =5.4\%\), 10.8\% and 21.6\%) and the dimensionless frequency \((f^+ = 0.49, 0.98\) and 1.96) on the von Kármán street behaviour can be analysed. Instantaneous two-dimensional in-plane velocity fields are measured in a plane containing the synthetic jet slot axis using multigrid/multipass cross-correlation digital particle image velocimetry. These measurements have been used to investigate the mean flow quantities and turbulent statistics of the phenomenon. In addition, the wake extent and behaviour (i.e. symmetric or asymmetric) are analysed as well as the drag coefficient, for each configuration. The extent of the wake region decreases as the momentum coefficient and/or the dimensionless frequency increase, while the symmetric/asymmetric wake behaviour is found to be governed by a different control parameter: the synthetic jet Reynolds number based on its impulse. As regards the drag coefficient, a maximum reduction, of approximately 35\%, is found for the configuration at \(C_\mu=10.8\%\) and \(f^+=0.98\).Flow-driven collapse of lubricant-infused surfaces.https://zbmath.org/1460.761882021-06-15T18:09:00+00:00"Asmolov, Evgeny S."https://zbmath.org/authors/?q=ai:asmolov.evgeny-s"Nizkaya, Tatiana V."https://zbmath.org/authors/?q=ai:nizkaya.tatiana-v"Vinogradova, Olga I."https://zbmath.org/authors/?q=ai:vinogradova.olga-iSummary: Lubricant-infused surfaces in an outer liquid flow generally reduce viscous drag. However, owing to the meniscus deformation, the infused state could collapse. Here, we discuss the transition between infused and collapsed states of transverse shallow grooves, considering the capillary number, liquid/lubricant viscosity ratio and the aspect ratio of the groove as parameters for inducing this transition. It is found that, depending on the depth of the grooves, two different scenarios occur. A collapse of lubricant-infused surfaces could happen due to a depinning of the meniscus from the front groove edge. However, for very shallow textures, the meniscus contacts the bottom wall before such a depinning could occur. Our interpretation could help avoid this generally detrimental effect in various applications.Flow induced by an oscillating circular cylinder close to a plane boundary in quiescent fluid.https://zbmath.org/1460.761802021-06-15T18:09:00+00:00"Zhao, Ming"https://zbmath.org/authors/?q=ai:zhao.ming.2|zhao.ming.1|zhao.mingSummary: Flow induced by an oscillating circular cylinder close to a plane boundary in quiescent fluid is simulated numerically by solving the two-dimensional Navier-Stokes equations. The aim of this study is to investigate the effects of the gap ratio between the cylinder and plane boundary \((G)\), the oscillation direction of the cylinder \((\beta)\) and the Keulegan-Carpenter \((KC)\) number on the flow at a low Reynolds number of 150. Simulations are conducted for \(G=0.1, 0.5, 1, 1.5, 2\) and 4, and \(KC\) numbers between 2 and 12. Streaklines generated by releasing massless particles near the cylinder surface and contours of vorticity are used to observe the behaviour of the flow around the cylinder. The vortex shedding process from the cylinder is found to be very similar to that of a cylinder without a plane boundary except for \(G=0.1\) and \(\beta =0^\circ\), where vortices cannot be generated below the cylinder. Two streakline streets exist for all the flow regimes if there was not a plane boundary. A streakline street from the cylinder can be affected by the plane boundary in three ways: (1) it is suppressed by the plane boundary and stops propagating; (2) it rolls up after it meets the boundary and forms a recirculation zone; and (3) it splits into two streakline streets and forms two recirculation zones after it attacks the plane boundary. A refined classification method for flow induced by an oscillating cylinder close to a plane boundary is proposed by including a variant number, which represents the behaviour of the streaklines, into the regime names, and all the identified flow regimes are mapped on the \(KC-G\) plane. The drag and inertia coefficients of the Morison equation are obtained using the least-squares method. A very small gap of \(G=0.1\) significantly increases both the drag and inertia coefficients especially when \(\beta =0^\circ\). If \(G=1\) and above, the plane boundary changes the drag coefficient by less than 10 \% compared with that of a cylinder without a plane boundary, and the effect of the plane boundary on the inertia coefficient is weak only when the \(KC\) number is sufficiently small and vortex shedding does not exist.Controlling the number of vortices and torque in Taylor-Couette flow.https://zbmath.org/1460.762252021-06-15T18:09:00+00:00"Wen, Jun"https://zbmath.org/authors/?q=ai:wen.jun"Zhang, Wen-Yun"https://zbmath.org/authors/?q=ai:zhang.wen-yun"Ren, Liu-Zhen"https://zbmath.org/authors/?q=ai:ren.liu-zhen"Bao, Lu-Yao"https://zbmath.org/authors/?q=ai:bao.lu-yao"Dini, Daniele"https://zbmath.org/authors/?q=ai:dini.daniele"Xi, Heng-Dong"https://zbmath.org/authors/?q=ai:xi.heng-dong"Hu, Hai-Bao"https://zbmath.org/authors/?q=ai:hu.haibaoSummary: We present an experimental study on controlling the number of vortices and the torque in a Taylor-Couette flow of water for Reynolds numbers from 660 to 1320. Different flow states are achieved in the annulus of width \(d\) between the inner rotating and outer stationary cylinders through manipulating the initial height of the water annulus. We show that the torque exerted on the inner cylinder of the Taylor-Couette system can be reduced by up to 20 \% by controlling the flow at a state where fewer than the nominal number of vortices develop between the cylinders. This flow state is achieved by starting the system with an initial water annulus height \(h_0\) (which nominally corresponds to \(h_0/d\) vortices), then gradually adding water into the annulus while the inner cylinder keeps rotating. During this filling process the flow topology is so persistent that the number of vortices does not increase; instead, the vortices are greatly stretched in the axial (vertical) direction. We show that this state with stretched vortices is sustainable until the vortices are stretched to around 2.05 times their nominal size. Our experiments reveal that by manipulating the initial height of the liquid annulus we are able to generate different flow states and demonstrate how the different flow states manifest themselves in global momentum transport.A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows.https://zbmath.org/1460.761732021-06-15T18:09:00+00:00"Montemuro, Brandon"https://zbmath.org/authors/?q=ai:montemuro.brandon"White, Christopher M."https://zbmath.org/authors/?q=ai:white.christopher-m"Klewicki, Joseph C."https://zbmath.org/authors/?q=ai:klewicki.joseph-c"Chini, Gregory P."https://zbmath.org/authors/?q=ai:chini.gregory-pSummary: Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number \(Re\) in which the effective Reynolds number governing the streak and roll dynamics is \(O(1)\). Consequently, these viscous ECS are not suitable candidates for quasi-coherent structures away from the wall that necessarily are inviscid in the mean. Specifically, viscous ECS cannot account for the singular nature of the inertial domain, where the flow self-organizes into uniform momentum zones (UMZs) separated by internal shear layers and the instantaneous streamwise velocity develops a staircase-like profile. In this investigation, a large-\(Re\) asymptotic analysis is performed to explore the potential for a three-dimensional, short streamwise- and spanwise-wavelength instability of the embedded shear layers to sustain a spatially distributed array of much larger-scale, effectively inviscid streamwise roll motions. In contrast to other self-sustaining process theories, the rolls are sufficiently strong to differentially homogenize the background shear flow, thereby providing a mechanistic explanation for the formation and maintenance of UMZs and interlaced shear layers that respects the leading-order balance structure of the mean dynamics.Effect of confinement in wall-bounded non-colloidal suspensions.https://zbmath.org/1460.768352021-06-15T18:09:00+00:00"Gallier, Stany"https://zbmath.org/authors/?q=ai:gallier.stany"Lemaire, Elisabeth"https://zbmath.org/authors/?q=ai:lemaire.elisabeth"Lobry, Laurent"https://zbmath.org/authors/?q=ai:lobry.laurent"Peters, Francois"https://zbmath.org/authors/?q=ai:peters.francoisSummary: This paper presents three-dimensional numerical simulations of non-colloidal dense suspensions in a wall-bounded shear flow at zero Reynolds number. Simulations rely on a fictitious domain method with a detailed modelling of particle-particle and wall-particle lubrication forces, as well as contact forces including particle roughness and friction. This study emphasizes the effect of walls on the structure, velocity and rheology of a moderately confined suspension (channel gap to particle radius ratio of 20) for a volume fraction range \(0.1\leqslant {\mathit\phi}\leqslant 0.5\). The wall region shows particle layers with a hexagonal structure. The size of this layered zone depends on volume fraction and is only weakly affected by friction. This structure implies a wall slip which is in good accordance with empirical models. Simulations show that this wall slip can be mitigated by reducing particle roughness. For \({\mathit\phi}\lessapprox 0.4\), wall-induced layering has a moderate impact on the viscosity and second normal stress difference \(N_{2}\). Conversely, it significantly alters the first normal stress difference \(N_{1}\) and can result in positive \(N_{1}\), in better agreement with some experiments. Friction enhances this effect, which is shown to be due to a substantial decrease in the contact normal stress \(|{\mathit\Sigma}_{xx}^{c}|\) (where \(x\) is the velocity direction) because of particle layering in the wall region.A regularity criterion for a 2D tropical climate model with fractional dissipation.https://zbmath.org/1460.353462021-06-15T18:09:00+00:00"Bisconti, Luca"https://zbmath.org/authors/?q=ai:bisconti.lucaSummary: Tropical climate model derived by \textit{D. M. W. Frierson} et al. [Commun. Math. Sci. 2, No. 4, 591--626 (2004; Zbl 1160.86303)] and its modified versions have been investigated in a number of papers [\textit{E. Titi} and \textit{J. Li}, Discrete Contin. Dyn. Syst. 36, No. 8, 4495--4516 (2016; Zbl 1339.35325); \textit{R. Wan}, J. Math. Phys. 57, No. 2, 021507, 13 p. (2016; Zbl 1338.86011); \textit{M. Wang} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 3, 919--941 (2016; Zbl 1353.35007)] and more recently \textit{Q. Shi} and \textit{C. Peng} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 178, 133--144 (2019; Zbl 1406.35370)]. Here, we deal with the \(2D\) tropical climate model with fractional dissipative terms in the equation of the barotropic mode \(u\) and in the equation of the first baroclinic mode \(v\) of the velocity, but without diffusion in the temperature equation, and we establish a regularity criterion for this system.Using machine learning to detect the turbulent region in flow past a circular cylinder.https://zbmath.org/1460.763892021-06-15T18:09:00+00:00"Li, Binglin"https://zbmath.org/authors/?q=ai:li.binglin"Yang, Zixuan"https://zbmath.org/authors/?q=ai:yang.zixuan"Zhang, Xing"https://zbmath.org/authors/?q=ai:zhang.xing"He, Guowei"https://zbmath.org/authors/?q=ai:he.guowei"Deng, Bing-Qing"https://zbmath.org/authors/?q=ai:deng.bing-qing"Shen, Lian"https://zbmath.org/authors/?q=ai:shen.lianSummary: Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, \(Re=100\) and 3900. Extreme gradient boosting (XGBoost) is utilized to train the detector, and after training, the detector is applied to identify the flow state at each point of the flow field. The trained detector is found robust in various tests, including the applications to the entire fields at successive snapshots and at a higher Reynolds number \(Re=5000\). The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.Relative decay conditions on Liouville type theorem for the steady Navier-Stokes system.https://zbmath.org/1460.352512021-06-15T18:09:00+00:00"Chae, Dongho"https://zbmath.org/authors/?q=ai:chae.donghoSummary: In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in \(\mathbb{R}^3\) under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth solution \((u,p)\) of the stationary Navier-Stokes equations satisfying \(u(x) \rightarrow 0\) as \(|x|\rightarrow +\infty\) and the condition of finite Dirichlet integral \(\int_{\mathbb{R}^3} | \nabla u|^2 dx <+\infty\) is trivial, if either \(|u(x)|/|Q(x)|=O(1)\) or \(|p(x)|/|Q(x)| =O(1)\) as \(|x|\rightarrow \infty \), where \(|Q|=\frac{1}{2} |u|^2 +p\) is the head pressure.Bifurcation scenario in the two-dimensional laminar flow past a rotating