Recent zbMATH articles in MSC 76Ehttps://zbmath.org/atom/cc/76E2021-06-15T18:09:00+00:00WerkzeugLinear and nonlinear double diffusive convection in a couple stress fluid saturated anisotropic porous layer with Soret effect and internal heat source.https://zbmath.org/1460.763012021-06-15T18:09:00+00:00"Shakya, Kanchan"https://zbmath.org/authors/?q=ai:shakya.kanchanThe aim of this paper is to study the Soret effect and an internal heat source with a couple stress fluid. The stability analysis of the Soret and internal heating effect on double diffusive convection in an anisotropic porous layer with a couple stress fluid was performed. To study linear stability analysis according to solving the eigenvalue problem, the author has used the time-dependent periodic disturbance in the horizontal plane.
The effects of the parameters in the governing equations on the onset of double diffusive convection are numerically and graphically determined. The stationary and oscillatory expressions for different values of the parameters, such as the Vadasz number, the couple stress parameter, the solute Rayleigh number, the mechanical anisotropic parameter, and the thermal anisotropic parameter are computed, and the results are depicted in several figures.
For the entire collection see [Zbl 06982489].
Reviewer: Ioan Pop (Cluj-Napoca)Weakly nonlinear analysis of viscous dissipation thermal instability in plane Poiseuille and plane Couette flows.https://zbmath.org/1460.763352021-06-15T18:09:00+00:00"Requilé, Y."https://zbmath.org/authors/?q=ai:requile.y"Hirata, S. C."https://zbmath.org/authors/?q=ai:hirata.silvia-c"Ouarzazi, Mohamed Najib"https://zbmath.org/authors/?q=ai:ouarzazi.mohamed-najib"Barletta, A."https://zbmath.org/authors/?q=ai:barletta.antonioSummary: The weakly nonlinear stability analysis of plane Poiseuille flow (PPF) and plane Couette flow (PCF) when viscous dissipation is taken into account is considered. The impermeable lower boundary is considered adiabatic, while the impermeable upper boundary is isothermal. The linear stability of this problem has been performed by the fourth author and \textit{D. A. Nield} [ibid. 662, 475--492 (2010; Zbl 1205.76113)] for PCF and by the fourth author et al. [ibid. 681, 499--514 (2011; Zbl 1241.76201)] for PPF. These authors found that longitudinal rolls are the preferred mode of convection and the onset of instability is described through the governing parameters \(\Lambda =Ge\, Pe^2\) and \(Pr\), where \(Ge\), \(Pe\) and \(Pr\) are respectively the Gebhart number, the Péclet number and the Prandtl number. The current study focuses on the near-threshold behaviour of longitudinal rolls by using a weakly nonlinear analysis. We determine numerically up to third order the coefficients of the Landau amplitude equation and investigate in detail the influences on bifurcation characteristics of the different nonlinearities present in the system. The results indicate that for both PPF and PCF configurations (i) the inertial terms have no influence on the nonlinear evolution of the disturbance amplitude (ii) the nonlinear thermal advection terms act in favour of pitchfork supercritical bifurcations and (iii) the nonlinearities associated with viscous dissipation promote subcritical bifurcations. The global impact of the different nonlinear contributions indicate that, independently of the Gebhart number, the bifurcation is subcritical if \(Pr<0.25 (Pr<0.77)\) for PPF (PCF). Otherwise, for higher Prandtl number, there exists a particular value of Gebhart number, \(Ge^*\) such that the bifurcation is supercritical (subcritical) if \(Ge<Ge^* (Ge>Ge^*)\). Finally, for both PPF and PCF, the amplitude analysis indicates that, in the supercritical bifurcation regime, the equilibrium amplitude decreases on increasing \(Pr\) and a substantial enhancement (reduction) in heat transfer rate is found for small \(Pr\) (moderate or large \(Pr)\).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.Fully nonlinear mode competition in magnetised Taylor-Couette flow.https://zbmath.org/1460.769192021-06-15T18:09:00+00:00"Ayats, Roger"https://zbmath.org/authors/?q=ai:ayats.roger"Deguchi, Kengo"https://zbmath.org/authors/?q=ai:deguchi.kengo"Mellibovsky, Fernando"https://zbmath.org/authors/?q=ai:mellibovsky.fernando"Meseguer, Álvaro"https://zbmath.org/authors/?q=ai:meseguer.alvaroSummary: We study the nonlinear mode competition of various spiral instabilities in magnetised Taylor-Couette flow. The resulting finite-amplitude mixed-mode solution branches are tracked using the annular-parallelogram periodic domain approach developed by the second author and \textit{S. Altmeyer} [``Fully nonlinear mode competitions of nearly bicritical spiral or Taylor vortices in Taylor-Couette flow'', Phys. Rev. E (3) 87, No. 4, Article ID 043017, 13 p. (2013; \url{doi:10.1103/PhysRevE.87.043017})]. Mode competition phenomena are studied in both the anticyclonic and cyclonic Rayleigh-stable regimes. In the anticyclonic sub-rotation regime, with the inner cylinder rotating faster than the outer, \textit{R. Hollerbach} et al. [``Nonaxisymmetric magnetorotational instabilities in cylindrical Taylor-Couette flow'', Phys. Rev. Lett. 104, No. 4, Article ID 044502, 4 p. (2010; \url{doi:10.1103/PhysRevLett.104.044502})] found competing axisymmetric and non-axisymmetric magneto-rotational linearly unstable modes within the parameter range where experimental investigation is feasible. Here we confirm the existence of mode competition and compute the nonlinear mixed-mode solutions that result from it. In the cyclonic super-rotating regime, with the inner cylinder rotating slower than the outer, the second author [``Linear instability in Rayleigh-stable Taylor-Couette flow'', Phys. Rev. E (3) 95, No. 2, Article ID 021102, 5 p. (2017; \url{doi:10.1103/PhysRevE.95.021102})] recently found a non-axisymmetric purely hydrodynamic linear instability that coexists with the non-axisymmetric magneto-rotational instability discovered a little earlier by \textit{G. Rüdiger} et al. [``Subcritical excitation of the current-driven Tayler instability by super-rotation'', Phys. Fluids 28, No. 1, Paper No. 014105 (2016; \url{doi:10.1063/1.4939270})]. We show that nonlinear interactions of these instabilities give rise to rich pattern-formation phenomena leading to drastic angular momentum transport enhancement/reduction.Rayleigh-Taylor instability by segregation in an evaporating multicomponent microdroplet.https://zbmath.org/1460.763192021-06-15T18:09:00+00:00"Li, Yaxing"https://zbmath.org/authors/?q=ai:li.yaxing"Diddens, Christian"https://zbmath.org/authors/?q=ai:diddens.christian"Segers, Tim"https://zbmath.org/authors/?q=ai:segers.tim"Wijshoff, Herman"https://zbmath.org/authors/?q=ai:wijshoff.herman"Verluis, Michel"https://zbmath.org/authors/?q=ai:versluis.michel"Lohse, Detlef"https://zbmath.org/authors/?q=ai:lohse.detlefSummary: The evaporation of multicomponent droplets is relevant to various applications but challenging to study due to the complex physicochemical dynamics. Recently, \textit{Y. Li} et al. [``Evaporation-triggered segregation of sessile binary droplet'', Phys. Rev. Lett. 120, No. 22, Article ID 224501, 5 p. (2018; \url{doi:10.1103/PhysRevLett.120.224501})] reported evaporation-triggered segregation in 1,2-hexanediol-water binary droplets. In this present work, we added 0.5 wt\% silicone oil to the 1,2-hexanediol-water binary solution. This minute silicone oil concentration dramatically modifies the evaporation process, as it triggers an early extraction of the 1,2-hexanediol from the mixture. Surprisingly, we observe that the segregation of 1,2-hexanediol forms plumes, rising up from the rim of the sessile droplet towards the apex during droplet evaporation. By orientating the droplet upside down, i.e. by studying a pendent droplet, the absence of the plumes indicates that the flow structure is induced by buoyancy, which drives a Rayleigh-Taylor instability (i.e. driven by density differences and gravitational acceleration). From micro particle image velocimetry measurement, we further prove that the segregation of the non-volatile component (1,2-hexanediol) hinders the evaporation near the contact line, which leads to a suppression of the Marangoni flow in this region. Hence, on long time scales, gravitational effects, rather than Marangoni flows, play the dominant role in the flow structure. We compare the measurement of the evaporation rate with the diffusion model of \textit{Y. O. Popov} [``Evaporative deposition patterns: spatial dimensions of the deposit'', Phys. Rev. E (3) 71, No. 3, Article ID 036313, 17 p. (2005; \url{doi:10.1103/PhysRevE.71.036313})], coupled with Raoult's law and the activity coefficient. This comparison indeed confirms that the silicone-oil-triggered segregation of the non-volatile 1,2-hexanediol significantly delays the evaporation. With an extended diffusion model, in which the influence of the segregation has been implemented, the evaporation can be well described.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.Instability of a thin viscous film flowing under an inclined substrate: the emergence and stability of rivulets.https://zbmath.org/1460.760532021-06-15T18:09:00+00:00"Ledda, Pier Giuseppe"https://zbmath.org/authors/?q=ai:ledda.pier-giuseppe"Lerisson, Gaétan"https://zbmath.org/authors/?q=ai:lerisson.gaetan"Balestra, Gioele"https://zbmath.org/authors/?q=ai:balestra.gioele"Gallaire, François"https://zbmath.org/authors/?q=ai:gallaire.francoisSummary: We study the pattern formation of a thin film flowing under an inclined planar substrate. The phenomenon is studied in the context of the Rayleigh-Taylor instability using the lubrication equation. Inspired by experimental observations, we numerically study the thin film response to a streamwise-invariant sinusoidal initial condition. The numerical response shows the emergence of predominant streamwise-aligned structures, modulated along the direction perpendicular to the flow, called rivulets. Oscillations of the thickness profile along the streamwise direction do not grow significantly when the inclination is very large or the liquid layer very thin. However, for small inclinations or thick films, streamwise perturbations grow on rivulets. A secondary stability analysis of one-dimensional and steady rivulets reveals a strong stabilization mechanism for large inclinations or very thin films. The theoretical results are compared with experimental measurements of the streamwise oscillations of the rivulet profile, showing a good agreement. The emergence of rivulets is investigated by studying the impulse response. Both the experimental observation and the numerical simulation show a marked anisotropy favouring streamwise-aligned structures. A weakly nonlinear model is proposed to rationalize the levelling of all but streamwise-aligned structures.Suppression of internal waves by thermohaline staircases.https://zbmath.org/1460.767382021-06-15T18:09:00+00:00"Radko, Timour"https://zbmath.org/authors/?q=ai:radko.timourSummary: This study attempts to quantify and explain the systematic weakening of internal gravity waves in fingering and diffusive thermohaline staircases. The interaction between waves and staircases is explored using a combination of direct numerical simulations (DNS) and an asymptotic multiscale model. The multiscale theory makes it possible to express the wave decay rate \((\lambda_d)\) as a function of its wavenumbers and staircase parameters. We find that the decay rates in fully developed staircases greatly exceed values that can be directly attributed to molecular dissipation. They rapidly increase with increasing wavenumbers, both vertical and horizontal. At the same time, \(\lambda_d\) is only weakly dependent on the thickness of layers in the staircase, the overall density ratio and the diffusivity ratio. The proposed physical mechanism of attenuation emphasizes the significance of eddy diffusion of temperature and salinity, whereas eddy viscosity plays a secondary role in damping internal waves. The asymptotic model is successfully validated by the DNS performed in numerically accessible regimes. We also discuss potential implications of staircase-induced suppression for diapycnal mixing by overturning internal waves in the ocean.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.Instability of the phase transition front during water injection into high-temperature rock.https://zbmath.org/1460.763212021-06-15T18:09:00+00:00"Tsypkin, G. G."https://zbmath.org/authors/?q=ai:tsypkin.george-gSummary: Water injection into a high-temperature geothermal reservoir saturated with superheated vapor is investigated. A solution to the one-dimensional problem in the form of a traveling wave is found. It is shown that there exist two types of solutions which correspond to the boiling of water and the condensation of vapor. In the condensation regime with high initial pressure, vapor ahead of the phase transition front is shown to be in a supercooled state. For moderate or law initial pressure, solutions with condensation and boiling are thermodynamically consistent. Linear stability of the phase transition surface between the water and vapor regions is analyzed. It is shown that the phase transition front moving at constant velocity is always unstable.Evolution of a condensation surface in a porous medium near the instability threshold.https://zbmath.org/1460.763172021-06-15T18:09:00+00:00"Il'ichev, A. T."https://zbmath.org/authors/?q=ai:ilichev.andrej-t"Tsypkin, G. G."https://zbmath.org/authors/?q=ai:tsypkin.george-gSummary: We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov-Petrovskii-Piskunov type equation.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.On the stability of solitary water waves with a point vortex.https://zbmath.org/1460.763422021-06-15T18:09:00+00:00"Varholm, Kristoffer"https://zbmath.org/authors/?q=ai:varholm.kristoffer"Wahlén, Erik"https://zbmath.org/authors/?q=ai:wahlen.erik"Walsh, Samuel"https://zbmath.org/authors/?q=ai:walsh.samuelSummary: This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally orbitally stable. In the process of obtaining this result, we develop a quite general stability/instability theory for bound state solutions of a large class of infinite-dimensional Hamiltonian systems in the presence of symmetry. This is in the spirit of the seminal work of Grillakis, Shatah, and Strauss (GSS) [\textit{M. Grillakis} et al., J. Funct. Anal. 74, 160--197 (1987; Zbl 0656.35122); J. Funct. Anal. 94, No. 2, 308--348 (1990; Zbl 0711.58013)], but with hypotheses that are relaxed in a number of ways necessary for the point vortex system, and for other hydrodynamical applications more broadly. In particular, we are able to allow the Poisson map to have merely dense range, as opposed to being surjective, and to be state-dependent.
As a second application of the general theory, we consider a family of nonlinear dispersive PDEs that includes the generalized Korteweg-de Vries (KdV) and Benjamin-Ono equations. The stability or instability of solitary waves for these systems has been studied extensively, notably by \textit{J. L. Bona} et al. [Proc. R. Soc. Lond., Ser. A 411, 395--412 (1987; Zbl 0648.76005)], who used a modification of the GSS method. We provide a new, more direct proof of these results, as a straightforward consequence of our abstract theory. At the same time, we allow fractional dispersion and obtain a new instability result for fractional KdV.Reduced-order modelling of thick inertial flows around rotating cylinders.https://zbmath.org/1460.760692021-06-15T18:09:00+00:00"Wray, Alexander W."https://zbmath.org/authors/?q=ai:wray.alexander-w"Cimpeanu, Radu"https://zbmath.org/authors/?q=ai:cimpeanu.raduSummary: A new model for the behaviour of a thick, two-dimensional layer of fluid on the surface of a rotating cylinder is presented, incorporating the effects of inertia, rotation, viscosity, gravity and capillarity. Comparisons against direct numerical simulations (DNS) show good accuracy for fluid layers of thickness of the same order as the cylinder radius, even for Reynolds numbers up to \(Re\sim 10\). A rich and complex parameter space is revealed, and is elucidated via a variety of analytical and numerical techniques. At moderate rotation rates and fluid masses, the system exhibits either periodic behaviour or converges to a steady state, with the latter generally being favoured by greater masses and lower rotation rates. These behaviours, and the bifurcation structure of the transitions between them, are examined using a combination of both the low-order model and DNS. Specific attention is dedicated to newly accessible regions of parameter space, including the multiple steady state solutions observed for the same parameter values by \textit{A. V. B. Lopes} et al. [ibid. 835, 540--574 (2018; Zbl 1421.76065)], where the corresponding triple limit point bifurcation structure is recovered by the new low-order model. We also inspect states in which the interface becomes multivalued -- and thus outside the reach of the reduced-order model -- via DNS. This leads to highly nonlinear multivalued periodic structures appearing at moderate thicknesses and relatively large rotation rates. Even much thicker films may eventually reach steady states (following complex early evolution), provided these are maintained by a combination of forces sufficiently large to counteract gravity.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.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.Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: convergence for classical solutions.https://zbmath.org/1460.352942021-06-15T18:09:00+00:00"Luo, Yi-Long"https://zbmath.org/authors/?q=ai:luo.yi-long"Ma, Yangjun"https://zbmath.org/authors/?q=ai:ma.yangjunSummary: In this paper we study the incompressible limit of the compressible inertial Qian-Sheng model for liquid crystal flow. We first derive the uniform energy estimates on the Mach number \(\epsilon\) for both the compressible system and its differential system with respect to time under uniformly in \(\epsilon\) small initial data. Then, based on these uniform estimates, we pass to the limit in the compressible system as \(\epsilon\rightarrow 0\), so that we establish the global classical solution of the incompressible system by compactness arguments. We emphasize that, on global in time existence of the incompressible inertial Qian-Sheng model under small size of initial data, the range of our assumptions on the coefficients are significantly enlarged, comparing to the results of \textit{F. De Anna} and \textit{A. Zarnescu} [J. Differ. Equations 264, No. 2, 1080--1118 (2018; Zbl 1393.35165)]. Moreover, we also obtain the convergence rates associated with \(L^2\)-norm with well-prepared initial data.Nonlinear evolution and secondary instability of steady and unsteady Görtler vortices induced by free-stream vortical disturbances.https://zbmath.org/1460.764082021-06-15T18:09:00+00:00"Xu, Dongdong"https://zbmath.org/authors/?q=ai:xu.dongdong"Zhang, Yongming"https://zbmath.org/authors/?q=ai:zhang.yongming"Wu, Xuesong"https://zbmath.org/authors/?q=ai:wu.xuesongSummary: We study the nonlinear development and secondary instability of steady and unsteady Görtler vortices which are excited by free-stream vortical disturbances (FSVD) in a boundary layer over a concave wall. The focus is on low-frequency (long-wavelength) components of FSVD, to which the boundary layer is most receptive. For simplification, FSVD are modelled by a pair of oblique modes with opposite spanwise wavenumbers \(\pm k_3\), and their intensity is strong enough (but still of low level) that the excitation and evolution of Görtler vortices are nonlinear. For the general case that the Görtler number \(G_\Lambda\) (based on the spanwise wavelength \(\Lambda\) of the disturbances) is \(O(1)\), the formation and evolution of Görtler vortices are governed by the nonlinear unsteady boundary-region equations, supplemented by appropriate upstream and far-field boundary conditions, which characterize the impact of FSVD on the boundary layer. This initial-boundary-value problem is solved numerically. FSVD excite steady and unsteady Görtler vortices, which undergo non-modal growth, modal growth and nonlinear saturation for FSVD of moderate intensity. However, for sufficiently strong FSVD the modal stage is bypassed. Nonlinear interactions cause Görtler vortices to saturate, with the saturated amplitude being independent of FSVD intensity when \(G_\Lambda \neq 0\). The predicted modified mean-flow profiles and structure of Görtler vortices are in excellent agreement with several steady experimental measurements. As the frequency increases, the nonlinearly generated harmonic component \((0,2)\) (which has zero frequency and wavenumber \(2k_3)\) becomes larger, and as a result the Görtler vortices appear almost steady. The secondary instability analysis indicates that Görtler vortices become inviscidly unstable in the presence of FSVD with a high enough intensity. Three types of inviscid unstable modes, referred to as sinuous (odd) modes I, II and varicose (even) modes I, are identified, and their relevance is delineated. The characteristics of dominant unstable modes, including their frequency ranges and eigenfunctions, are in good agreement with experiments. The secondary instability is intermittent when FSVD are unsteady and of low frequency. However, the intermittence diminishes as the frequency increases. The present theoretical framework, which allows for a detailed and integrated description of the key transition processes, from generation, through linear and nonlinear evolution, to the onset of secondary instability, represents a useful step towards predicting the pre-transitional flow and transition itself of the boundary layer over a blade in turbomachinery.Nonlinear stability in three-layer channel flows.https://zbmath.org/1460.760632021-06-15T18:09:00+00:00"Papaefthymiou, E. S."https://zbmath.org/authors/?q=ai:papaefthymiou.e-s"Papageorgiou, D. T."https://zbmath.org/authors/?q=ai:papageorgiou.demetrios-tSummary: The nonlinear stability of viscous, immiscible multilayer flows in plane channels driven both by a pressure gradient and gravity is studied. Three fluid phases are present with two interfaces. Weakly nonlinear models of coupled evolution equations for the interfacial positions are derived and studied for inertialess, stably stratified flows in channels at small inclination angles. Interfacial tension is demoted and high-wavenumber stabilisation enters due to density stratification through second-order dissipation terms rather than the fourth-order ones found for strong interfacial tension. An asymptotic analysis is carried out to demonstrate how these models arise. The governing equations are \(2\times 2\) systems of second-order semi-linear parabolic partial differential equations (PDEs) that can exhibit inertialess instabilities due to interaction between the interfaces. Mathematically this takes place due to a transition of the nonlinear flux function from hyperbolic to elliptic behaviour. The concept of hyperbolic invariant regions, found in nonlinear parabolic systems, is used to analyse this inertialess mechanism and to derive a transition criterion to predict the large-time nonlinear state of the system. The criterion is shown to predict nonlinear stability or instability of flows that are stable initially, i.e. the initial nonlinear fluxes are hyperbolic. Stability requires the hyperbolicity to persist at large times, whereas instability sets in when ellipticity is encountered as the system evolves. In the former case the solution decays asymptotically to its uniform base state, while in the latter case nonlinear travelling waves can emerge that could not be predicted by a linear stability analysis. The nonlinear analysis predicts threshold initial disturbances above which instability emerges.