cylinder.https://zbmath.org/1460.762482021-06-15T18:09:00+00:00"Sierra, J."https://zbmath.org/authors/?q=ai:sierra.jose-luis|sierra.jose-maria|sierra.jose-camara|sierra.jesus|sierra.jose-carlos|sierra.juan-pazos|sierra.j-l-suarez|sierra.jose-manuel"Fabre, D."https://zbmath.org/authors/?q=ai:fabre.david"Citro, V."https://zbmath.org/authors/?q=ai:citro.vincenzo"Giannetti, F."https://zbmath.org/authors/?q=ai:giannetti.flavioSummary: The aim of this paper is to provide a complete description of the bifurcation scenario of a uniform flow past a rotating circular cylinder up to \(Re = 200\). Linear stability theory is used to depict the neutral curves and analyse the arising unstable global modes. Three codimension-two bifurcation points are identified, namely a Takens-Bogdanov, a cusp and generalised Hopf, which are closely related to qualitative changes in orbit dynamics. The occurrence of the cusp and Takens-Bogdanov bifurcations for very close parameters (corresponding to an imperfect codimension-three bifurcation) is shown to be responsible for the existence of multiple steady states, as already observed in previous studies. Two bistability regions are identified, the first with two stable fixed points and the second with a fixed point and a cycle. The presence of homoclinic and heteroclinic orbits, which are classical in the presence of Takens-Bogdanov bifurcations, is confirmed by direct numerical simulations. Finally, a weakly nonlinear analysis is performed in the neighbourhood of the generalised Hopf, showing that above this point the Hopf bifurcation is subcritical, leading to a third range of bistability characterised by both a stable fixed point and a stable cycle.Laminar separated flows over finite-aspect-ratio swept wings.https://zbmath.org/1460.765932021-06-15T18:09:00+00:00"Zhang, Kai"https://zbmath.org/authors/?q=ai:zhang.kai"Hayostek, Shelby"https://zbmath.org/authors/?q=ai:hayostek.shelby"Amitay, Michael"https://zbmath.org/authors/?q=ai:amitay.michael"Burtsev, Anton"https://zbmath.org/authors/?q=ai:burtsev.anton"Theofilis, Vassilios"https://zbmath.org/authors/?q=ai:theofilis.vassilios"Taira, Kunihiko"https://zbmath.org/authors/?q=ai:taira.kunihikoSummary: We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-based Reynolds number of \(Re = 400\) to reveal a variety of wake structures generated for a range of aspect ratios (semi aspect ratio \(sAR=0.5-4)\), angles of attack \((\alpha =16^\circ -30^\circ)\) and sweep angles \((\varLambda =0^\circ -45^\circ)\). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unsteady vortex shedding takes place near the midspan of higher-\(AR\) wings due to weakened downwash induced by the tip vortices. With increasing sweep angle, the source of three-dimensionality transitions from the tip to the midspan. The three-dimensional midspan effects are responsible for the formation of the stationary vortical structures at the inboard part of the span, which expands the steady wake region to higher aspect ratios. At higher aspect ratios, the midspan effects of swept wings diminish at the outboard region, allowing unsteady vortex shedding to develop near the tip. In the wakes of highly swept wings, streamwise finger-like structures form repetitively along the wing span, providing a stabilizing effect. The insights revealed from this study can aid the design of high-lift devices and serve as a stepping stone for understanding the complex wake dynamics at higher Reynolds numbers and those generated by unsteady wing manoeuvres.Deflected wake interaction of tandem flapping foils.https://zbmath.org/1460.762402021-06-15T18:09:00+00:00"Lagopoulos, N. S."https://zbmath.org/authors/?q=ai:lagopoulos.n-s"Weymouth, G. D."https://zbmath.org/authors/?q=ai:weymouth.gabriel-d"Ganapathisubramani, B."https://zbmath.org/authors/?q=ai:ganapathisubramani.bharathramSummary: Symmetric flapping foils are known to produce deflected jets at high frequency-amplitude combinations even at a zero mean angle of attack. This reduces the frequency range of useful propulsive configurations without side force. In this study, we numerically analyse the interaction of these deflected jets for tandem flapping foils undergoing coupled heave-to-pitch motion in a two-dimensional domain. The impact of the flapping Strouhal number, foil spacing and phasing on wake interaction is investigated. Our primary finding is that the back foil is capable of cancelling the wake deflection and mean side force of the front foil, even when located up to five chord lengths downstream. This is achieved by attracting the incoming dipoles and disturbing their cohesion within the limits of the back foil's range of flapping motion. We also show that the impact on cycle-averaged thrust varies from high augmentation to drag generation depending on the wake patterns downstream of the back foil. These findings provide new insights towards the design of biomimetic tandem propulsors, as they expand their working envelope and ability to rapidly increase or decrease the forward speed by manipulating the size of the shed vortices.Hydrodynamics of an inertial active droplet.https://zbmath.org/1460.769672021-06-15T18:09:00+00:00"Dhar, A."https://zbmath.org/authors/?q=ai:dhar.atul|dhar.ananda-rabi|dhar.amit-kumar|dhar.anirban|dhar.arup-kumar|dhar.avinash|dhar.asoke-kumar|dhar.arun-k|dhar.abhishek|dhar.anindya-sundar|dhar.aparna"Burada, P. S."https://zbmath.org/authors/?q=ai:burada.p-sekhar"Raja Sekhar, G. P."https://zbmath.org/authors/?q=ai:sekhar.g-p-raja|rajasekhar.g-pSummary: Extensive studies have focused on the self-propulsion of a droplet in a viscous environment driven by the Marangoni effect in the absence of inertial effects. In order to capture the influence of inertia on the self-propulsion of a droplet, we use the singular perturbation solution for small but finite Reynolds number \((Re)\) flow past a spherical droplet with inhomogeneous surface tension. We calculate the swimming speed and the corresponding flow fields generated by the droplet in an axisymmetric unbounded medium at \(O(Re^2)\). The present results reveal how the choice of the stress parameter \(\sigma\), which is the ratio of the first two modes of the induced stress field, distinguishes between the different swimming styles, and determines the role of inertia on the swimming speed, energy expenditure and swimming efficiency of the droplet. Inertia enhances the swimming speed and the associated swimming efficiency of the droplet by abating the energy expenditure. It is striking to observe how a droplet swimmer with \(\sigma <0\) has a competitive advantage over a rigid squirmer with an equivalent surface activity due to the existence of an internal flow. We independently treat the potential influence of the viscosity ratio on the swimming properties of the droplet at finite \(Re\). Additionally, using linear stability analysis, we provide insights into the stability of the estimated migration velocity at \(O(Re)\). We argue that the droplet achieves a distinct stable equilibrium velocity, which occurs due to the inertial effect of the surrounding medium.Energy transfer in turbulent flows behind two side-by-side square cylinders.https://zbmath.org/1460.765632021-06-15T18:09:00+00:00"Zhou, Yi"https://zbmath.org/authors/?q=ai:zhou.yi"Nagata, Koji"https://zbmath.org/authors/?q=ai:nagata.koji.1"Sakai, Yasuhiko"https://zbmath.org/authors/?q=ai:sakai.yasuhiko"Watanabe, Tomoaki"https://zbmath.org/authors/?q=ai:watanabe.tomoaki"Ito, Yasumasa"https://zbmath.org/authors/?q=ai:ito.yasumasa"Hayase, Toshiyuki"https://zbmath.org/authors/?q=ai:hayase.toshiyukiSummary: Our previous study [\textit{Y. Zhou} et al. , ibid. 874, 677--698 (2019; Zbl 1419.76391)] confirmed that two different types of \(-5/3\) energy spectra (i.e. non-Kolmogorov and quasi-Kolmogorov \(-5/3\) spectra) can be found in turbulent flows behind two side-by-side square cylinders. In the upstream region (i.e. \(X/T_0=6\) with \(T_0\) being the cylinder thickness), albeit the turbulent flow is highly inhomogeneous and intermittent and Kolmogorov's hypothesis does not hold, the energy spectrum exhibits a well-defined \(-5/3\) power-law range for over one decade. Meanwhile, the power-law exponent of the corresponding second-order structure function is 1, which is significantly larger than the expected value, i.e. \(2/3\). At the downstream location, i.e. \(X/T_0=26\), in contrast, the quasi-Kolmogorov \(-5/3\) energy spectrum (and also the 2/3 scaling of the second-order structure) can be identified. Through decomposing the streamwise velocity fluctuations into the spanwise average of instantaneous velocity and the turbulent residual, we demonstrate that the non-Kolmogorov \(-5/3\) spectrum at \(X/T_0=6\) is caused by the turbulent residual part. To shed light on the physics of the scale-by-scale energy transfer, we resort to the Kármán-Howarth-Monin-Hill equation. At \(X/T_0=6\), the expected balance between the nonlinear term and the dissipation term cannot be detected. Instead, the contributions from the non-local pressure, advection, nonlinear transport and turbulent transport terms are dominant. Moreover, because the corresponding flow field is highly intermittent, the magnitudes of the non-local pressure, advection, nonlinear transport and turbulent transport terms are significantly larger than that of the dissipation term. At a far downstream location, i.e. \(X/T_0=26\), where the dual-wake flow is fully turbulent and becomes much more homogeneous and isotropic, within a short intermediate range the two dominant terms in the two-point turbulent kinetic energy budget are the nonlinear transport term and the dissipation term, which to some extent echoes Kolmogorov's scenario, albeit the contribution from the large-scale advection term cannot be ignored. By comparing the behaviour of the one-point and two-point energy transfer, it can be seen that the two different energy transfer processes are actually closely related, that is, the similar relative importance of the viscous dissipation and the same role of the non-negligible terms in terms of being a source or sink term.Computational analysis of vortex dynamics and performance enhancement due to body-fin and fin-fin interactions in fish-like locomotion.https://zbmath.org/1460.769792021-06-15T18:09:00+00:00"Liu, Geng"https://zbmath.org/authors/?q=ai:liu.geng"Ren, Yan"https://zbmath.org/authors/?q=ai:ren.yan"Dong, Haibo"https://zbmath.org/authors/?q=ai:dong.haibo"Akanyeti, Otar"https://zbmath.org/authors/?q=ai:akanyeti.otar"Liao, James C."https://zbmath.org/authors/?q=ai:liao.james-c"Lauder, George V."https://zbmath.org/authors/?q=ai:lauder.george-vSummary: Numerical simulations are used to investigate the hydrodynamic benefits of body-fin and fin-fin interactions in a fish model in carangiform swimming. The geometry and kinematics of the model are reconstructed in three-dimensions from high-speed videos of a live fish, Crevalle Jack (\textit{Caranx hippos}), during steady swimming. The simulations employ an immersed-boundary-method-based incompressible Navier-Stokes flow solver that allows us to quantitatively characterize the propulsive performance of the fish median fins (the dorsal and the anal fins) and the caudal fin using three-dimensional full body simulations. This includes a detailed analysis of associated performance enhancement mechanisms and their connection to the vortex dynamics. Comparisons are made using three different models containing different combinations of the fish body and fins to provide insights into the force production. The results indicate that the fish produces high performance propulsion by utilizing complex interactions among the fins and the body. By connecting the vortex dynamics and surface force distribution, it is found that the leading-edge vortices produced by the caudal fin are associated with most of the thrust production in this fish model. These vortices could be strengthened by the vorticity capture from the vortices generated by the posterior body during undulatory motion. Meanwhile, the pressure difference between the two sides of posterior body resulting from the posterior body vortices (PBVs) helps with the alleviation of the body drag. The appearance of the median fins in the posterior region further strengthens the PBVs and caudal-fin wake capture mechanism. This work provides new physical insights into how body-fin and fin-fin interactions enhance thrust production in swimming fishes, and emphasizes that movements of both the body and fins contribute to overall swimming performance in fish locomotion.Direct numerical simulation of stratified Ekman layers over a periodic rough surface.https://zbmath.org/1460.765472021-06-15T18:09:00+00:00"Lee, Sungwon"https://zbmath.org/authors/?q=ai:lee.sungwon"Gohari, S. M. Iman"https://zbmath.org/authors/?q=ai:gohari.s-m-iman"Sarkar, Sutanu"https://zbmath.org/authors/?q=ai:sarkar.sutanuSummary: Ekman layers over a rough surface are studied using direct numerical simulation. The roughness takes the form of periodic two-dimensional bumps whose non-dimensional amplitude