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.Bidispersive thermal convection with relatively large macropores.https://zbmath.org/1460.767492021-06-15T18:09:00+00:00"Gentile, M."https://zbmath.org/authors/?q=ai:gentile.maurizio|gentile.marc"Straughan, B."https://zbmath.org/authors/?q=ai:straughan.brianSummary: We derive linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature when Darcy theory is employed in the micropores whereas Brinkman theory is utilized in the macropores. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. The coincidence of the linear and nonlinear stability boundaries is established under general thermal boundary conditions.Instability of a thin viscous film flowing under an inclined substrate: steady patterns.https://zbmath.org/1460.760542021-06-15T18:09:00+00:00"Lerisson, Gaétan"https://zbmath.org/authors/?q=ai:lerisson.gaetan"Ledda, Pier Giuseppe"https://zbmath.org/authors/?q=ai:ledda.pier-giuseppe"Balestra, Gioele"https://zbmath.org/authors/?q=ai:balestra.gioele"Gallaire, François"https://zbmath.org/authors/?q=ai:gallaire.francoisSummary: The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a stationary localized perturbation, a front develops that we predict with the group velocity of the unstable wave packet. We compare our experimental measurements with numerical solutions of the nonlinear lubrication equation with complete curvature. Streamwise structures dominate and saturate after some distance. We recover their profile with a one-dimensional lubrication equation suitably modified to ensure an invariant profile along the streamwise direction and compare them with the solution of a purely two-dimensional pendent drop, showing overall a very good agreement. Finally, those different profiles agree also with a two-dimensional simulation of the Stokes equations.Bifurcation diagram of one generalized integrable model of vortex dynamics.https://zbmath.org/1460.763412021-06-15T18:09:00+00:00"Ryabov, Pavel E."https://zbmath.org/authors/?q=ai:ryabov.p-e"Shadrin, Artemiy A."https://zbmath.org/authors/?q=ai:shadrin.artemiy-aSummary: This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics of two point vortices enclosed in a harmonic trap in a Bose-Einstein condensate and the dynamics of two point vortices bounded by a circular region in an ideal fluid. New bifurcation diagrams are obtained and three-into-one and four-into-one tori bifurcations are observed for some values of the physical parameters of the model. The presence of such bifurcations in the integrable model of vortex dynamics with positive intensities indicates a complex transition and a connection between bifurcation diagrams in both limiting cases. In this paper, we analytically derive equations that define the parametric family of bifurcation diagrams of the generalized model, including bifurcation diagrams of the specified limiting cases. The dynamics of the bifurcation diagram in a general case is shown using its implicit parameterization. A stable bifurcation diagram, related to the problem of dynamics of two vortices bounded by a circular region in an ideal fluid, is observed for particular parameters' values.A Ginzburg-Landau model for linear global modes in open shear flows.https://zbmath.org/1460.763842021-06-15T18:09:00+00:00"Gupta, Vikrant"https://zbmath.org/authors/?q=ai:gupta.vikrant"He, Wei"https://zbmath.org/authors/?q=ai:he.wei.2|he.wei|he.wei.1|he.wei.3"Wan, Minping"https://zbmath.org/authors/?q=ai:wan.minping"Chen, Shiyi"https://zbmath.org/authors/?q=ai:chen.shiyi"Li, Larry K. B."https://zbmath.org/authors/?q=ai:li.larry-k-bSummary: The Ginzburg-Landau equation (GLE) can phenomenologically model several key features of non-equilibrium systems including those in fluid mechanics. Its validity in real flows, however, remains questionable. Here, we show that the linear GLE can be formulated such that it has the same Wentzel-Kramers-Brillouin (WKB) approximation as for the linear global stability problem in open shear flows. We use the GLE to model the linear global modes of three different wakes and find that it can accurately capture the linear growth rate and frequency to first order in the WKB approximation. Furthermore, we find that it can also provide the shapes of the direct and adjoint eigenvectors and the regions of maximal structural sensitivity. The proposed model requires only the basic flow as input, but gives robust predictions and is computationally inexpensive. As well as opening up new possibilities for GLE-based control strategies, the proposed model makes accurate stability calculations possible, even for some computationally intractable open shear flows.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 \(R=4\).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.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.Electromagnetically driven flow of electrolyte in a thin annular layer: axisymmetric solutions.https://zbmath.org/1460.769392021-06-15T18:09:00+00:00"Suslov, Sergey A."https://zbmath.org/authors/?q=ai:suslov.sergey-a"Pérez-Barrera, James"https://zbmath.org/authors/?q=ai:perez-barrera.james"Cuevas, Sergio"https://zbmath.org/authors/?q=ai:cuevas.sergioSummary: Experimental observations of an azimuthal electrolyte flow driven by Lorentz force in a thin annular fluid layer placed on top of a magnet show that it develops a robust vortical system near the outer cylindrical wall. It appears to be a result of instabilities developing on a background of steady axisymmetric flow. Therefore, the goal of this paper is to establish a scene for a future comprehensive stability analysis of such a flow. We discuss popular depth-averaged and quasi-two-dimensional approximate solutions that take advantage of the thin-layer assumption first, and argue that they cannot lead to the observed flow patterns. Thus, three-dimensional toroidal flows are considered. Their similarities to various other well-studied rotating flow configurations are outlined, but no close match is found. Multiple axisymmetric solutions are detected numerically for the same governing parameters, indicating the possibility of subcritical bifurcations, namely type 1, consisting of a single torus, and type 2, developing a second counter-rotating toroidal flow near the outer cylinder. It is suggested that the transition between these two axisymmetric solutions is likely to be caused by the centrifugal instability, while the shear-type instability of the type 2 solution may be responsible for the observed vortex structures. However, a dedicated stability analysis which is currently underway and will be reported in a separate publication is required to confirm these hypotheses.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.Analytical model of nonlinear evolution of single-mode Rayleigh-Taylor instability in cylindrical geometry.https://zbmath.org/1460.763392021-06-15T18:09:00+00:00"Zhao, Zhiye"https://zbmath.org/authors/?q=ai:zhao.zhiye"Wang, Pei"https://zbmath.org/authors/?q=ai:wang.pei"Liu, Nansheng"https://zbmath.org/authors/?q=ai:liu.nansheng"Lu, Xiyun"https://zbmath.org/authors/?q=ai:lu.xiyunSummary: We present an analytical model of nonlinear evolution of two-dimensional single-mode Rayleigh-Taylor instability (RTI) in cylindrical geometry at arbitrary Atwood number for the first time. Our model covers a full scenario of bubble evolution from the earlier exponential growth to the nonlinear regime with the bubbles growing in time as \(\frac{1}{2} a_bt^2\) for cylindrical RTI, other than as \(V_bt\) for planar RTI, where \(a_b\) and \(V_b\) are the bubble acceleration and velocity, respectively. It is found that from this model the saturating acceleration \(a_b\) is formulated as a simplified function of the external acceleration, Atwood number and number of perturbation waves. This model's predictions are in good agreement with data from direct numerical simulations.Aspect ratio effect on electroconvection in a suspended liquid crystal film with a rectangular boundary.https://zbmath.org/1460.760342021-06-15T18:09:00+00:00"Guo, Xuefei"https://zbmath.org/authors/?q=ai:guo.xuefei"Le, Yongkang"https://zbmath.org/authors/?q=ai:le.yongkang"Cao, Bochao"https://zbmath.org/authors/?q=ai:cao.bochaoSummary: The aspect ratio dependence of the electroconvection phenomenon in a suspended nematic liquid crystal film with a rectangular boundary is investigated. Two-dimensional global stability analysis is carried out on the coupled electrohydrodynamic system to calculate the instability boundary of the phenomenon for different aspect ratios. The calculated critical \(R\) number (Rayleigh-like number) shows a rapidly decreasing trend in the low-aspect-ratio region (roughly \(\gamma <1.5\), where \(\gamma\) is defined as the aspect ratio of the film), and then the variation becomes slow until \(\gamma \approx 2.5\), where the critical \(R\) number starts to increase slightly. Convective patterns of liquid films with different aspect ratios are also obtained from stability analysis and validated by particle image velocimetry measurement.Stability of temperature modulated convection in a vertical fluid layer.https://zbmath.org/1460.763022021-06-15T18:09:00+00:00"Singh, Jitender"https://zbmath.org/authors/?q=ai:singh.jitender"Bajaj, Renu"https://zbmath.org/authors/?q=ai:bajaj.renuSummary: We investigate the effect of time periodic oscillations of the boundary temperatures on the onset of natural convection in a fluid layer bounded by two vertical planes. The fluids with Prandtl number up to 12.5 are considered. For these fluids, the mode of instability with constant temperature gradient is the steady convection mode. The parametric instability of the modulated fluid layer is found to appear either in the form of harmonic oscillations or in the form of subharmonic oscillations, depending upon the modulation parameters and the Prandtl number. The transition of the instability between harmonic and subharmonic oscillations occurs via an intermediate bicritical state in which the fluid layer oscillates with coexistence of distinct harmonic and subharmonic wave numbers. A proper tuning of the modulation parameters offers a good control over the mode of instability in the fluid layer.Calming the waves, not the storm: measuring the Kelvin-Helmholtz instability in a tangential magnetic field.https://zbmath.org/1460.763252021-06-15T18:09:00+00:00"Kögel, Armin"https://zbmath.org/authors/?q=ai:kogel.armin"Völkel, Alexandra"https://zbmath.org/authors/?q=ai:volkel.alexandra"Richter, Reinhard"https://zbmath.org/authors/?q=ai:richter.reinhard-j|richter.reinhardSummary: We measure the Kelvin-Helmholtz instability in between a layer of a diamagnetic fluid flowing in a channel and a layer of ferrofluid resting on top. When the diamagnetic fluid exceeds a critical flow velocity the interface in between both fluids becomes unstable and waves develop. It has been predicted by \textit{G. G. Sutyrin} and \textit{N. G. Taktarov} [J. Appl. Math. Mech. 39, 520--524 (1975; Zbl 0326.76052); translation from Prikl. Mat. Mekh. 39, 547--550 (1975)] that a homogeneous magnetic field, oriented horizontally, stabilizes the liquid interface. To test this prediction we apply in a closed flow channel a local periodic perturbation of the interface by magnetic or mechanic means. From the measured growth and decay rates of the interface undulations we determine the critical flow velocity for various driving frequencies and applied magnetic fields. In this way we confirm quantitatively the stabilizing effect of the horizontal field. Moreover we measure the dispersion relation of the interfacial waves.Stability of a growing cylindrical blob.https://zbmath.org/1460.763182021-06-15T18:09:00+00:00"Krechetnikov, R."https://zbmath.org/authors/?q=ai:krechetnikov.rouslan|krechetnikov.r-vSummary: The stability of an accelerating cylindrical blob of a time-varying radius is considered with the goals of understanding the effects of time dependence of the underlying base state on a Rayleigh-Plateau instability as well as of evaluating a contribution due to a lateral acceleration of the blob, treated as a perturbation here. All of the key processes contributing to instability development are dissected, with analytical analyses of the exact incompressible inviscid potential flow formulation. Herein, without invoking the `frozen' base state assumption, the entire time interval of the evolution of a perturbation is explored, discerning physical mechanisms at each stage of development. It transpires that the stability picture proves to be cardinally different from Rayleigh's standard analysis.Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow.https://zbmath.org/1460.763312021-06-15T18:09:00+00:00"Lopez, Juan M."https://zbmath.org/authors/?q=ai:lopez.juan-manuel.1|lopez.juan-m|lopez.juan-manuel"Gutierrez-Castillo, Paloma"https://zbmath.org/authors/?q=ai:gutierrez-castillo.palomaSummary: The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.Mineral dissolution and wormholing from a pore-scale perspective.https://zbmath.org/1460.767682021-06-15T18:09:00+00:00"Soulaine, Cyprien"https://zbmath.org/authors/?q=ai:soulaine.cyprien"Roman, Sophie"https://zbmath.org/authors/?q=ai:roman.sophie"Kovscek, Anthony"https://zbmath.org/authors/?q=ai:kovscek.anthony-r"Tchelepi, Hamdi A."https://zbmath.org/authors/?q=ai:tchelepi.hamdi-aSummary: A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy-Brinkman-Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian-Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.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.Shear-induced instabilities of flows through submerged vegetation.https://zbmath.org/1460.763142021-06-15T18:09:00+00:00"Wong, Clint Y. H."https://zbmath.org/authors/?q=ai:wong.clint-y-h"Trinh, Philippe H."https://zbmath.org/authors/?q=ai:trinh.philippe-h"Chapman, S. Jonathan"https://zbmath.org/authors/?q=ai:chapman.stephen-jonathanSummary: We consider the instabilities of flows through a submerged canopy and show how the full governing equations of the fluid-structure interactions can be reduced to a compact framework that captures many key features of vegetative flow. First, by modelling the canopy as a collection of homogeneous elastic beams, we predict the steady configuration of the plants in response to a unidirectional flow. This treatment couples the beam equations in the canopy to the fluid momentum equations. Subsequently, a linear stability analysis suggests new insights into the development of instabilities at the surface of the vegetative region. In particular, we show that shear at the top of the canopy is a dominant factor in determining the onset of instabilities known as monami. Based on numerical and asymptotic analysis of the quadratic eigenvalue problem, the system is shown to be stable if the canopy is sufficiently sparse.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.Consistent formulations for stability of fluid flow through deformable channels and tubes.https://zbmath.org/1460.769572021-06-15T18:09:00+00:00"Patne, Ramkarn"https://zbmath.org/authors/?q=ai:patne.ramkarn"Giribabu, D."https://zbmath.org/authors/?q=ai:giribabu.d"Shankar, V."https://zbmath.org/authors/?q=ai:shankar.venkatesh|shankar.viswanathan|shankar.v-s-vijaya|shankar.vijaya|shankar.varunSummary: In the formulation of stability of fluid flow through channels and tubes with deformable walls, while the fluid is naturally treated in an Eulerian framework, the solid can be treated either in a Lagrangian or Eulerian framework. A consistent formulation, then, should yield results that are independent of the chosen framework. Previous studies have demonstrated this consistency for the stability of plane Couette flow past a deformable solid layer modelled as a neo-Hookean solid, in the creeping-flow limit. However, a similar exercise carried out in the creeping-flow limit for the stability of pressure-driven flow in a neo-Hookean tube shows that while the flow is stable in the Lagrangian formulation, it is unstable in the existing Eulerian formulation. The present work resolves this discrepancy by presenting consistent Lagrangian and Eulerian frameworks for performing stability analyses in flow through deformable tubes and channels. The resolution is achieved by making important modifications to the Lagrangian formulation to make it fundamentally consistent, as well as by proposing a proper formulation for the neo-Hookean constitutive relation in the Eulerian framework. In the neo-Hookean model, the Cauchy stress tensor in the solid is proportional to the Finger tensor. We demonstrate that the neo-Hookean constitutive model within the Eulerian formulation used in the previous studies is a special case of the Mooney-Rivlin solid, with the Cauchy stress tensor being proportional to the inverse of the Finger tensor unlike in a true neo-Hookean solid. Remarkably, for plane Couette flow subjected to two-dimensional perturbations, there is perfect agreement between the results obtained using earlier Eulerian and Lagrangian formulations despite the crucial difference in the constitutive relation owing to the rather simple kinematics of the base state. However, the consequences are drastic for pressure-driven flow in a tube even for axisymmetric disturbances. We propose a consistent neo-Hookean constitutive relation in the Eulerian framework, which yields results that are in perfect agreement with the results from the Lagrangian formulation for both plane Couette and tube flows at arbitrary Reynolds number. The present study thus provides an unambiguous formulation for carrying out stability analyses in flow through deformable channels and tubes. We further show that unlike plane Couette flow and Hagen-Poiseuille flow in rigid-walled conduits where there is a remarkable similarity in the linear stability characteristics between these two flows, the stability behaviour for these two flows is very different when the walls are deformable. The instability of plane Couette flow past a deformable wall is very robust and is not sensitive to the constitutive nature of the solid, but the stability of pressure-driven flow in a deformable tube is rather sensitive to the constitutive nature of the deformable solid, especially at low Reynolds number.Dynamics of strong swept-shock/turbulent-boundary-layer interactions.https://zbmath.org/1460.764462021-06-15T18:09:00+00:00"Adler, Michael C."https://zbmath.org/authors/?q=ai:adler.michael-c"Gaitonde, Datta V."https://zbmath.org/authors/?q=ai:gaitonde.datta-vSummary: The mechanisms of unsteadiness in nominally two-dimensional (2-D) shock/turbulent-boundary-layer interactions (STBLIs) cannot be directly extended to three-dimensional (3-D) STBLIs, because of differences in interaction structure; swept 3-D interactions, including the sharp-fin and swept-compression-ramp configurations, are of particular interest in this work. Complications arise from the observation that the separation length employed to scale low-frequency unsteadiness in 2-D (spanwise homogeneous) interactions is not a global property of 3-D (swept) interactions, due to the quasi-conical symmetry of the latter. Also, flow separation in 3-D interactions is topologically different, in that closure of the primary separation cannot occur without breaking the quasi-conical symmetry of the interaction -- consequently, the unsteady properties of the separation are different. To address these points, large-eddy simulations are performed to assess unsteadiness in 3-D interactions, with the aim of understanding key differences relative to analogous 2-D interactions, the former of which have received less attention in the literature. The mechanism underlying the prominent band of low-frequency unsteadiness (two decades below the characteristic boundary-layer frequency) is shown to be significantly muted in swept interactions. An interesting scaling for the band of mid-frequency unsteadiness is uncovered (at least one decade below the characteristic boundary-layer frequency). This is a consequence of the observed connection between coherent fluctuations in the separated shear layer and local mean-flow gradients, indicating a mix between competing 2-D and 3-D free-interaction scaling laws. In contrast, high-frequency fluctuations largely retain the 2-D scaling introduced by the incoming turbulent boundary layer. The spatial structure of the mid-frequency coherence in 3-D STBLIs is isolated, revealing the significant influence of these convective coherent structures on shock rippling/corrugation, as well as a spanwise dependence of coherence size consistent with the 3-D mean-flow similarity scaling. Finally, the dynamic linear response of a representative 3-D interaction is compared to that of a representative 2-D interaction; the absolute instability present in the 2-D interaction is not present in the 3-D interaction. The coincident absence of both the absolute instability and associated band of low-frequency unsteadiness in 3-D STBLIs underscores the significance of this absolute instability in facilitating low-frequency unsteadiness in 2-D interactions.Nonlinear response of swirling premixed flames to helical flow disturbances.https://zbmath.org/1460.800022021-06-15T18:09:00+00:00"Acharya, Vishal"https://zbmath.org/authors/?q=ai:acharya.vishal"Lieuwen, Timothy"https://zbmath.org/authors/?q=ai:lieuwen.timothy-cSummary: This paper considers the relationship between nonlinearly interacting helical flow disturbances and flame area response in a swirling premixed flame. The present study was performed to determine whether there are nonlinear mechanisms through which helical modes \((m_u\neq 0)\) can lead to non-zero unsteady heat release rate oscillations. The results show that for single frequency content (at \(\omega_0)\), helical modes excite unsteady heat release rate response of \(O( \epsilon^3)\) and that two-frequency excitation (e.g. at \(\omega_0\) and \(2 \omega_0)\), leads to a response of \(O( \epsilon^2)\) at \(\omega_0\). There are two mechanisms through which this can occur: First, helical flow disturbances can distort the time-averaged flame shape to have an azimuthal component that matches that of the incident disturbance, \( \exp (im_u \theta )\). Second, multiple helical modes can nonlinearly interact to cause axisymmetric unsteady flame wrinkling. The paper derives the various modal contributions in the incident velocity disturbance that satisfy these criteria. These results suggest that it is only the \(m_u=0\) mode which controls the linear dynamics (e.g. instability inception conditions) of these flames (where \(\epsilon \ll 1)\), but that their nonlinear dynamics is also controlled by the \(m_u\neq 0\) helical modes.Linear instability analysis of low-\(Re\) incompressible flow over a long rectangular finite-span open cavity.https://zbmath.org/1460.763912021-06-15T18:09:00+00:00"Liu, Qiong"https://zbmath.org/authors/?q=ai:liu.qiong"Gómez, Francisco"https://zbmath.org/authors/?q=ai:gomez.francisco-j"Theofilis, Vassilios"https://zbmath.org/authors/?q=ai:theofilis.vassiliosSummary: TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions \(L\)~:~\(D\)~:~\(W\)\(=\) 6~:~1~:~2 to unsteadiness. The steady laminar three-dimensional flow loses stability at \(\mathit{Re}_{D,cr}1080\) as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.Thermal instability of a micropolar fluid layer with temperature-dependent viscosity.https://zbmath.org/1460.762992021-06-15T18:09:00+00:00"Dhiman, Joginder Singh"https://zbmath.org/authors/?q=ai:dhiman.joginder-singh"Sharma, Nivedita"https://zbmath.org/authors/?q=ai:sharma.niveditaThe authors studied the effect of temperature-dependent viscosity on the onset of thermal convection in micropolar fluid layer heated from below. The validity of principle of exchange of stabilities is investigated for this more general problem by conjugate eigen functions. A single-term Galerkin method is used to find general expressions and dynamically free boundaries. The value of the critical Rayleigh numbers for each condition is computed numerically for the case of stationary convection. The effects of micro-rotation parameters and the viscosity variation parameter on critical Rayleigh numbers are computed numerically.
Reviewer: K. N. Shukla (Gurgaon)Linear stability of Hill's vortex to axisymmetric perturbations.https://zbmath.org/1460.763042021-06-15T18:09:00+00:00"Protas, Bartosz"https://zbmath.org/authors/?q=ai:protas.bartosz"Elcrat, Alan"https://zbmath.org/authors/?q=ai:elcrat.alan-rSummary: We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a three-dimensional axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex under the constraint of constant circulation. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a highly accurate spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally stable eigenvalues. By considering a family of suitably regularized (smoothed) eigenvalue problems solved with a range of numerical resolutions, we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localized at the front and rear stagnation points. These findings thus refine the results of the classical analysis by \textit{H. K. Moffatt} and \textit{D. W. Moore} [ibid. 87, 749--760 (1978; Zbl 0387.76033)].Intermittency route to self-excited chaotic thermoacoustic oscillations.https://zbmath.org/1460.766982021-06-15T18:09:00+00:00"Guan, Yu"https://zbmath.org/authors/?q=ai:guan.yu"Gupta, Vikrant"https://zbmath.org/authors/?q=ai:gupta.vikrant"Li, Larry K. B."https://zbmath.org/authors/?q=ai:li.larry-k-bSummary: In nonlinear dynamics, there are three classic routes to chaos, namely the period-doubling route, the Ruelle-Takens-Newhouse route and the intermittency route. The first two routes have previously been observed in self-excited thermoacoustic systems, but the third has not. In this experimental study, we present evidence of the intermittency route to chaos in the self-excited regime of a prototypical thermoacoustic system -- a laminar flame-driven Rijke tube. We identify the intermittency to be of type II from the Pomeau-Manneville scenario through an analysis of (i) the probability distribution of the quiescent epochs between successive bursts of chaos, (ii) the first return map, and (iii) the recurrence plot. By establishing the last of the three classic routes to chaos, this study strengthens the universality of how strange attractors arise in self-excited thermoacoustic systems, paving the way for the application of generic suppression strategies based on chaos control.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.The first 180 Lyapunov exponents for two-dimensional complex Ginzburg-Landau-type equation.https://zbmath.org/1460.763002021-06-15T18:09:00+00:00"Kozitskiy, S. B."https://zbmath.org/authors/?q=ai:kozitskii.s-bSummary: Dynamic patterns of three-dimensional double-diffusive convection in horizontally infinite liquid layer at large Rayleigh numbers have been simulated with the use of the previously derived system of complex Ginzburg-Landau-type amplitude equations valid in the neighborhoods of Hopf bifurcation points. For the special case of convection the first 180 Lyapunov exponents of the system have been calculated and 164 of them are positive. The spatial autocorrelation function is shown to be localized. Thus the system exhibits spatiotemporal chaos.Anisotropic micropolar fluids subject to a uniform microtorque: the unstable case.https://zbmath.org/1460.763342021-06-15T18:09:00+00:00"Remond-Tiedrez, Antoine"https://zbmath.org/authors/?q=ai:remond-tiedrez.antoine"Tice, Ian"https://zbmath.org/authors/?q=ai:tice.ianSummary: We study a three-dimensional, incompressible, viscous, micropolar fluid with anisotropic microstructure on a periodic domain. Subject to a uniform microtorque, this system admits a unique nontrivial equilibrium. We prove that this equilibrium is nonlinearly unstable. Our proof relies on a nonlinear bootstrap instability argument which uses control of higher-order norms to identify the instability at the \(L^2\) level.A four-zone model and nonlinear dynamic analysis of solution multiplicity of buoyancy ventilation in underground building.https://zbmath.org/1460.766752021-06-15T18:09:00+00:00"Wang, Yuxing"https://zbmath.org/authors/?q=ai:wang.yuxing"Wei, Chunyu"https://zbmath.org/authors/?q=ai:wei.chunyuSummary: The solution multiplicity of natural ventilation in buildings is very important to personnel safety and ventilation design. In this paper, a four-zone model of buoyancy ventilation in typical underground building is proposed. The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of three scenarios and obtain the criterions to determine the stability and existence of solutions for two scenarios. According to these criterions, the multiple steady states of buoyancy ventilation in any four-zone underground buildings for different stack height ratios and the strength ratios of the heat sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in underground buildings. Compared with the two-zone model in [\textit{Y. Liu} et al., ``Nonlinear dynamic analysis of solution multiplicity of buoyancy ventilation in a typical underground structure'', Build. Environ. 171, Article ID 106674 (2020; \url{doi:10.1016/j.buildenv.2020.106674})], the results of the proposed four-zone model are more consistent with CFD results in [\textit{Y. Liu} et al., ``The formation of multi-steady-states of buoyancy ventilation in underground building'', Tunnelling and Underground Space Technol. 82, 613--626 (2018; \url{doi:10.1016/j.tust.2018.09.008})]. In addition, the results of proposed four-zone model are more specific and more detailed in the unstable equilibrium point interval. We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.Electrostatic forcing of thin leaky dielectric films under periodic and steady fields.https://zbmath.org/1460.760652021-06-15T18:09:00+00:00"Pillai, Dipin S."https://zbmath.org/authors/?q=ai:pillai.dipin-s"Narayanan, R."https://zbmath.org/authors/?q=ai:narayanan.rishikesh|narayanan.ramesh|narayanan.radha|narayanan.rajamani-s|narayanan.ranga|narayanan.ram-m|narayanan.rajendranSummary: The linear and nonlinear dynamics of an interface separating a thin liquid film and a hydrodynamically passive ambient medium, subject to normal electrostatic forcing, are investigated. A reduced-order model is developed for the case where both fluids are taken to be leaky dielectrics (LD). Cases of time periodic as well as steady forcing are studied. In the former case, an important result is the elucidation of two forms of resonant instability than can occur in LD films. These correspond to an inertial resonance due to mechanical inertia of the fluid and an inertialess resonance due to charge capacitance at the interface that is similar to mechanically forced films with an insoluble surfactant. In the case of steady forcing, the long-time dynamics exhibits spontaneous sliding as the interface approaches the wall, for the two limiting cases of a perfect conductor-perfect dielectric pair as well as a pair of perfect dielectrics. Under these limits, only the normal component of the Maxwell stress at the interface is significant and the interface dynamics resembles that of a Rayleigh-Taylor unstable interface. For a general pair of leaky dielectrics studied in the limit of fast relaxation times, the presence of interfacial charge prevents the onset of sliding. For the special case when the square of the conductivity ratio equals the permittivity ratio, the interface exhibits cascading structures, similar to those reported for the long-wave Marangoni instability.A variational framework for computing nonlinear optimal disturbances in compressible flows.https://zbmath.org/1460.763282021-06-15T18:09:00+00:00"Huang, Zhu"https://zbmath.org/authors/?q=ai:huang.zhu"Hack, M. J. Philipp"https://zbmath.org/authors/?q=ai:hack.m-j-philippSummary: A variational framework for the identification and analysis of general nonlinear optimal disturbances in compressible flows is derived. The formulation is based on the compressible Navier-Stokes equations in conserved variables for an ideal gas with temperature-dependent viscosity. A discretely consistent implementation based on generalized coordinates allows the accurate analysis of a wide range of settings. An application in the identification of the optimal disturbances which experience the highest amplification in kinetic energy in pipe flow is presented. At low Mach numbers and moderate initial amplitude, the disturbances undergo a sequence of Orr mechanism, oblique nonlinear interaction and lift-up mechanism, and the energy amplification is consistent with results reported for incompressible flow [\textit{C. C. T. Pringle} and \textit{R. R. Kerswell}, ``Using nonlinear transient growth to construct the minimal seed for shear flow turbulence'', Phys. Rev. Lett. 105, No. 15, Article ID 154502, 4 p. (2010; \url{doi:10.1103/PhysRevLett.105.154502})]. When the Mach number is increased, the gain in perturbation kinetic energy grows appreciably, and the initial disturbance field becomes increasingly localized. Nonlinear optimal disturbances which are rescaled to higher initial kinetic energy than prescribed in the optimization procedure are demonstrated to evolve into a chaotic state. For a constant time horizon, the initial perturbation energy to reach a high-energy state decreases monotonically with Mach number.