is fixed at a small value \((h^+=15)\) and whose mean slope is gentle. The neutral Ekman layer is subjected to a stabilizing cooling flux for approximately one inertial period \((2\pi /f)\) to impose the stratification. The Ekman boundary layer is in a transitionally rough regime and, without stratification, the effect of roughness is found to be mild in contrast to the stratified case. Roughness, whose effect increases with the slope of the bumps, changes the boundary layer qualitatively from the very stable [\textit{L. Mahrt}, Theor. Comput. Fluid Dyn. 11, No. 3--4, 263--279 (1998; Zbl 0948.76029)] regime, which has a strong thermal inversion and a pronounced low-level jet, in the flat case to the stable regime, which has a weaker thermal inversion and stronger surface-layer turbulence, in the rough cases. The flat case exhibits initial collapse of turbulence which eventually recovers, albeit with inertial oscillations in turbulent kinetic energy. The roughness elements interrupt the initial collapse of turbulence. In the quasi-steady state, the thickness of the turbulent stress profiles and of the near-surface region with subcritical gradient Richardson number increase in the rough cases. Analysis of the turbulent kinetic energy (TKE) budget shows that, in the surface layer, roughness counteracts the stability-induced reduction of TKE production. The flow component, coherent with the surface undulations, is extracted by a triple decomposition, and leads to a dispersive component of near-surface turbulent fluxes. The significance of the dispersive component increases in the stratified cases.Global large solutions and optimal time-decay estimates to the Korteweg system.https://zbmath.org/1460.353002021-06-15T18:09:00+00:00"Zhai, Xiaoping"https://zbmath.org/authors/?q=ai:zhai.xiaoping"Li, Yongsheng"https://zbmath.org/authors/?q=ai:li.yongshengSummary: We prove the global solutions to the Korteweg system without smallness condition imposed on the vertical component of the incompressible part of the velocity. The weighted Chemin-Lerner-norm technique which is well-known for the incompressible Navier-Stokes equations is introduced to derive the a priori estimates. As a byproduct, we obtain the optimal time decay rates of the solutions by using the pure energy argument (independent of spectral analysis). In contrast to the compressible Navier-Stokes system, the time-decay estimates are more accurate owing to smoothing effect from the Korteweg tensor.Cox-Voinov theory with slip.https://zbmath.org/1460.762622021-06-15T18:09:00+00:00"Chan, Tak Shing"https://zbmath.org/authors/?q=ai:chan.tak-shing-t"Kamal, Catherine"https://zbmath.org/authors/?q=ai:kamal.catherine"Snoeijer, Jacco H."https://zbmath.org/authors/?q=ai:snoeijer.jacco-h"Sprittles, James E."https://zbmath.org/authors/?q=ai:sprittles.james-e"Eggers, Jens"https://zbmath.org/authors/?q=ai:eggers.jens-gSummary: Most of our understanding of moving contact lines relies on the limit of small capillary number \(Ca\). This means the contact line speed is small compared to the capillary speed \(\gamma /\eta\), where \(\gamma\) is the surface tension and \(\eta\) the viscosity, so that the interface is only weakly curved. The majority of recent analytical work has assumed in addition that the angle between the free surface and the substrate is also small, so that lubrication theory can be used. Here, we calculate the shape of the interface near a slip surface for arbitrary angles, and for two phases of arbitrary viscosities, thereby removing a key restriction in being able to apply small capillary number theory. Comparing with full numerical simulations of the viscous flow equation, we show that the resulting theory provides an accurate description up to \(Ca \approx 0.1\) in the dip coating geometry, and a major improvement over theories proposed previously.Size-dependent spontaneous oscillations of Leidenfrost droplets.https://zbmath.org/1460.767942021-06-15T18:09:00+00:00"Liu, Dongdong"https://zbmath.org/authors/?q=ai:liu.dongdong"Tran, Tuan"https://zbmath.org/authors/?q=ai:tran.tuan-duy|tran.tuan-anhSummary: A liquid droplet hovering on a hot solid surface is commonly referred to as a Leidenfrost droplet. In this study, we discover that a Leidenfrost droplet spontaneously performs a series of distinct oscillations as it shrinks during the span of its life. The oscillation first starts out erratically, followed by a stage with stable frequencies, and finally turns into periodic bouncing with signatures of a parametric oscillation and occasional resonances. The last bouncing stage exhibits nearly perfect collisions. We showed experimentally and theoretically the enabling effects of each oscillation mode and how the droplet switches between such modes. We finally show that these spontaneous oscillation modes and the conditions for transitioning between modes are universal for all tested combinations of liquids and surfaces.Taylor drop in a closed vertical pipe.https://zbmath.org/1460.761942021-06-15T18:09:00+00:00"Picchi, Davide"https://zbmath.org/authors/?q=ai:picchi.davide"Suckale, J."https://zbmath.org/authors/?q=ai:suckale.jenny"Battiato, I."https://zbmath.org/authors/?q=ai:battiato.ileniaSummary: In this work, we study the ascent dynamics of a liquid Taylor drop formed from a lock-exchange configuration in a closed vertical pipe. We focus on the buoyancy-driven motion of an elongated drop surrounded by a denser fluid when viscous forces dominate over inertial and surface tension effects. While gaseous Taylor bubbles have been studied extensively, a liquid Taylor drop moving in a closed pipe is less well understood. We formulate an analytical model for estimating the ascent speed and drop thickness from first principles. First, we use a lubrication approximation to solve for the velocity profiles in the two fluids. Then, we analyse the mechanical energy balance of the whole system, including the effect of viscous dissipation, to understand how the ascent speed and drop thickness scale with the viscosity ratio. We show that a drop with density ratio \(\mathcal{R}\) reaches a stationary state with a uniform dimensionless thickness of \(\sqrt{2}/{2}\) in the absence of dissipation and \(\sqrt{2\mathcal{R}}/{2}\) in the dissipative regime. Through a comparison with existing experimental data, we demonstrate that our model correctly predicts the ascent speed of a Taylor drop if the material properties of the fluids and the geometry of the conduit are known. Our theoretical framework can be generalized to an isolated Taylor drop rising in a vertical pipe.Start-up flow in shallow deformable microchannels.https://zbmath.org/1460.761902021-06-15T18:09:00+00:00"Martínez-Calvo, Alejandro"https://zbmath.org/authors/?q=ai:martinez-calvo.alejandro"Sevilla, Alejandro"https://zbmath.org/authors/?q=ai:sevilla.alejandro"Peng, Gunnar G."https://zbmath.org/authors/?q=ai:peng.gunnar-g"Stone, Howard A."https://zbmath.org/authors/?q=ai:stone.howard-aSummary: Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of \textit{I. C. Christov} et al. [ibid. 841, 267--286 (2018; Zbl 1419.76308)] by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modelled as an elastic plate under pure bending satisfying the Kirchhoff-Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter \(\beta\), which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter \(\gamma\) that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, \(\gamma \rightarrow 0\), a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with \(\beta\) as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier-Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.On endpoint regularity criterion of the 3D Navier-Stokes equations.https://zbmath.org/1460.352602021-06-15T18:09:00+00:00"Li, Zhouyu"https://zbmath.org/authors/?q=ai:li.zhouyu"Zhou, Daoguo"https://zbmath.org/authors/?q=ai:zhou.daoguoSummary: Let \((u,\pi)\) with \(u = (u_1, u_2, u_3)\) be a suitable weak solution of the three-dimensional Navier-Stokes equations in \(\mathbb{R}^3 \times (0, T)\). Denote by \(\dot{\mathcal{B}}^{-1}_{\infty,\infty}\) the closure of \(C^\infty_0\) in \(\dot{B}^{-1}_{\infty,\infty} \). We prove that if \(u \in L^\infty (0, T; \dot{B}^{-1}_{\infty,\infty})\), \(u(x, T) \in \dot{\mathcal{B}}^{-1}_{\infty,\infty})\), and \(u_3 \in L^\infty (0, T; L^{3,\infty})\) or \(u_3 \in L^\infty (0, T; \dot{B}^{-1+3/p}_{p,q})\) with \(3 < p, q < \infty \), then \(u\) is smooth in \(\mathbb{R}^3 \times (0, T]\). Our result improves a previous result established by \textit{W. Wang} and \textit{Z. Zhang} [Sci. China, Math. 60, No. 4, 637--650 (2017; Zbl 1387.35471)].Universality of capillary rising in corners.https://zbmath.org/1460.762742021-06-15T18:09:00+00:00"Zhou, Jiajia"https://zbmath.org/authors/?q=ai:zhou.jiajia"Doi, Masao"https://zbmath.org/authors/?q=ai:doi.masaoSummary: We study the dynamics of viscous capillary rising in small corners between two curved walls described by a function \(y=cx^n\) with \(n \geq 1\). Using the Onsager principle, we derive a partial differential equation that describes the time evolution of the meniscus profile. By solving the equation both numerically and analytically, we show that the capillary rising dynamics is quite universal. Our theory explains the surprising finding by \textit{A. Ponomarenko} et al. [ibid. 666, 146--154 (2011; Zbl 1225.76023)] that the time dependence of the height not only obeys the universal power-law of \(t^{1/3}\), but also that the prefactor is almost independent of \(n\).Optimal feedback control for one motion model of a nonlinearly viscous fluid.https://zbmath.org/1460.762932021-06-15T18:09:00+00:00"Zvyagin, Viktor Grigor'evich"https://zbmath.org/authors/?q=ai:zvyagin.viktor-grigorevich"Zvyagin, Andreĭ Viktorovich"https://zbmath.org/authors/?q=ai:zvyagin.andrey-v"Hong, Nguyen Minh"https://zbmath.org/authors/?q=ai:hong.nguyen-minhSummary: An optimal control problem with a feedback is considered for an initial boundary problem describing a motion of non-linearly viscous liquid. An existence of an optimal solution minimising a given quality functional is proved. A topological approximation approach to study of mathematical problems of hydrodynamics is used in the proof of existence of an optimal solution.Variation of leading-edge suction during stall for unsteady aerofoil motions.https://zbmath.org/1460.762172021-06-15T18:09:00+00:00"Narsipur, Shreyas"https://zbmath.org/authors/?q=ai:narsipur.shreyas"Hosangadi, Pranav"https://zbmath.org/authors/?q=ai:hosangadi.pranav"Gopalarathnam, Ashok"https://zbmath.org/authors/?q=ai:gopalarathnam.ashok"Edwards, Jack R."https://zbmath.org/authors/?q=ai:edwards.jack-rSummary: The suction force at the leading edge of a round-nosed aerofoil is an important indicator of the state of the flow over the leading edge and, often, the entire aerofoil. The leading-edge suction parameter (LESP) is a non-dimensional version of this force. In recent works, the LESP was calculated with good accuracy for attached flows at low Reynolds numbers (10 000--100 000) from unsteady aerofoil theory. In contrast to this `inviscid' LESP, results from viscous computations and experiments are used here to calculate the `viscous' LESP on aerofoils undergoing pitching motions at low subsonic speeds. The LESP formulation is also updated to account for the net velocity of the aerofoil. Spanning multiple aerofoils, Reynolds numbers and kinematics, the cases include motions in which dynamic stall occurs with or without leading-edge vortex (LEV) formation. Inflections in the surface pressure and skin-friction distributions near the leading edge are shown to be reliable indicators of LEV initiation. Critical LESP, which is the LESP value at LEV initiation, was found to be nearly independent of pivot location, weakly dependent on pitch rate and strongly dependent on Reynolds number. The viscous LESP was seen to drop to near-zero values when the flow is separated at the leading edge, irrespective of LEV formation. This behaviour was shown to correlate well with the loss of streamline curvature at the leading edge due to flow separation. These findings serve to improve our understanding and extend the applicability of the leading-edge suction behaviour gained from earlier works.Langmuir-type vortices in wall-bounded flows driven by a criss-cross wavy wall topography.https://zbmath.org/1460.762042021-06-15T18:09:00+00:00"Akselsen, Andreas H."https://zbmath.org/authors/?q=ai:akselsen.andreas-h"Ellingsen, Simen Å."https://zbmath.org/authors/?q=ai:ellingsen.simen-aSummary: We investigate a mechanism to manipulate wall-bounded flows whereby wave-like undulations of the wall topography drives the creation of bespoke longitudinal vortices. A resonant interaction between the ambient vorticity of the undisturbed shear flow and the undulation of streamlines enforced by the wall topography serves to slightly rotate the spanwise vorticity of the mean flow into the streamwise direction, creating a swirling motion, in the form of regular streamwise rolls. The process is kinematic and essentially identical to the `direct drive' CL1 mechanism for Langmuir circulation (LC) proposed by \textit{A. D. D. Craik} [ibid. 41, 801--821 (1970; Zbl 0202.27203)]. Wall shear is modelled by selecting suitable primary flow profiles. A simple, easily integrable expression for the cross-plane streamfunction is found in two asymptotic regimes: the resonant onset of the essentially inviscid instability at early times, and the fully developed steady-state viscous flow. Linear-order solutions for flow over undulating boundaries are obtained, fully analytical in the special case of a power-law profile. These solutions allow us to quickly map out the circulation response to boundary design parameters. The study is supplemented with direct numerical simulations which verify the manifestation of boundary induced Langmuir vortices in laminar flows with no-slip boundaries. Simulations show good qualitative agreement with theory. Quantitatively, the comparisons rest on a displacement length closure parameter adopted in the perturbation theory. While wall-driven LC appear to become unstable in turbulent flows, we propose that the mechanism can promote swirling motion in boundary layers, a flow feature which has been reported to reduce drag in some situations.Optimal perturbations in viscous round jets subject to Kelvin-Helmholtz instability.https://zbmath.org/1460.762442021-06-15T18:09:00+00:00"Nastro, Gabriele"https://zbmath.org/authors/?q=ai:nastro.gabriele"Fontane, Jérôme"https://zbmath.org/authors/?q=ai:fontane.jerome"Joly, Laurent"https://zbmath.org/authors/?q=ai:joly.laurentSummary: We investigate the development of three-dimensional instabilities on a time-dependent round jet undergoing the axisymmetric Kelvin-Helmholtz (KH) instability. A non-modal linear stability analysis of the resulting unsteady roll-up into a vortex ring is performed based on a direct-adjoint approach. Varying the azimuthal wavenumber \(m\), the Reynolds number \(Re\) and the aspect ratio \(\alpha\) of the jet base flow, we explore the potential for secondary energy growth beyond the initial phase when the base flow is still quasi-parallel and universal shear-induced transient growth occurs. For \(Re=1000\) and \(\alpha =10\), the helical \(m=1\) and double-helix \(m=2\) perturbations stand as global optimals with larger growth rates in the post roll-up phase. The secondary energy growth stems from the development of elliptical (E-type) and hyperbolic (H-type) instabilities. For \(m>2\), the maximum of the kinetic energy of the optimal perturbation moves from the large scale vortex core towards the thin vorticity braid. With a Reynolds number one order of magnitude larger, the kinetic energy of the optimal perturbations exhibits sustained growth well after the saturation time of the base flow KH wave and the underlying length scale selection favours higher azimuthal wavenumbers associated with H-type instability in the less diffused vorticity braid. Doubling the jet aspect ratio yields initially thinner shear layers only slightly affected by axisymmetry. The resulting unsteady base flow loses scale selectivity and is prone to a common path of initial transient growth followed by the optimal secondary growth of a wide range of wavenumbers. Increasing both the aspect ratio and the Reynolds number thus yields an even larger secondary growth and a lower wavenumber selectivity. At a lower aspect ratio of \(\alpha =5\), the base flow is smooth and a genuine round jet affected by the axisymmetry condition. The axisymmetric modal perturbation of the base flow parallel jet only weakly affects the first common phase of transient growth and the optimal helical perturbation \(m=1\) dominates with energy gains considerably larger than those of larger azimuthal wavenumbers whatever the horizon time.Numerical analysis of the lattice Boltzmann method for the Boussinesq equations.https://zbmath.org/1460.766512021-06-15T18:09:00+00:00"Yong, Wen-An"https://zbmath.org/authors/?q=ai:yong.wen-an"Zhao, Weifeng"https://zbmath.org/authors/?q=ai:zhao.weifengSummary: This paper is concerned with the lattice Boltzmann method (LBM) with BGK collision models for the two-dimensional Bousinessq equations on periodic domains. We show the numerical stability of the LBM linearized at a quiescent state and conduct a formal asymptotic analysis which indicates the consistency of the method to the Boussinesq equations. With these, we establish the convergence of the LBM for the nonlinear equations. Moreover, our present analysis provides some important hints on how to construct initial data and how to add force terms in the LBM. It can be straightforwardly extended to other LB models or three-dimensional cases.Optimal growth of counter-rotating vortex pairs interacting with walls.https://zbmath.org/1460.762082021-06-15T18:09:00+00:00"Dehtyriov, Daniel"https://zbmath.org/authors/?q=ai:dehtyriov.daniel"Hourigan, Kerry"https://zbmath.org/authors/?q=ai:hourigan.kerry"Thompson, Mark C."https://zbmath.org/authors/?q=ai:thompson.mark-christopherSummary: The transient growth of a counter-rotating equal strength vortex pair, which descends under mutual induction towards a ground plane, is examined through non-modal linear stability analysis and direct numerical simulation. The vortex pair is studied at a height of five vortex spacing distances above the wall, consistent with the first mode of vortex instability/wall interaction observed by experiment. Three regimes are identified in which the optimal mode topology and non-modal growth mechanisms are distinct, correlated with the widely studied Crow and elliptic instabilities, alongside a wall-modified long-wavelength-displacement-type instability. The initial optimal amplification mechanisms are found to be weakly influenced by the wall, with the long- and short-wave mechanisms consisting of anti-symmetric amplification at the leading hyperbolic point and symmetric amplification at the trailing hyperbolic point, respectively, as observed by out-of-wall studies previously. The linear growth of the Crow instability is found to be impeded by the wall, and the evolution results in the suppression of both the secondary structure formation and vortex rebound. The linear elliptic mode remains largely uninhibited however, and substantially outgrows the long-wave modes, illustrating the importance of the elliptic instability on the wall-bounded interaction. Both the wall-modified long-wave and elliptic optimal growth modes show substantial amplification in the secondary vortices. At finite perturbation amplitudes, the nonlinear formation of both long- and short-wavelength secondary vortex tongues are shown to play a critical role in the vortex dynamics as the pair strongly interacts with the wall.Vortex-induced vibrations of a flexible cylinder at subcritical Reynolds number.https://zbmath.org/1460.762322021-06-15T18:09:00+00:00"Bourguet, Rémi"https://zbmath.org/authors/?q=ai:bourguet.remiSummary: The flow past a fixed rigid cylinder becomes unsteady beyond a critical Reynolds number close to 47, based on the body diameter and inflow velocity. The present paper explores numerically the vortex-induced vibrations (VIV) that may develop for a flexible cylinder at subcritical Reynolds number \((Re)\), i.e. for \(Re<47\). Flexible-cylinder VIV are found to occur down to \(Re\approx 20\), as previously reported for elastically mounted rigid cylinders. A detailed analysis is carried out for \(Re=25\), in two steps: the system behaviour is examined from the emergence of VIV to the excitation of the first structural modes; and then focus is placed on higher-mode responses. In all cases, a single vibration frequency is excited in each direction. The cross-flow and in-line responses exhibit contrasting magnitudes (peak amplitudes of 0.35 versus 0.01 diameters), as well as distinct symmetry properties and evolutions (e.g. standing/travelling waves). The flow, unsteady once the cylinder vibrates, is found to be temporally and spatially locked with body motion. The synchronization with the cross-flow standing-wave responses is accompanied by the formation of cellular wake patterns, regardless of the modes involved in the vibrations. Body trajectory varies along the span, but dominant orbits can be identified. Despite the low amplitudes of the in-line responses, connections are uncovered between orbit orientation and flow-structure energy transfer, with different trends in each direction.Investigation of passive control of the wake past a thick plate by stability and sensitivity analysis of experimental data.https://zbmath.org/1460.762332021-06-15T18:09:00+00:00"Camarri, S."https://zbmath.org/authors/?q=ai:camarri.simone"Trip, R."https://zbmath.org/authors/?q=ai:trip.r"Fransson, J. H. M."https://zbmath.org/authors/?q=ai:fransson.jens-h-mSummary: In this paper we propose a strategy, entirely relying on available experimental data, to estimate the effect of a small control rod on the frequency of vortex shedding in the wake past a thick perforated plate. The considered values of the flow Reynolds number range between \(Re\simeq 6.6\times 10^3\) and \(Re=5.3\times 10^4\). By means of particle image velocimetry, an experimental database consisting of instantaneous flow fields is collected for different values of suction through the body surface. The strategy proposed here is based on classical stability and sensitivity analysis applied to mean flow fields and on the formulation of an original \textit{ad hoc} model for the mean flow. The mean flow model is obtained by calibrating the closure of the Reynolds averaged Navier-Stokes equations on the basis of the available experimental data through an optimisation algorithm. As a result, it is shown that the predicted control map agrees reasonably well with the equivalent one measured experimentally. Moreover, it is shown that even when turbulence effects are neglected, the stability analysis applied to the mean flow fields provides a reasonable estimation of the vortex shedding frequency, confirming what is known in the literature and extending it up to \(Re=5.3\times 10^4\). It is also shown that, when turbulence is taken into account in the stability analysis using the same closure that is calibrated for the corresponding mean flow model, the prediction of the vortex shedding frequency is systematically improved.Free rings of bouncing droplets: stability and dynamics.https://zbmath.org/1460.762562021-06-15T18:09:00+00:00"Couchman, Miles M. P."https://zbmath.org/authors/?q=ai:couchman.miles-m-p"Bush, John W. M."https://zbmath.org/authors/?q=ai:bush.john-w-mSummary: We present the results of a combined experimental and theoretical investigation of the stability of rings of millimetric droplets bouncing on the surface of a vibrating liquid bath. As the bath's vibrational acceleration is increased progressively, droplet rings are found to destabilize into a rich variety of dynamical states including steady rotational motion, periodic radial or azimuthal oscillations and azimuthal travelling waves. The instability observed is dependent on the ring's initial radius and drop number, and whether the drops are bouncing in- or out-of-phase relative to their neighbours. As the vibrational acceleration is further increased, more exotic dynamics emerges, including quasi-periodic motion and rearrangement into regular polygonal structures. Linear stability analysis and simulation of the rings based on the theoretical model of \textit{M. M. P. Couchman} et al. [ibid. 871, 212--243 (2019; Zbl 1419.76188)] largely reproduce the observed behaviour. We demonstrate that the wave amplitude beneath each drop has a significant influence on the stability of the multi-droplet structures: the system seeks to minimize the mean wave amplitude beneath the drops at impact. Our work provides insight into the complex interactions and collective motions that arise in bouncing-droplet aggregates.Reflection of oscillating internal shear layers: nonlinear corrections.https://zbmath.org/1460.762602021-06-15T18:09:00+00:00"Le Dizès, Stéphane"https://zbmath.org/authors/?q=ai:le-dizes.stephaneSummary: In this work, we perform weakly nonlinear analysis of the reflection process of a thin oscillating wave beam on a non-critical surface in a fluid rotating and stratified along the same vertical axis in the limit of weak viscosity, i.e. small Ekman number \(E\). We assume that the beam has the self-similar viscous structure obtained by \textit{D. W. Moore} and \textit{P. G. Saffman} [Philos. Trans. R. Soc. Lond., Ser. A 264, 597--634 (1969; Zbl 0191.56301)] and \textit{N. H. Thomas} and \textit{T. N. Stevenson} [J. Fluid Mech. 54, 495--506 (1972; Zbl 0247.76095)]. Such a solution describes the viscous internal shear layers of width \(O(E^{1/3})\) generated by a localized oscillating source. We first show that the