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.On the instability of buoyancy-driven flows in porous media.https://zbmath.org/1460.767502021-06-15T18:09:00+00:00"Gopalakrishnan, Shyam Sunder"https://zbmath.org/authors/?q=ai:gopalakrishnan.shyam-sunderSummary: The interface between two miscible solutions in porous media and Hele-Shaw cells (two glass plates separated by a thin gap) in a gravity field can destabilise due to buoyancy-driven and double-diffusive effects. In this paper the conditions for instability to arise are presented within an analytical framework by considering the eigenvalue problem based on the tools used extensively by Chandrasekhar. The model considered here is Darcy's law coupled to evolution equations for the concentrations of different solutes. We have shown that, when there is an interval in the spatial domain where the first derivative of the base-state density profile is negative, the flows are unstable to stationary or oscillatory modes. Whereas for base-state density profiles that are strictly monotonically increasing downwards such that the first derivative of the base-state density profile is positive throughout the domain (for instance, when a lighter solution containing a species A overlies a denser solution containing another species B), a necessary and sufficient condition for instability is the presence of a point on either side of the initial interface where the second derivative of the base-state density profile is zero such that it changes sign. In such regimes the instability arises as non-oscillatory modes (real eigenvalues). The neutral stability curve, which delimits the stable from the unstable regime, that follows from the discussion presented here along with the other results are in agreement with earlier observations made using numerical computations. The analytical approach adopted in this work could be extended to other instabilities arising in porous media.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.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.A model for foamed cementing of oil and gas wells.https://zbmath.org/1460.767872021-06-15T18:09:00+00:00"Hanachi, Nikoo"https://zbmath.org/authors/?q=ai:hanachi.nikoo"Maleki, Amir"https://zbmath.org/authors/?q=ai:maleki.amir"Frigaard, Ian"https://zbmath.org/authors/?q=ai:frigaard.ian-aSummary: We present a two-dimensional model of the primary cementing process for foamed cement slurries. Foamed cement slurries have a number of claimed advantages, but also have a pressure-dependent density and rheology. The rheology is hard to quantify fully over all ranges of foam quality, which compromises the accuracy of models. The density variation is due to expansion/compression of the gas phase along the well, caused by variations in the static pressure. We show that in the absence of careful control, buoyancy-driven instabilities can result in the annulus, as the foamed slurry expands and the density drops below that of the displaced drilling mud. These instabilities appear to be of a classic porous media/Hele-Shaw cell fingering type, triggered by a threshold unstable density difference. We show that these instabilities are amplified by wellbore eccentricity, occurring lower in the well than in a concentric annulus. Our results question the safe usage of foamed cements in primary cementing.The bypass transition mechanism of the Stokes boundary layer in the intermittently turbulent regime.https://zbmath.org/1460.764072021-06-15T18:09:00+00:00"Xiong, Chengwang"https://zbmath.org/authors/?q=ai:xiong.chengwang"Qi, Xiang"https://zbmath.org/authors/?q=ai:qi.xiang"Gao, Ankang"https://zbmath.org/authors/?q=ai:gao.ankang"Xu, Hui"https://zbmath.org/authors/?q=ai:xu.hui"Ren, Chengjiao"https://zbmath.org/authors/?q=ai:ren.chengjiao"Cheng, Liang"https://zbmath.org/authors/?q=ai:cheng.liangSummary: This numerical study focuses on the coherent structures and bypass transition mechanism of the Stokes boundary layer in the intermittently turbulent regime. In particular, the initial disturbance is produced by a temporary roughness element that is removed immediately after triggering a two-dimensional vortex tube under an inflection-point instability. The present study reveals a complete scenario of self-induced motion of a vortex tube after rollup from the boundary layer. The trajectory of the vortex tube is reasonably described based on the Helmholtz point-vortex equation. The three-dimensional transition of the vortex tube is attributed to the Crow instability, which leads to a sinusoidal disturbance that eventually evolves into a ring-like structure, especially for the weaker vortex. Further investigation demonstrates that three-dimensional or quasi-three-dimensional vortex perturbations in the free stream play a critical role in the boundary layer transition through a bypass mechanism, which is featured by the non-modal and explosive transient growth of the subsequent boundary layer instabilities. This transition scenario is found to be analogous to the oblique transition in the steady boundary layer, both of which are characterised by the formation of streaks, rollup of hairpin-like vortices and burst into turbulent spots. In addition, the streamwise propagation of turbulent spots is discussed in detail. To shed more light on the nature of the intermittently turbulent Stokes boundary layer, a conceptual model is proposed for the periodically self-sustaining mechanism of the turbulent spots based on the present numerical results and experimental evidence reported in the literature.Water film falling down an ice sheet.https://zbmath.org/1460.860452021-06-15T18:09:00+00:00"Jiang, Lu-Ye"https://zbmath.org/authors/?q=ai:jiang.lu-ye"Cheng, Ze"https://zbmath.org/authors/?q=ai:cheng.ze"Peng, Jie"https://zbmath.org/authors/?q=ai:peng.jieSummary: A gravity-driven water film falling down an ice sheet is considered within the framework of a long-wave approximation. The integral-boundary-layer method, modified with the account of the phase transition, is adopted to describe the evolution of both the free surface of a water film and the interface between the ice and water. A set of governing equations consisting of five coupled nonlinear partial differential equations is established. The linear instability analysis of the uniform base flow is performed, and the result is in good agreement with the Orr-Sommerfeld analysis of the linearized Navier-Stokes equations. The phase transition at the interface between the ice and water plays a role in stabilizing the system linearly with long-wavelength perturbations. The nonlinear solutions of the steady travelling waves are constructed numerically. The phase transition tends to suppress the dispersion of the interfacial wave. Comparisons to direct numerical simulation of the Navier-Stokes equations, which are performed with an extended marker and cell method, show a remarkable agreement. The integral-boundary-layer method captures the water film thickness and the topography of the ice sheet satisfactorily. The phase transition is observed to enhance the backflow phenomenon in the capillary region of the solitary-like interfacial wave.Invariant states in inclined layer convection. II: Bifurcations and connections between branches of invariant states.https://zbmath.org/1460.767252021-06-15T18:09:00+00:00"Reetz, Florian"https://zbmath.org/authors/?q=ai:reetz.florian"Subramanian, Priya"https://zbmath.org/authors/?q=ai:subramanian.priya"Schneider, Tobias M."https://zbmath.org/authors/?q=ai:schneider.tobias-mSummary: Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flows. As a function of the strength of thermal driving and the angle of inclination, a multitude of convection patterns is observed in experiments and numerical simulations. Several observed patterns have been linked to exact invariant states of the fully nonlinear three-dimensional Oberbeck-Boussinesq equations. These exact equilibria, travelling waves and periodic orbits reside in state space and, depending on their stability properties, are transiently visited by the dynamics or act as attractors. To explain the dependence of observed convection patterns on control parameters, we study the parameter dependence of the state space structure. Specifically, we identify the bifurcations that modify the existence, stability and connectivity of invariant states. We numerically continue exact invariant states underlying spatially periodic convection patterns at \(Pr=1.07\) under changing control parameters for a temperature difference between the walls and inclination angle. The resulting state branches cover various inclinations from horizontal layer convection to vertical layer convection and beyond. The collection of all computed branches represents an extensive bifurcation network connecting 16 different invariant states across control parameter values. Individual bifurcation structures are discussed in detail and related to the observed complex dynamics of individual convection patterns. Together, the bifurcations and associated state branches indicate at what control parameter values which invariant states coexist. This provides a nonlinear framework to explain the multitude of complex flow dynamics arising in inclined layer convection.
For part I, see [\textit{F. Reetz} and \textit{T. M. Schneider}, ibid. 898, Paper No. A22, 31 p. (2020; Zbl 1460.76333)].Stability of the anabatic Prandtl slope flow in a stably stratified medium.https://zbmath.org/1460.763242021-06-15T18:09:00+00:00"Xiao, Cheng-Nian"https://zbmath.org/authors/?q=ai:xiao.cheng-nian"Senocak, Inanc"https://zbmath.org/authors/?q=ai:senocak.inancSummary: In the Prandtl model for anabatic slope flows, a uniform positive buoyancy flux at the surface drives an upslope flow against a stable background stratification. In the present study, we conduct linear stability analysis of the anabatic slope flow under this model and contrast it against the katabatic case as presented in [the authors, ibid. 865, Paper No. R2, 14 p. (2019; Zbl 1429.86005)]. We show that the buoyancy component normal to the sloped surface is responsible for the emergence of stationary longitudinal rolls, whereas a generalised Kelvin-Helmholtz (KH) type of mechanism consisting of shear instability modulated by buoyancy results in a streamwise-travelling mode. In the anabatic case, for slope angles larger than \(9^\circ\) to the horizontal, the travelling KH mode is dominant whereas, at lower inclination angles, the formation of the stationary vortex instability is favoured. The same dynamics holds qualitatively for the katabatic case, but the mode transition appears at slope angles of approximately \(62^\circ\). For a fixed slope angle and Prandtl number, we demonstrate through asymptotic analysis of linear growth rates that it is possible to devise a classification scheme that demarcates the stability of Prandtl slope flows into distinct regimes based on the dimensionless stratification perturbation number. We verify the existence of the instability modes with the help of direct numerical simulations, and observe close agreements between simulation results and predictions of linear analysis. For slope angle values in the vicinity of the junction point in the instability map, both longitudinal rolls and travelling waves coexist simultaneously and form complex flow structures.Acoustic impedance and hydrodynamic instability of the flow through a circular aperture in a thick