reflected beam conserves at leading order the self-similar structure of the incident beam and is modified by an \(O(E^{1/6})\) correction with a different self-similar structure. We then analyse the nonlinear interaction of the reflected beam with the incident beam of amplitude \(\varepsilon\) and demonstrate that a second-harmonic beam and localized meanflow correction, both of amplitude \(\varepsilon^2 E^{-1/3}\), are created. We further show that for the purely stratified case (respectively the purely rotating case), a non-localized meanflow correction of amplitude \(\varepsilon^2 E^{-1/6}\) is generated, except when the boundary is horizontal (respectively vertical). In this latter case, the meanflow correction remains localized but exhibits a triple-layer structure with a large \(O(E^{4/9})\) viscous layer.Wake behind contaminated bubbles in a solid-body rotating flow.https://zbmath.org/1460.762462021-06-15T18:09:00+00:00"Rastello, Marie"https://zbmath.org/authors/?q=ai:rastello.marie"Marié, Jean-Louis"https://zbmath.org/authors/?q=ai:marie.jean-louisSummary: A bubble injected into a flow rotating about a horizontal axis comes to an equilibrium location. The drag and lift exerted on the bubble can be measured and the bubble wake visualized [\textit{M. Rastello} et al., ibid. 624, 159--178 (2009; Zbl 1171.76318); \textit{M. Rastello} et al., ibid. 682, 434--459 (2011; Zbl 1241.76045); ibid. 831, 592--617 (2017; Zbl 1421.76235)]. For a contaminated bubble, interface deformation remains limited. The bubble is freely rotating, which results in a complex separated wake, influenced by rotational flow and bubble spinning. The wake is described by analysing the near- and far-wake geometry and behaviour from laser-sheet visualizations, as a function of the relevant non-dimensional numbers: bubble Reynolds number \(Re\), Rossby number \(Ro\), and non-dimensional spinning rate \(\Omega^*\). As the far-wake length increases with \(Re\), it deflects towards the rotation axis of the flow, the deflection angle increasing with \(Re\) and being twice the angle that would occur without deflection. Deflection is stronger for bubbles located close to the rotation axis of the flow (small \(Ro)\). The far wake is more curved than the incoming streamlines. The near wake exhibits three distinct regimes as a function of \(Re\). For \(Re\leqslant 140\), the near wake is structured by the bubble spinning. Its size is related to \(\Omega^*\) and grows faster with \(Re\) than for a stationary sphere in a uniform flow. As the bubble spinning is saturating \((140<Re\leqslant 240)\), these differences vanish and \(Re\) dependences for the two situations becomes comparable. For \(Re>240\), wake instability generates a bubble precession that makes the near wake decrease rapidly for higher \(Re\). These regimes coincide with the changes in the lift coefficients that we have noted in our studies.On the effects of vertical offset and core structure in streamwise-oriented vortex-wing interactions.https://zbmath.org/1460.762052021-06-15T18:09:00+00:00"Barnes, C. J."https://zbmath.org/authors/?q=ai:barnes.c-j"Visbal, M. R."https://zbmath.org/authors/?q=ai:visbal.miguel-r"Huang, P. G."https://zbmath.org/authors/?q=ai:huang.pinganSummary: This article explores the three-dimensional flow structure of a streamwise-oriented vortex incident on a finite aspect-ratio wing. The vertical positioning of the incident vortex relative to the wing is shown to have a significant impact on the unsteady flow structure. A direct impingement of the streamwise vortex produces a spiralling instability in the vortex just upstream of the leading edge, reminiscent of the helical instability modes of a Batchelor vortex. A small negative vertical offset develops a more pronounced instability while a positive vertical offset removes the instability altogether. These differences in vertical position are a consequence of the upstream influence of pressure gradients provided by the wing. Direct impingement or a negative vertical offset subject the vortex to an adverse pressure gradient that leads to a reduced axial velocity and diminished swirl conducive to hydrodynamic instability. Conversely, a positive vertical offset removes instability by placing the streamwise vortex in line with a favourable pressure gradient, thereby enhancing swirl and inhibiting the growth of unstable modes. In every case, the helical instability only occurs when the properties of the incident vortex fall within the instability threshold predicted by linear stability theory. The influence of pressure gradients associated with separation and stall downstream also have the potential to introduce suction-side instabilities for a positive vertical offset. The influence of the wing is more severe for larger vortices and diminishes with vortex size due to weaker interaction and increased viscous stability. Helical instability is not the only possible outcome in a direct impingement. Jet-like vortices and a higher swirl ratio in wake-like vortices can retain stability upon impact, resulting in the laminar vortex splitting over either side of the wing.Spin coating of capillary tubes.https://zbmath.org/1460.762722021-06-15T18:09:00+00:00"Primkulov, B. K."https://zbmath.org/authors/?q=ai:primkulov.bauyrzhan-k"Pahlavan, A. A."https://zbmath.org/authors/?q=ai:pahlavan.amir-a"Bourouiba, L."https://zbmath.org/authors/?q=ai:bourouiba.lydia"Bush, J. W. M."https://zbmath.org/authors/?q=ai:bush.john-w-m"Juanes, R."https://zbmath.org/authors/?q=ai:juanes.rubenSummary: We present the results of a combined experimental and theoretical study of the spin coating of the inner surface of capillary tubes with viscous liquids, and the modified Rayleigh-Plateau instability that arises when the spinning stops. We show that during the spin coating, the thinning of the film is governed by the balance of viscous and centrifugal forces, resulting in the film thickness scaling as \(h\sim t^{-1/2}\). We demonstrate that the method enables us to reach uniform micrometre-scale films on the tube walls. Finally, we discuss potential applications with curable polymers that enable precise control of film geometry and wettability.Multiplicative control problems for nonlinear reaction-diffusion-convection model.https://zbmath.org/1460.352772021-06-15T18:09:00+00:00"Brizitskii, R. V."https://zbmath.org/authors/?q=ai:brizitskii.roman-victorovich|brizitskii.r-v|brizitskii.roman-viktorovich"Saritskaia, Zh. Yu."https://zbmath.org/authors/?q=ai:saritskaia.zh-yuSummary: Global solvability of a boundary value problem for a generalized Boussinesq model is proved in the case, when reaction coefficient depends nonlinearly on concentration of substance. Maximum principle is stated for substance's concentration. Solvability of control problem is proved, when the role of controls is played by diffusion and mass exchange coefficients from the equations and from the boundary conditions of the model. For a considered multiplicative control problem, optimality systems are obtained. On the base of the analysis of these systems for particular reaction coefficients and cost functionals, local stability estimates are deduced for optimal solutions.Acoustic propulsion of a small, bottom-heavy sphere.https://zbmath.org/1460.769862021-06-15T18:09:00+00:00"Nadal, François"https://zbmath.org/authors/?q=ai:nadal.francois"Michelin, Sébastien"https://zbmath.org/authors/?q=ai:michelin.sebastienSummary: We present here a comprehensive derivation for the speed of a small bottom-heavy sphere forced by a transverse acoustic field and thereby establish how density inhomogeneities may play a critical role in acoustic propulsion. The sphere is trapped at the pressure node of a standing wave whose wavelength is much larger than the sphere diameter. Due to its inhomogeneous density, the sphere oscillates in translation and rotation relative to the surrounding fluid. The perturbative flows induced by the sphere's rotation and translation are shown to generate a rectified inertial flow responsible for a net mean force on the sphere that is able to propel the particle within the zero-pressure plane. To avoid an explicit derivation of the streaming flow, the propulsion speed is computed exactly using a suitable version of the Lorentz reciprocal theorem. The propulsion speed is shown to scale as the inverse of the viscosity, the cube of the amplitude of the acoustic field and is a non-trivial function of the acoustic frequency. Interestingly, for some combinations of the constitutive parameters (fluid-to-solid density ratio, moment of inertia and centroid to centre of mass distance), the direction of propulsion is reversed as soon as the frequency of the forcing acoustic field becomes larger than a certain threshold. The results produced by the model are compatible with both the observed phenomenology and the orders of magnitude of the measured velocities.Vortex formation on a pitching aerofoil at high surging amplitudes.https://zbmath.org/1460.762232021-06-15T18:09:00+00:00"Smith, Luke R."https://zbmath.org/authors/?q=ai:smith.luke-r"Jones, Anya R."https://zbmath.org/authors/?q=ai:jones.anya-rSummary: In many applications, conventional aerofoils are subject to a number of simultaneous motions that complicate the prediction of flow separation. The purpose of this work is to evaluate the impact of a large-amplitude free-stream oscillation on the timing of vortex formation for a simultaneously surging and pitching wing. Experimental flow field measurements were obtained on a NACA 0012 aerofoil over a wide range of surge amplitudes \((1.50 \leq \lambda \leq 2.25)\) and reduced frequencies \((0.1 \leq k \leq 0.3)\). Particular attention was paid to how various mechanisms of flow separation, specifically the velocity induced by the trailing wake and unsteady effects in the boundary layer, were impacted by a change in the properties of the surge motion. In the regime where \(k \leq 0.3\), a change in the surge kinematics primarily manifested as a change in the relative strength of the trailing wake. Boundary layer unsteadiness was found to have a negligible influence on the timing of vortex formation in the same flow regime. Thus, the timing of leading-edge vortex formation was well predicted by a combination of an unsteady inviscid flow solver and a quasi-steady treatment of the boundary layer, a promising result for low-order predictions of vortex behaviour in unsteady aerofoil flows.Blow-up criterion and examples of global solutions of forced Navier-Stokes equations.https://zbmath.org/1460.352672021-06-15T18:09:00+00:00"Wu, Di"https://zbmath.org/authors/?q=ai:wu.diSummary: In this paper we first show a blow-up criterion for solutions to the Navier-Stokes equations with a time-independent force by using the profile decomposition method. Based on the orthogonal properties related to the profiles, we give some examples of global solutions to the Navier-Stokes equations with a time-independent force, whose initial data are large.Algebraic disturbance growth by interaction of Orr and lift-up mechanisms.https://zbmath.org/1460.761972021-06-15T18:09:00+00:00"Hack, M. J. Philipp"https://zbmath.org/authors/?q=ai:hack.m-j-philipp"Moin, Parviz"https://zbmath.org/authors/?q=ai:moin.parvizSummary: Algebraic disturbance growth in spatially developing boundary-layer flows is investigated using an optimization approach. The methodology builds on the framework of the parabolized stability equations and avoids some of the limitations associated with adjoint-based schemes. In the Blasius boundary layer, non-parallel effects are shown to significantly enhance the energy gain due to algebraic growth mechanisms. In contrast to parallel flow, the most energetic perturbations have finite frequency and are generated by the simultaneous activity of the Orr and lift-up mechanisms. The highest amplification occurs in a limited region of the parameter space that is characterized by a linear relation between the wavenumber and frequency of the disturbances. The frequency of the most highly amplified perturbations decreases with Reynolds number. Adverse streamwise pressure gradient further enhances the amplification of disturbances while preserving the linear trend between the wavenumber and frequency of the most energetic perturbations.Nonlinear evolution of the centrifugal instability using a semilinear model.https://zbmath.org/1460.763382021-06-15T18:09:00+00:00"Yim, Eunok"https://zbmath.org/authors/?q=ai:yim.eunok"Billant, P."https://zbmath.org/authors/?q=ai:billant.paul"Gallaire, F."https://zbmath.org/authors/?q=ai:gallaire.francoisSummary: We study the nonlinear evolution of the axisymmetric centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semilinear approach. The model consists of two coupled equations: one for the linear evolution of the most unstable perturbation on the axially averaged mean flow and another for the evolution of the mean flow under the effect of the