plate.https://zbmath.org/1460.766952021-06-15T18:09:00+00:00"Fabre, David"https://zbmath.org/authors/?q=ai:fabre.david"Longobardi, R."https://zbmath.org/authors/?q=ai:longobardi.raffaele"Citro, V."https://zbmath.org/authors/?q=ai:citro.vincenzo"Luchini, P."https://zbmath.org/authors/?q=ai:luchini.paoloSummary: We study the unsteady flow of a viscous fluid passing through a circular aperture in a plate characterized by a non-zero thickness. We investigate this problem by solving the incompressible linearized Navier-Stokes equations around a laminar base flow, in both the forced case (allowing us to characterize the coupling of the flow with acoustic resonators) and the autonomous regime (allowing us to identify the possibility of purely hydrodynamic instabilities). In the forced case, we calculate the impedances and discuss the stability properties in terms of a Nyquist diagram. We show that such diagrams allow us to predict two kinds of instabilities: (i) a conditional instability linked to the over-reflexion of an acoustic wave but requiring the existence of a conveniently tuned external acoustic resonator, and (ii) a purely hydrodynamic instability existing even in a strictly incompressible framework. A parametric study is conducted to predict the range of existence of both instabilities in terms of the Reynolds number and the aspect ratio of the aperture. Analysing the structure of the linearly forced flow allows us to show that the instability mechanism is closely linked to the existence of a recirculation region within the thickness of the plate. We then investigate the autonomous regime using the classical eigenmode analysis. The analysis confirms the existence of the purely hydrodynamic instability in accordance with the impedance-based criterion. The spatial structure of the unstable eigenmodes are found to be similar to the structure of the corresponding unsteady flows computed using the forced problem. Analysis of the adjoint eigenmodes and of the adjoint-based structural sensitivity confirms that the origin of the instability lies in the recirculation region existing within the thickness of the plate.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.Trough instabilities in Boussinesq formulations for water waves.https://zbmath.org/1460.761022021-06-15T18:09:00+00:00"Madsen, Per A."https://zbmath.org/authors/?q=ai:madsen.per-a"Fuhrman, David R."https://zbmath.org/authors/?q=ai:fuhrman.david-rSummary: Modern Boussinesq-type formulations for water waves typically incorporate fairly accurate linear dispersion relations and similar accuracy in nonlinear properties. This has extended their application range to higher values of \(kh\) (\(k\) being wavenumber and \(h\) the water depth) and has allowed for a better representation of nonlinear irregular waves with a fairly large span of short waves and long waves. Unfortunately, we have often experienced a number of `mysterious' breakdowns or blowups, which have perplexed us for some time. A closer inspection has revealed that short-period noise can typically evolve in the deep troughs of wave trains in cases having relatively high spatial resolution. It appears that these potential `trough instabilities' have not previously been discussed in the literature. In the present work, we analyse this problem in connection with the fourth- and fifth-order Padé formulations by \textit{Y. Agnon} et al. [ibid. 399, 319--333 (1999; Zbl 0960.76011)] the one-step Padé and the two-step Taylor-Padé formulations by \textit{P. A. Madsen} et al. [ibid. 462, 1--30 (2002; Zbl 1061.76009)] and the multi-layer formulations by \textit{Z. B. Liu} et al. [ibid. 842, 323--353 (2018; Zbl 1419.76210)]. For completeness, we also analyse the popular, but older, formulations by \textit{O. Nwogu} [``Alternative form of Boussinesq equations for nearshore wave propagation'', ASCE J. Waterway Port Coastal Ocean Eng. 119, No. 6, 618--638 (1993; \url{doi:10.1061/(ASCE)0733-950X(1993)119:6(618)})] and \textit{G. Wei} et al. [J. Fluid Mech. 294, 71--92 (1995; Zbl 0859.76009)]. We generally conclude that trough instabilities may occur in any Boussinesq-type formulation incorporating nonlinear dispersive terms. This excludes most of the classical Boussinesq formulations, but includes all of the so-called `fully nonlinear' formulations. Our instability analyses are successfully verified and confirmed by making simple numerical simulations of the same formulations implemented in one dimension on a horizontal bottom. Furthermore, a remedy is proposed and tested on the one-step and two-step formulations by Madsen et al. [loc. cit.]. This demonstrates that the trough instabilities can be moved or removed by a relatively simple reformulation of the governing Boussinesq equations. Finally, we discuss the option of an implicit Taylor formulation combined with exact linear dispersion, which is the starting point for the explicit perturbation formulation by \textit{D. G. Dommermuth} and \textit{D. K. P. Yue} [ibid. 184, 267--288 (1987; Zbl 0638.76016)], i.e. the popular higher-order-spectral formulations. In this case, we find no sign of trough instabilities.Large-amplitude membrane flutter in inviscid flow.https://zbmath.org/1460.763322021-06-15T18:09:00+00:00"Mavroyiakoumou, C."https://zbmath.org/authors/?q=ai:mavroyiakoumou.christiana"Alben, S."https://zbmath.org/authors/?q=ai:alben.silasSummary: We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed-free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow.Effect of initial interface orientation on patterns produced by vibrational forcing in microgravity.https://zbmath.org/1460.763202021-06-15T18:09:00+00:00"Salgado Sánchez, Pablo"https://zbmath.org/authors/?q=ai:salgado-sanchez.pablo"Gaponenko, Y."https://zbmath.org/authors/?q=ai:gaponenko.yu-a"Yasnou, V."https://zbmath.org/authors/?q=ai:yasnou.v"Mialdun, A."https://zbmath.org/authors/?q=ai:mialdun.aliaksandr"Porter, J."https://zbmath.org/authors/?q=ai:porter.john-r|porter.j-l|porter.james-f|porter.john-f|porter.joseph|porter.j-g|porter.j-h|porter.john-e|porter.james-e-iii|porter.jack-r|porter.jeff|porter.j-david|porter.jack-ray|porter.j-mark|porter.joshua-r|porter.j-w"Shevtsova, V."https://zbmath.org/authors/?q=ai:shevtsova.valentina-mSummary: When a container with two distinct fluids is subjected to vibrations in microgravity, the interface may undergo a variety of instabilities and develop towards a complex structure, as seen in recent parabolic flight experiments using both miscible and immiscible liquids. Among other things, the selected pattern depends on the frequency and amplitude of the forcing and, crucially, on its orientation with respect to the initial interface. In a parabolic flight experiment, this initial orientation is largely determined by the stage of the parabolic manoeuvre when the forcing is started and the residual gravity level during the period of microgravity. It plays a key role in the appearance of defects and irregularities during the evolution of the interface triggered by the frozen wave instability. Using numerical simulations, we systematically investigate the effect of initial interface orientation on pattern selection in microgravity for both miscible and immiscible fluids, and compare to available experiments. When the interface and the forcing are nearly aligned, the frozen wave instability is dominant, leading to the development of approximately regular columnar patterns. As the initial angle becomes more oblique, the frozen wave growth becomes more irregular and asymmetric and may involve thin auxiliary columns. Sufficiently large angles suppress the frozen wave instability and, depending on the container aspect ratio, may result in a simple two-column final state.Linear modes in a planar turbulent jet.https://zbmath.org/1460.763082021-06-15T18:09:00+00:00"Matsubara, Masaharu"https://zbmath.org/authors/?q=ai:matsubara.masaharu"Alfredsson, P. Henrik"https://zbmath.org/authors/?q=ai:alfredsson.per-henrik"Segalini, Antonio"https://zbmath.org/authors/?q=ai:segalini.antonioSummary: A planar jet issuing from a fully developed two-dimensional turbulent channel flow is studied, with a focus on the transverse flapping of the jet core. The streamwise and transverse velocities were measured with hot-wire anemometry using an X-type probe. The mean velocity field and the velocity covariances were first characterised to assess the undisturbed flow field. Periodic excitations were introduced from a slot mounted at the channel exit and the coherent fluctuating part of the signal was obtained by using a phase-locked averaging technique, where the periodic initial forcing was used as trigger. This enabled the eduction of the coherent structure associated with the introduced perturbation. Its amplitude was found to be directly proportional to the intensity of the initial forcing and, within a certain range of the initial forcing amplitude, the growth curves were identical as well as the spatial distribution of the extracted fluctuations. Parallel and non-parallel linear stability theory captures qualitatively and quantitatively the features of the educed coherent structure. The existence of the linear mode in the turbulent jet implies that the large-scale perturbations observed in natural (unforced) jets can be regarded as an incoherent set of linear modes.Stability of the solitary wave boundary layer subject to finite-amplitude disturbances.https://zbmath.org/1460.763972021-06-15T18:09:00+00:00"Önder, Asim"https://zbmath.org/authors/?q=ai:onder.asim"Liu, Philip L.-F."https://zbmath.org/authors/?q=ai:liu.philip-l-fSummary: The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite-amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output analysis, in which the environment noise is modelled as distributed body forces. The most `dangerous' perturbations in a time frame until flow reversal are found to be arranged as counter-rotating streamwise-constant vortices. One of these vortex configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via the lift-up mechanism. By means of secondary stability analysis and direct numerical simulations, the dual role of streaks in the boundary-layer transition is shown. When the amplitude of streaks remains moderate, these elongated features remain stable until the adverse-pressure-gradient stage and have a dampening effect on the instabilities developing thereafter. In contrast, when the low-speed streaks reach high amplitudes exceeding 15 \% of the free stream velocity at the respective phase, they become highly unstable to secondary sinuous modes in the outer shear layers. Consequently, a subcritical transition to turbulence, i.e. bypass transition, can be initiated already in the favourable-pressure-gradient region ahead of the wave crest.Streaky dynamo equilibria persisting at infinite Reynolds numbers.https://zbmath.org/1460.769242021-06-15T18:09:00+00:00"Deguchi, Kengo"https://zbmath.org/authors/?q=ai:deguchi.kengoSummary: Nonlinear three-dimensional dynamo equilibrium solutions of viscous-resistive magneto-hydrodynamic equations are continued to formally infinite magnetic and hydrodynamic Reynolds numbers. The external driving mechanism of the dynamo is a uniform shear, which constitutes the base laminar flow and cannot support any kinematic dynamo. Nevertheless, an efficient subcritical nonlinear instability mechanism is found to be able to generate large-scale coherent structures known as streaks, for both velocity and magnetic fields. A finite amount of magnetic field generation is identified at the self-consistent asymptotic limit of the nonlinear solutions, thereby confirming the existence of an effective nonlinear dynamo action at astronomically large Reynolds numbers.Convergent Richtmyer-Meshkov instability of light gas layer with perturbed outer surface.https://zbmath.org/1460.766202021-06-15T18:09:00+00:00"Li, Jianming"https://zbmath.org/authors/?q=ai:li.jianming"Ding, Juchun"https://zbmath.org/authors/?q=ai:ding.juchun"Si, Ting"https://zbmath.org/authors/?q=ai:si.ting"Luo, Xisheng"https://zbmath.org/authors/?q=ai:luo.xishengSummary: The Richtmyer-Meshkov instability of a helium layer surrounded by air is studied in a semi-annular convergent shock tube by high-speed schlieren photography. The gas layer is generated by an improved soap film technique such that its boundary shapes and thickness are precisely controlled. It is observed that the inner interface of the shocked light gas layer remains nearly undisturbed during the experimental time, even after the reshock, which is distinct from its counterpart in the heavy gas layer. This can be ascribed to the faster decay of the perturbation amplitude of the transmitted shock in the helium layer and Rayleigh-Taylor stabilization on the inner surface (light/heavy) during flow deceleration. The outer interface first experiences `accelerated' phase inversion owing to geometric convergence, and later suffers a continuous deformation. Compared with a sole heavy/light interface, the wave influence (interface coupling) inhibits (promotes) growth of instability of the outer interface.