axially averaged Reynolds stresses due to the perturbation. Such a model is similar to the self-consistent model of \textit{V. C. Mantič-Lugo} [``Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake'', Phys. Rev. Lett. 113, No. 8, Article ID 084501, 5 p. (2014; \url{doi:10.1103/PhysRevLett.113.084501})] except that the time averaging is replaced by a spatial averaging. The nonlinear evolutions of the mean flow and the perturbations predicted by this semilinear model are in very good agreement with direct numerical simulations for the Rossby number \(Ro=-4\) and both values of the Reynolds numbers investigated: \(Re=800\) and \(2000\) (based on the initial maximum angular velocity and radius of the vortex). An improved model, taking into account the second-harmonic perturbations, is also considered. The results show that the angular momentum of the mean flow is homogenized towards a centrifugally stable profile via the action of the Reynolds stresses of the fluctuations. The final velocity profile predicted by \textit{R. C. Kloosterziel} et al. [J. Fluid Mech. 583, 379--412 (2007; Zbl 1116.76031)] in the inviscid limit is extended to finite high Reynolds numbers. It is in good agreement with the numerical simulations.Turbulent drag reduction over curved walls.https://zbmath.org/1460.765652021-06-15T18:09:00+00:00"Banchetti, Jacopo"https://zbmath.org/authors/?q=ai:banchetti.jacopo"Luchini, Paolo"https://zbmath.org/authors/?q=ai:luchini.paolo"Quadrio, Maurizio"https://zbmath.org/authors/?q=ai:quadrio.maurizioSummary: This work studies the effects of skin-friction drag reduction in a turbulent flow over a curved wall, with a view to understanding the relationship between the reduction of friction and changes to the total aerodynamic drag. Direct numerical simulations are carried out for an incompressible turbulent flow in a channel where one wall has a small bump; two bump geometries are considered, that produce mildly separated and attached flows. Friction drag reduction is achieved by applying streamwise-travelling waves of spanwise velocity (StTW). The local friction reduction produced by the StTW is found to vary along the curved wall, leading to a global friction reduction that, for the cases studied, is up to 10 \% larger than that obtained in the plane wall case. Moreover, the modified skin friction induces non-negligible changes of pressure drag, which is favourably affected by StTW and globally reduces by up to 10 \%. The net power saving, accounting for the power required to create the StTW, is positive and, for the cases studied, is one half larger than the net saving of the planar case. The study suggests that reducing friction at the surface of a body of complex shape induces further effects, a simplistic evaluation of which might lead to underestimating the total drag reduction.Approximations of stochastic 3D tamed Navier-Stokes equations.https://zbmath.org/1460.352642021-06-15T18:09:00+00:00"Peng, Xuhui"https://zbmath.org/authors/?q=ai:peng.xuhui"Zhang, Rangrang"https://zbmath.org/authors/?q=ai:zhang.rangrangSummary: In this paper, we are concerned with 3D tamed Navier-Stokes equations with periodic boundary conditions, which can be viewed as an approximation of the classical 3D Navier-Stokes equations. We show that the strong solution of 3D tamed Navier-Stokes equations driven by Poisson random measure converges weakly to the strong solution of 3D tamed Navier-Stokes equations driven by Gaussian noise on the state space \(\mathcal{D}([0,T];\mathbb{H}^1)\).Elastohydrodynamic wake and wave resistance.https://zbmath.org/1460.760372021-06-15T18:09:00+00:00"Arutkin, Maxence"https://zbmath.org/authors/?q=ai:arutkin.maxence"Ledesma-Alonso, René"https://zbmath.org/authors/?q=ai:ledesma-alonso.rene"Salez, Thomas"https://zbmath.org/authors/?q=ai:salez.thomas"Raphaël, Élie"https://zbmath.org/authors/?q=ai:raphael.elieSummary: The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. As a continuation of our previous work on viscous wakes [\textit{R. Ledesma-Alonso} et al., ibid. 792, 829--849 (2016; Zbl 1381.76026)], we study theoretically the effects of an external pressure disturbance moving at constant speed along the surface of a thin lubricated elastic sheet. In the comoving frame, the imposed pressure field creates a stationary deformation of the free interface that spatially vanishes in the far-field region. The shape of the wake and the way it decays depend on the speed and size of the external disturbance, as well as the rheological properties of both the elastic and liquid layers. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail.Interfacial pattern selection in defiance of linear growth.https://zbmath.org/1460.760642021-06-15T18:09:00+00:00"Picardo, Jason R."https://zbmath.org/authors/?q=ai:picardo.jason-r"Narayanan, R."https://zbmath.org/authors/?q=ai:narayanan.ramesh|narayanan.rishikesh|narayanan.rajamani-s|narayanan.ram-m|narayanan.radha|narayanan.ranga|narayanan.rajendranSummary: In this study, we revisit Rayleigh's visionary hypothesis [\textit{J. W. Strutt}, ``On the capillary phenomena of jets'', Proc R. Soc. Lond. 29, 196--199 (1879; \url{doi:10.1098/rspl.1879.0015})], that patterns resulting from interfacial instabilities are dominated by the fastest-growing linear mode, as we study nonlinear pattern selection in the context of a linear growth (dispersion) curve that has two peaks of equal height. Such a system is obtained in a physical situation consisting of two liquid layers suspended from a heated ceiling, and exposed to a passive gas. Both interfaces are then susceptible to thermocapillary and Rayleigh-Taylor instabilities, which lead to rupture/pinch off via a subcritical bifurcation. The corresponding mathematical model consists of long-wavelength evolution equations which are amenable to extensive numerical exploration. We find that, despite having equal linear growth rates, either one of the peak-modes can completely dominate the other as a result of nonlinear interactions. Importantly, the dominant peak continues to dictate the pattern even when its growth rate is made slightly smaller, thereby providing a definite counter-example to Rayleigh's conjecture. Although quite complex, the qualitative features of the peak-mode interaction are successfully captured by a low-order three-mode ordinary differential equation model based on truncated Galerkin projection. Far from being governed by simple linear theory, the final pattern is sensitive even to the phase difference between peak-mode perturbations. For sufficiently long domains, this phase effect is shown to result in the emergence of coexisting patterns, wherein each peak-mode dominates in a different region of the domain.A uniqueness result for 3D incompressible fluid-rigid body interaction problem.https://zbmath.org/1460.352962021-06-15T18:09:00+00:00"Muha, Boris"https://zbmath.org/authors/?q=ai:muha.boris"Nečasová, Šárka"https://zbmath.org/authors/?q=ai:necasova.sarka"Radošević, Ana"https://zbmath.org/authors/?q=ai:radosevic.anaSummary: We study a 3D nonlinear moving boundary fluid-structure interaction problem describing the interaction of the fluid flow with a rigid body. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations called Euler equations for the rigid body. The equations are fully coupled via dynamical and kinematic coupling conditions. We consider two different kinds of kinematic coupling conditions: no-slip and slip. In both cases we prove a generalization of the well-known weak-strong uniqueness result for the Navier-Stokes equations to the fluid-rigid body system. More precisely, we prove that weak solutions that additionally satisfy the Prodi-Serrin \(\mathrm{L}^r-\mathrm{L}^s\) condition are unique in the class of Leray-Hopf weak solutions.Film spreading from a miscible drop on a deep liquid layer.https://zbmath.org/1460.760432021-06-15T18:09:00+00:00"Dandekar, Raj"https://zbmath.org/authors/?q=ai:dandekar.raj"Pant, Anurag"https://zbmath.org/authors/?q=ai:pant.anurag"Puthenveettil, Baburaj A."https://zbmath.org/authors/?q=ai:puthenveettil.baburaj-aSummary: We study the spreading of a film from ethanol-water droplets of radii \(0.9\,\text{mm}<r_d<1.1\,\text{mm}\) on the surface of a deep water layer for various concentrations of ethanol in the drop. Since the drop is lighter \((\xi = \rho_l/ \rho_d>1.03)\), it stays at the surface of the water layer during the spreading of the film from the drop; the film is more viscous than the underlying water layer since \(\chi= \mu_l/ \mu _d>0.38\). Inertial forces are not dominant in the spreading since the Reynolds numbers based on the film thickness \(h_f\) are in the range \(0.02<Re_f<1.4\). The spreading is surface-tension-driven since the film capillary numbers are in the range \(0.0005<Ca_f<0.0069\) and the drop Bond numbers are in the range \(0.19<Bo_d<0.56\). We observe that, when the drop is brought in contact with the water surface, capillary waves propagate from the point of contact, followed by a radially expanding, thin circular film of ethanol-water mixture. The film develops instabilities at some radius to form outward-moving fingers at its periphery while it is still expanding, till the expansion stops at a larger radius. The film then retracts, during which time the remaining major part of the drop, which stays at the centre of the expanding film, thins and develops holes and eventually mixes completely with water. The radius of the expanding front of the film scales as \(r_f\sim t^{1/4}\) and shows a dependence on the concentration of ethanol in the drop as well as on \(r_d\), and is independent of the layer height \(h_l\). Using a balance of surface tension and viscous forces within the film, along with a model for the fraction of the drop that forms the thin film, we obtain an expression for the dimensionless film radius \(r_f^* =r_f/r_d\), in the form \(fr_f^*={t_{\mu d}^*}^{1/4}\), where \(t_{\mu d}^* =t/t_{\mu d}\), with the time scale \(t_{\mu d}=\mu_dr_d/\Delta\sigma\) and \(f\) is a function of \(Bo_d\). Similarly, we show that the dimensionless velocity of film spreading, \(Ca_d=u_f\mu_d/\Delta \sigma \), scales as \(4f^4Ca_d={r_f^*}^{-3}\).Radiation of internal waves from groups of surface gravity waves.https://zbmath.org/1460.762772021-06-15T18:09:00+00:00"Haney, S."https://zbmath.org/authors/?q=ai:haney.samuel"Young, W. R."https://zbmath.org/authors/?q=ai:young.walter-r|young.william-rSummary: Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This `Stokes pumping' creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.Control of viscous instability by variation of injection rate in a fluid with time-dependent rheology.https://zbmath.org/1460.762512021-06-15T18:09:00+00:00"Beeson-Jones, Tim H."https://zbmath.org/authors/?q=ai:beeson-jones.tim-h"Woods, Andrew W."https://zbmath.org/authors/?q=ai:woods.andrew-wSummary: Using variational calculus, we investigate the time-dependent injection rate that minimises the growth of the Saffman-Taylor instability when a finite volume of fluid is injected in a finite time, \(t_f\), into a Hele-Shaw cell. We first consider a planar interface, and show that, with a constant viscosity ratio, the constant injection rate is optimal. When the viscosity of the displacing fluid, \(\mu_1(t)\), gradually increases over time, as may occur with a slowly gelling polymer solution, the optimal injection rate, \(U^*(t)\), involves a gradual increase in the flow rate with time. This leads to a smaller initial value of flow rate than the constant injection rate, finishing with a larger value. Such optimisation can lead to a substantial suppression of the instability as compared to the constant injection case if the characteristic gelling time is comparable to \(t_f\). In contrast, for either relatively slow or fast gelling, there is much less benefit in selecting the optimal injection rate, \(U^*(t)\), as compared to the constant injection rate. In the case of a constant injection rate from a point source, \(Q\), then with a constant viscosity ratio the fastest-growing perturbation on the radially spreading front involves axisymmetric modes whose wavenumber increases with time. Approximating the discrete azimuthal modes by a continuous distribution, we find the injection rate that minimises growth, \(Q^*(t)\). We find that there is a critical time for injection, \(t_f^\dagger\), such that if \(t_f>t_f^\dagger\) then \(Q^*(t)\) can be chosen so that the interface is always stable. This critical time emerges from the case with an injection rate given by \(Q^*\sim t^{-1/3}\). As the total injection time is reduced to values \(t_f<t_f^\dagger\), the system becomes progressively more unstable, and the optimal injection rate for an idealised continuous distribution of azimuthal modes asymptotes to a flow rate that increases linearly with time. As for the one-dimensional case, if the viscosity of the injection fluid gradually increases over time, then the optimal injection rate has a smaller initial value but gradually increases to larger values than for the analogous constant viscosity problem. If the displacing fluid features shear-thinning rheology, then the optimal injection rate involves a smaller flow rate at early times, although not as large a reduction as in the Newtonian case, and a larger flow rate at late times, although not as large an increase as in the Newtonian case.Impact of ambient stable stratification on gravity currents propagating over a submerged canopy.https://zbmath.org/1460.761812021-06-15T18:09:00+00:00"Zhou, Jian"https://zbmath.org/authors/?q=ai:zhou.jian|zhou.jian.3|zhou.jian.2|zhou.jian.1"Venayagamoorthy, Subhas K."https://zbmath.org/authors/?q=ai:venayagamoorthy.subhas-karanSummary: The structure and propagation of lock-release bottom gravity currents in a linearly stratified ambient with the presence of a submerged canopy are investigated for the first time using large-eddy simulations. The canopy density (i.e. the solid volume fraction), the strength of ambient stratification and the canopy height are varied to study their respective effects on the gravity current. Both denser canopies and stronger ambient stratification tend to switch the horizontal boundary along which the current propagates from the channel bed towards the canopy top (i.e. the through-to-over flow transition). It is found that the dilution of the current density is enhanced by denser canopies but is weakened by stronger ambient stratification. The non-monotonic relationship between front velocity and canopy density proposed by \textit{J. Zhou} et al. [ibid. 831, 394--417 (2017; Zbl 1460.76562)] in homogeneous environments is also observed in stratified environments. However, as the ambient stratification is strengthened, the present study shows a shift of the turning point (beyond which increasing canopy density leads to faster current propagation) towards sparser canopies, accompanied by a more pronounced recovery of the front velocity. This is the combined action of three stratification-induced mechanisms: the promotion of through-to-over flow transition (less canopy drag), the upward displacement of current nose in a stably stratified water column (more buoyancy gain) and the weakening of current dilution (less buoyancy loss). Under stronger ambient stratification, the propagation of gravity currents shows a lower sensitivity to the retarding effect of the submerged canopy.Shape curvature effects in viscous streaming.https://zbmath.org/1460.769642021-06-15T18:09:00+00:00"Bhosale, Yashraj"https://zbmath.org/authors/?q=ai:bhosale.yashraj"Parthasarathy, Tejaswin"https://zbmath.org/authors/?q=ai:parthasarathy.tejaswin"Gazzola, Mattia"https://zbmath.org/authors/?q=ai:gazzola.mattiaSummary: Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length scales are involved has not been looked into in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analysing the system through the lens of bifurcation theory. Our set-up consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system, and in particular the role of bifurcations in determining the local flow topology, can be then generalized to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.The formation of grounding zone wedges: theory and experiments.https://zbmath.org/1460.760522021-06-15T18:09:00+00:00"Kowal, Katarzyna N."https://zbmath.org/authors/?q=ai:kowal.katarzyna-n"Worster, M. Grae"https://zbmath.org/authors/?q=ai:worster.m-graeSummary: We present a fluid-mechanical explanation of the formation of sedimentary wedges deposited at ice-stream grounding zones. We model both ice and till as layers of viscous fluid spreading under gravity into an inviscid ocean. To test the fundamentals of our theory, we perform a series of laboratory experiments in which we find that a similar wedge of underlying, less viscous fluid accumulates spontaneously around the grounding line. We formulate a simple local condition relating wedge slopes, which determines wedge geometry. It expresses a balance of fluxes of till either side of the grounding line and involves upstream and downstream gradients of till thicknesses as well as the upper surface gradient of the ice. It shows that a wedge will form, that is the upstream till thickness gradients are positive, when the flux of till driven by the glaciostatic pressure gradient of the overlying ice is greater than the flux of till ahead of the grounding zone. This is related to the unloading of the till as the ice sheet crosses the grounding line.Phase separation effects on a partially miscible viscous fingering dynamics.https://zbmath.org/1460.762552021-06-15T18:09:00+00:00"Suzuki, Ryuta X."https://zbmath.org/authors/?q=ai:suzuki.ryuta-x"Nagatsu, Yuichiro"https://zbmath.org/authors/?q=ai:nagatsu.yuichiro"Mishra, Manoranjan"https://zbmath.org/authors/?q=ai:mishra.manoranjan"Ban, Takahiko"https://zbmath.org/authors/?q=ai:ban.takahikoSummary: Classical viscous fingering (VF) instability, the formation of finger-like interfacial patterns, occurs when a less viscous fluid displaces a more viscous one in porous media in immiscible and fully miscible systems. However, the dynamics in partially miscible fluid pairs, exhibiting a phase separation due to its finite solubility into each other, has not been largely understood so far. This study has succeeded in experimentally changing the solution system from immiscible to fully miscible or partially miscible by varying the compositions of the components in an aqueous two-phase system (ATPS) while leaving the viscosities relatively unchanged at room temperature and atmospheric pressure. Here, we have experimentally discovered a new topological transition of VF instability by performing a Hele-Shaw cell experiment using the partially miscible system. The finger formation in the investigated partially miscible system changes to the generation of spontaneously moving multiple droplets. Through additional experimental investigations, we determine that such anomalous VF dynamics is driven by thermodynamic instability such as phase separation due to spinodal decomposition and Korteweg convection induced by compositional gradient during such phase separation. We perform the numerical simulation by coupling hydrodynamics with such chemical thermodynamics and the spontaneously moving droplet dynamics is obtained, which is in good agreement with the experimental investigations of the ATPS. This numerical result strongly supports our claim that the origin of such anomalous VF dynamics is thermodynamic instability.Reference map technique for incompressible fluid-structure interaction.https://zbmath.org/1460.761772021-06-15T18:09:00+00:00"Rycroft, Chris H."https://zbmath.org/authors/?q=ai:rycroft.chris-h"Wu, Chen-Hung"https://zbmath.org/authors/?q=ai:wu.chen-hung"Yu, Yue"https://zbmath.org/authors/?q=ai:yu.yue"Kamrin, Ken"https://zbmath.org/authors/?q=ai:kamrin.kenSummary: We present a general simulation approach for fluid-solid interactions based on the fully Eulerian reference map technique. The approach permits the modelling of one or more finitely deformable continuum solid bodies interacting with a fluid and with each other. A key advantage of this approach is its ease of use, as the solid and fluid are discretized on the same fixed grid, which greatly simplifies the coupling between the phases. We use the method to study a number of illustrative examples involving an incompressible Navier-Stokes fluid interacting with multiple neo-Hookean solids. Our method has several useful features including the ability to model solids with sharp corners and the ability to model actuated solids. The latter permits the simulation of active media such as swimmers, which we demonstrate. The method is validated favourably in the flag-flapping geometry, for which a number of experimental, numerical and analytical studies have been performed. We extend the flapping analysis beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping.A quantitative assessment of viscous asymmetric vortex pair interactions.https://zbmath.org/1460.762112021-06-15T18:09:00+00:00"Folz, Patrick J. R."https://zbmath.org/authors/?q=ai:folz.patrick-j-r"Nomura, Keiko K."https://zbmath.org/authors/?q=ai:nomura.keiko-kSummary: The interactions of two like-signed vortices in viscous fluid are investigated using two-dimensional numerical simulations performed across a range of vortex strength ratios, \(\Lambda= \Gamma_1/ \Gamma_2\leqslant 1\), corresponding to vortices of circulation, \(\Gamma_i\), with differing initial size and/or peak vorticity. In all cases, the vortices evolve by viscous diffusion before undergoing a primary convective interaction, which ultimately results in a single vortex. The post-interaction vortex is quantitatively evaluated in terms of an enhancement factor, \(\varepsilon = \Gamma_{end}/ \Gamma_{2,start}\), which compares its circulation, \(\Gamma_{end}\), to that of the stronger starting vortex, \( \Gamma_{2,start}\). Results are effectively characterized by a mutuality parameter, \(MP\equiv (S/ \omega )_1/(S/ \omega )_2\), where the ratio of induced strain rate, \(S\), to peak vorticity, \( \omega \), for each vortex, \((S/ \omega )_i\), is found to have a critical value, \((S/ \omega )_{cr}\approx 0.135\), above which core detrainment occurs. If \(MP\) is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to \(\varepsilon >1\), i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to \(MP<,=,>1\), respectively. As \(MP\) deviates from unity, \( \varepsilon\) decreases until a critical value, \(MP_{cr}\) is reached, beyond which there is only a one-way interaction; one vortex detrains and is destroyed by the other, which dominates and survives. There is no entrainment and \(\varepsilon \sim 1\), i.e. only a straining out occurs. Although \((S/ \omega)_{cr}\) appears to be independent of Reynolds number, \(MP_{cr}\) shows a dependence. Comparisons are made with available experimental data from \textit{P. Meunier} [Etude expérimentale de deux tourbillons corotatifs. Marseille: Université de Provence-Aix-Marseille I (PhD Thesis) (2001)].Bifurcations in a quasi-two-dimensional Kolmogorov-like flow.https://zbmath.org/1460.761792021-06-15T18:09:00+00:00"Tithof, Jeffrey"https://zbmath.org/authors/?q=ai:tithof.jeffrey"Suri, Balachandra"https://zbmath.org/authors/?q=ai:suri.balachandra"Pallantla, Ravi Kumar"https://zbmath.org/authors/?q=ai:pallantla.ravi-kumar"Grigoriev, Roman O."https://zbmath.org/authors/?q=ai:grigoriev.roman-o"Schatz, Michael F."https://zbmath.org/authors/?q=ai:schatz.michael-fSummary: We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a two-dimensional (2D) model [\textit{B. Suri} et al., ``Velocity profile in a two-layer Kolmogorov-like flow'', Phys. Fluids 26, No. 5, Paper No. 053601, 15 p. (2014; \url{doi:10.1063/1.4873417})], derived from first principles by depth-averaging the full three-dimensional Navier-Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.Global linear stability analysis of jets in cross-flow.https://zbmath.org/1460.763102021-06-15T18:09:00+00:00"Regan, Marc A."https://zbmath.org/authors/?q=ai:regan.marc-a"Mahesh, Krishnan"https://zbmath.org/authors/?q=ai:mahesh.krishnanSummary: The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation [\textit{P. S. Iyer} and the second author, ibid. 790, 275--307 (2016; Zbl 1382.76138)] and experiment [\textit{S. Megerian} et al., ibid. 593, 93--129 (2007; Zbl 1151.76335)]. Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between \(R=2\) to \(R=4\) observed by Megerian [loc. cit.], where \(R=\overline{v}_{jet}/u_\infty\) is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when \(R=2\), whereas downstream shear-layer instabilities are shown to dominate when \(R=4\).Stability of the boundary layer expansion for the 3D plane parallel MHD flow.https://zbmath.org/1460.769252021-06-15T18:09:00+00:00"Ding, Shijin"https://zbmath.org/authors/?q=ai:ding.shijin"Lin, Zhilin"https://zbmath.org/authors/?q=ai:lin.zhilin"Niu, Dongjuan"https://zbmath.org/authors/?q=ai:niu.dongjuanSummary: In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic flow with the no-slip boundary condition of velocity and perfectly conducting walls for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space-time uniform norm \(L^\infty (H^1)\). In addition, similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.
{\copyright 2021 American Institute of Physics}Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks.https://zbmath.org/1460.761652021-06-15T18:09:00+00:00"Daddi-Moussa-Ider, Abdallah"https://zbmath.org/authors/?q=ai:daddi-moussa-ider.abdallah"Sprenger, Alexander R."https://zbmath.org/authors/?q=ai:sprenger.alexander-r"Amarouchene, Yacine"https://zbmath.org/authors/?q=ai:amarouchene.yacine"Salez, Thomas"https://zbmath.org/authors/?q=ai:salez.thomas"Schönecker, Clarissa"https://zbmath.org/authors/?q=ai:schonecker.clarissa"Richter, Thomas"https://zbmath.org/authors/?q=ai:richter.thomas|richter.thomas-michael"Löwen, Hartmut"https://zbmath.org/authors/?q=ai:lowen.hartmut"Menzel, Andreas M."https://zbmath.org/authors/?q=ai:menzel.andreas-mSummary: We investigate theoretically, on the basis of the steady Stokes equations for a viscous incompressible fluid, the flow induced by a stokeslet located on the centre axis of two coaxially positioned rigid disks. The stokeslet is directed along the centre axis. No-slip boundary conditions are assumed to hold at the surfaces of the disks. We perform the calculation of the associated Green's function in large parts analytically, reducing the spatial evaluation of the flow field to one-dimensional integrations amenable to numerical treatment. To this end, we formulate the solution of the hydrodynamic problem for the viscous flow surrounding the two disks as a mixed boundary-value problem, which we then reduce to a system of four dual integral equations. We show the existence of viscous toroidal eddies arising in the fluid domain bounded by the two disks, manifested in the plane containing the centre axis through adjacent counter-rotating eddies. Additionally, we probe the effect of the confining disks on the slow dynamics of a point-like particle by evaluating the hydrodynamic mobility function associated with axial motion. Thereupon, we assess the appropriateness of the commonly employed superposition approximation and discuss its validity and applicability as a function of the geometrical properties of the system. Additionally, we complement our semi-analytical approach by finite-element computer simulations, which reveals a good agreement. Our results may find applications in guiding the design of microparticle-based sensing devices and electrokinetic transport in small-scale capacitors.A body in nonlinear near-wall shear flow: impacts, analysis and comparisons.https://zbmath.org/1460.768552021-06-15T18:09:00+00:00"Palmer, Ryan A."https://zbmath.org/authors/?q=ai:palmer.ryan-a"Smith, Frank T."https://zbmath.org/authors/?q=ai:smith.frank-tSummary: Interaction between body motion and fluid motion is considered inside a nonlinear viscous wall layer, with this unsteady two-way coupling leading to impact of the body on the wall. The present paper involves a reduced system analysis which is shown to be consistent with computational solutions from direct numerical simulations for a basic flat-plate shape presented in an allied paper [the authors, ibid. 915, Paper No. A35, 28 p. (2021; Zbl 07331647)]. The occurrence of impact depends mainly on fluid parameters and initial conditions. The body considered is translating upstream or downstream relative to the wall. Subsequent analysis focusses on the unusual nature of the impact at the leading edge. The impacting flow structure is found to have two nonlinear viscous-inviscid regions lying on either side of a small viscous region. The flow properties in the regions dictate the lift and torque which drive the body towards the wall. Pronounced flow separations are common as the impact then cuts off the mass flux in the gap between the body and the wall; here, a nonlinear similarity solution sheds extra light on the separations. Comparisons are made between results from direct simulations and asymptotics at increased flow rate.Quasi-periodic intermittency in oscillating cylinder flow.https://zbmath.org/1460.762132021-06-15T18:09:00+00:00"Glaz, Bryan"https://zbmath.org/authors/?q=ai:glaz.bryan"Mezić, Igor"https://zbmath.org/authors/?q=ai:mezic.igor"Fonoberova, Maria"https://zbmath.org/authors/?q=ai:fonoberova.maria-a"Loire, Sophie"https://zbmath.org/authors/?q=ai:loire.sophieSummary: Fluid dynamics induced by periodically forced flow around a cylinder is analysed computationally for the case when the forcing frequency is much lower than the von Kármán vortex shedding frequency corresponding to the constant flow velocity condition. By using the Koopman mode decomposition approach, we find a new normal form equation that extends the classical Hopf bifurcation normal form by a time-dependent term for Reynolds numbers close to the Hopf bifurcation value. The normal form describes the dynamics of an observable and features a forcing (control) term that multiplies the state, and is thus a parametric -- i.e. not an additive -- forcing effect. We find that the dynamics of the flow in this regime is characterized by alternating instances of quiescent and strong oscillatory behaviour and that this pattern persists indefinitely. Furthermore, the spectrum of the associated Koopman operator is shown to possess quasi-periodic features. We establish the theoretical underpinnings of this phenomenon -- that we name quasi-periodic intermittency -- using the new normal form model and show that the dynamics is caused by the tendency of the flow to oscillate between the unstable fixed point and the stable limit cycle of the unforced flow. The quasi-periodic intermittency phenomenon is also characterized by positive finite-time Lyapunov exponents that, over a long period of time, asymptotically approach zero.Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach.https://zbmath.org/1460.762542021-06-15T18:09:00+00:00"Ladd, Anthony J. C."https://zbmath.org/authors/?q=ai:ladd.anthony-j-c"Yu, Liang"https://zbmath.org/authors/?q=ai:yu.liang"Szymczak, Piotr"https://zbmath.org/authors/?q=ai:szymczak.piotrSummary: We apply conformal mapping to find the evolving shapes of a dissolving cylinder in a potential flow. Similar equations can be used to describe melting in a flowing liquid phase. Results are compared with microfluidic experiments and numerical simulations. Shapes predicted by conformal mapping agree almost perfectly with experimental observations, after a modest (20\%) rescaling of the time. Finite-volume simulations show that the differences with experiment are connected to the underlying assumptions of the analytical model: potential flow and diffusion-limited dissolution. Approximate solutions of the equations describing the evolution of the shape of the undissolved solid can be derived from a Laurent expansion of the mapping function from the unit circle. Asymptotic expressions for the evolution of the area of the disk and the shift in its centre of mass have been derived at low and high Péclet number. Analytic approximations to the leading-order Laurent coefficients provide additional insight into the mechanisms underlying pore-scale dissolution.Harmonic generation by nonlinear self-interaction of a single internal wave mode.https://zbmath.org/1460.762842021-06-15T18:09:00+00:00"Wunsch, Scott"https://zbmath.org/authors/?q=ai:wunsch.scottSummary: Weakly nonlinear theory is used to explore the dynamics of a single-mode internal tide in variable stratification with rotation. Nonlinear self-interaction in variable stratification generates a perturbation which is forced with double the original frequency and wavenumber. The dynamics of the perturbation is analogous to a forced harmonic oscillator, with the steady-state solution corresponding to a bound harmonic matching the forcing frequency and wavenumber. When the forcing frequency is near a natural frequency of the system, even a small-amplitude (nearly linear) internal tide may induce a significant harmonic response. Idealized stratification profiles are utilized to explore the relevance of this effect for oceanic \(M_2\) baroclinic internal tides, and the results indicate that a rapidly growing harmonic may occur in some environments near the Equator, but is unlikely at higher latitudes. The results are relevant to recent observations of \(M_4\) (harmonic) internal tides in the South China Sea and elsewhere. More generally, nonlinear self-interaction may contribute to the transfer of energy to smaller scales and the dissipation of baroclinic internal tides, especially in equatorial waters.Near- and far-field structure of shallow mixing layers between parallel streams.https://zbmath.org/1460.762072021-06-15T18:09:00+00:00"Cheng, Zhengyang"https://zbmath.org/authors/?q=ai:cheng.zhengyang"Constantinescu, George"https://zbmath.org/authors/?q=ai:constantinescu.georgeSummary: The dynamics of coherent structures forming in a turbulent shallow mixing layer (ML) between two parallel streams advancing in a constant-depth, open channel is investigated using three-dimensional, time-accurate simulations. The large channel length to flow depth ratio \((L_x/H = 400-800)\) allows characterization of the spatial evolution of shallow MLs until the mean velocity difference between the two streams becomes less than 3\% of the initial value at the end of the splitter plate. Away from the ML origin, the dynamics and coherence of the Kelvin-Helmholtz (KH) billows are affected by the destabilizing effect of the mean shear between the two streams and by the stabilizing effect of the bed friction. A linear decay of the entrainment coefficient \(\alpha\) with the bed-friction factor, \(S\), applies only over the region where merging of neighbouring KH billows is still observed (transition to quasi-equilibrium regime). At larger distances from the origin, where the billows are severely stretched in the streamwise direction before being destroyed, the rates of increase of the ML width, \(\delta\), and centreline shift, \(l_{cy}\), become very small and \(\alpha\) is exponentially decaying with increasing \(S\) toward zero (quasi-equilibrium regime). During the initial stages of the quasi-equilibrium regime where the KH vortices are severely stretched, the ML assumes an undulatory shape in horizontal planes. New relationships are proposed to characterize the downstream variation of the non-dimensional ML width and centreline shift over the transition and quasi-equilibrium regimes. During the transition to equilibrium regime, the ML boundary on the fast-stream side remains close to vertical, while that on the slow-stream side becomes strongly tilted. The ML boundary on the slow-stream side becomes again close to vertical once the quasi-equilibrium regime is reached. During the transition to the equilibrium regime, the passage of the KH billows and the generation of streamwise cells of secondary flow generate regions of high instantaneous bed shear stress, such that the region where the erosive capacity of the flow peaks does not correspond to the fast stream. The paper also investigates the effects of flow shallowness and initial velocity ratio between the two streams on the turbulent kinetic energy inside the ML, the depth-averaged lateral momentum fluxes, the passage frequency and size of the KH billows and the wavelength and period of the undulatory motions of the ML during the early stages of the quasi-equilibrium regime.A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality.https://zbmath.org/1460.600042021-06-15T18:09:00+00:00"Akemann, Gernot"https://zbmath.org/authors/?q=ai:akemann.gernot"Byun, Sung-Soo"https://zbmath.org/authors/?q=ai:byun.sung-soo"Kang, Nam-Gyu"https://zbmath.org/authors/?q=ai:kang.nam-gyuSummary: We consider the complex eigenvalues of a Wishart type random matrix model \(X = X_1 X_2^*\), where two rectangular complex Ginibre matrices \(X_{1,2}\) of size \(N \times (N + \nu)\) are correlated through a non-Hermiticity parameter \(\tau \in [0,1]\). For general \(\nu = O(N)\) and \(\tau \), we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian generalisation of the Marchenko-Pastur distribution, which is recovered at maximal correlation \(X_1 = X_2\) when \(\tau = 1\). The square root of the complex Wishart eigenvalues, corresponding to the nonzero complex eigenvalues of the Dirac matrix \(\mathcal{D} = \begin{pmatrix} 0 & X_1 \\ X_2^* & 0 \end{pmatrix},\) are supported in a domain parametrised by a quartic equation. It displays a lemniscate type transition at a critical value \(\tau_c,\) where the interior of the spectrum splits into two connected components. At multi-criticality, we obtain the limiting local kernel given by the edge kernel of the Ginibre ensemble in squared variables. For the global statistics, we apply Frostman's equilibrium problem to the 2D Coulomb gas, whereas the local statistics follows from a saddle point analysis of the kernel of orthogonal Laguerre polynomials in the complex plane.The two-phase Navier-Stokes equations with surface tension in cylindrical domains.https://zbmath.org/1460.352662021-06-15T18:09:00+00:00"Wilke, Mathias"https://zbmath.org/authors/?q=ai:wilke.mathiasSummary: This article is concerned with the well-posedness of a model for the dynamics of two immiscible and incompressible fluids in cylindrical domains, which are separated by a sharp interface, forming a contact angle with the solid wall of the container. We prove that the nonlinear system has a unique strong global solution in the \(L_p\)-sense, provided that the initial data is small. To this end, we show maximal \(L_p\)-regularity of the linearized problem and apply the contraction mapping principle in order to solve the nonlinear problem.