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.Low-order Boussinesq models based on \(\sigma\) coordinate series expansions.https://zbmath.org/1460.761502021-06-15T18:09:00+00:00"Kirby, James T."https://zbmath.org/authors/?q=ai:kirby.james-tSummary: We derive weakly dispersive Boussinesq equations using a \(\sigma\) coordinate for the vertical direction, employing a series expansion in powers of \(\sigma\). We restrict attention initially to the case of constant still-water depth \(h\) in order to simplify subsequent analysis, and consider equations based on expansions about the bottom elevation \(\sigma =0\), and then about a reference elevation \(\sigma_\alpha\) in order to improve linear dispersion properties. We use a perturbation analysis, suggested recently by \textit{P. A. Madsen} and \textit{D. R. Fuhrman} [ibid. 889, Article ID A38, 25 p. (2020; Zbl 1460.76102)], to show that the resulting models are not subject to the trough instability studied there. A similar analysis is performed to develop a model for interfacial waves in a two-layer fluid, with comparable results. We argue, by extension, that a necessary condition for eliminating trough instabilities is that the model's nonlinear dispersive terms should not contain still-water depth \(h\) and surface displacement \(\eta\) separately.Instability of a dense seepage layer on a sloping boundary.https://zbmath.org/1460.763162021-06-15T18:09:00+00:00"Forbes, Lawrence K."https://zbmath.org/authors/?q=ai:forbes.lawrence-k"Walters, Stephen J."https://zbmath.org/authors/?q=ai:walters.stephen-j"Farrow, Duncan E."https://zbmath.org/authors/?q=ai:farrow.duncan-eSummary: When open-cut mines are eventually abandoned, they leave a large hole with sloping sides. The hole fills with rain water, and there is also contaminated run-off from surrounding land, that moves through the rock and eventually through the sloping sides of the abandoned mine. This paper considers a two-dimensional unsteady model motivated by this leaching flow through the rock and into the rain-water reservoir. The stability of the interface between the two fluids is analysed in the inviscid limit. A viscous Boussinesq model is also presented, and a closed-form solution is presented to this problem, after it has been linearized in a manner consistent with Boussinesq theory. That solution suggests that the interfacial zone is effectively neutrally stable as it evolves in time. However, an asymptotic theory in the interfacial region shows the interface to be unstable. In addition, the nonlinear Boussinesq model is solved using a spectral method. Interfacial travelling waves and roll-up are observed and discussed, and compared against the predictions of asymptotic Boussinesq theory.Dynamics of front propagation in a compliant channel.https://zbmath.org/1460.763152021-06-15T18:09:00+00:00"Cuttle, Callum"https://zbmath.org/authors/?q=ai:cuttle.callum"Pihler-Puzović, Draga"https://zbmath.org/authors/?q=ai:pihler-puzovic.draga"Juel, Anne"https://zbmath.org/authors/?q=ai:juel.anneSummary: Front-propagating systems provide some of the most fundamental physical examples of interfacial instability and pattern formation. However, their nonlinear dynamics is rarely addressed. Here, we present an experimental study of air displacing a viscous fluid within a collapsed, compliant channel -- a model for pulmonary airway reopening. Air injected at a constant flow rate from one end of the liquid-filled, collapsed channel results in the propagation of a reopening finger. Depending on the imposed flow rate, we observe a wide variety of finger-tip morphologies, which occur persistently or evolve transiently as the finger propagates. Persistent fingers are stable in the sense that they propagate with approximately constant bubble pressure. We find that their pressure increases monotonically as a function of bubble speed along two disconnected lines. Although the line associated with higher bubble speed exhibits a minimum pressure value, the low-speed line supports finger propagation down to the smallest flow rates investigated. We present evidence that the lower and higher-speed fingers are dominated by viscous and elastic forces, respectively. We also find a range of bubble speeds separating the two pressure lines where no stable finger propagation is observed. Instead, complex transient dynamics leads to the long-term selection of stable fingers depending on initial conditions. The early transient evolution of these fingers is characterised by an increase in bubble pressure alongside a reduction in bubble speed. We hypothesise the existence of a weakly unstable, steady mode, which orchestrates the transient evolution of the finger towards either low- or high-speed modes of propagation.Control of radial miscible viscous fingering.https://zbmath.org/1460.763112021-06-15T18:09:00+00:00"Sharma, Vandita"https://zbmath.org/authors/?q=ai:sharma.vandita"Nand, Sada"https://zbmath.org/authors/?q=ai:nand.sada"Pramanik, Satyajit"https://zbmath.org/authors/?q=ai:pramanik.satyajit"Chen, Ching-Yao"https://zbmath.org/authors/?q=ai:chen.chingyao"Mishra, Manoranjan"https://zbmath.org/authors/?q=ai:mishra.manoranjanSummary: We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is determined by an interplay between advection and diffusion during the initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius \(r_0\) of the circular region initially occupied by the less-viscous fluid in the porous medium. For each \(r_0\), we further determine the stability in terms of Péclet number \((Pe)\) and log-mobility ratio \((M)\). The \(Pe-M\) parameter space is divided into stable and unstable zones: the boundary between the two zones is well approximated by \(M_c= \alpha (r_0)Pe_c^{-0.55}\). In the unstable zone, the instability is reduced with an increase in \(r_0\). Thus, a natural control measure for miscible radial VF in terms of \(r_0\) is established. Finally, the results are validated by performing experiments that provide good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.Rayleigh-Bénard convection in viscoelastic liquid bridges.https://zbmath.org/1460.760252021-06-15T18:09:00+00:00"Lappa, Marcello"https://zbmath.org/authors/?q=ai:lappa.marcello"Boaro, Alessio"https://zbmath.org/authors/?q=ai:boaro.alessioSummary: Rayleigh-Bénard convection in a floating zone held by the surface tension between two supporting disks at different temperatures is considered. Through direct numerical solution of the mixed parabolic-elliptic-hyperbolic set of governing equations in complete time-dependent and nonlinear form, we investigate the still unknown patterns and spatio-temporal states that are produced when the fluid has viscoelastic properties. The following conditions are examined: Prandtl number \(Pr=8\), aspect ratio (\(A=\text{length/diameter})\) in the range \(0.17 \leq A \leq 1\) and different values of the elasticity number \((0 \leq \theta \leq 0.2)\). It is shown that, in addition to elastic overstability, an important ingredient of the considered dynamics is the existence of multiple solutions i.e. `attractors' coexisting in the space of phases and differing with respect to the basin of attraction. We categorize the emerging states as modes with dominant vertical or horizontal vorticity and analyse the related waveforms, generally consisting of standing waves with central symmetry or oscillatory modes featuring almost parallel rolls, which periodically break and reform in time with a new orientation in space. In order to characterize the peculiar features of these flows, the notions of disturbance node and the topological concept of `knot' are used. Azimuthally travelling waves are also possible in certain regions of the space of parameters, though they are generally taken over by convective modes with dominant pulsating nature as the elasticity parameter is increased. The case of an infinite horizontal layer is finally considered as an idealized model to study the asymptotic fluid-dynamic behaviour of the liquid bridge in the limit as its aspect ratio tends to zero.Rayleigh-Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour.https://zbmath.org/1460.763372021-06-15T18:09:00+00:00"Wei, Tao"https://zbmath.org/authors/?q=ai:wei.tao"Zhang, Mengqi"https://zbmath.org/authors/?q=ai:zhang.mengqiSummary: We investigate the three-dimensional surface pattern and nonlinear dynamics of a condensing liquid layer suspended from a cooled substrate and in contact with a mixture of its vapour and an inert gas below. A vapour boundary layer (VBL) is introduced, to which the changes in gaseous composition and temperature are assumed to be confined. An interfacial transport equation is derived, which incorporates the physical effects of convection and diffusion of vapour within the VBL, coupled with a long-wave evolution equation for the location of the free surface. This work extends the study of \textit{K. Kanatani} [ibid. 732, 128--149 (2013; Zbl 1294.76248)] on a sessile evaporating film to the Rayleigh-Taylor unstable condensing/evaporating case with nonlinear analyses which also accounts for the effect of vapour recoil due to mass transfer on interfacial evolution and that of gravity combined with buoyancy on the internal convection of pendent drops in a condensate layer. The coupled nonlinear evolutionary system is referred to as a 1.5-sided model. It can be reduced to the conventional one-sided model when phase change is limited by processes in the liquid. An extended basic state is obtained, whose stability is investigated with pseudo-steady linear theory and time-dependent nonlinear simulations. With the one-sided model, the influences of vapour recoil and Marangoni effects are illustrated with three representative cases. In the one-sided simulations with a random perturbation, the interface is prone to finite-time rupture and the surface patterns feature isolated droplets when vapour recoil is significant, while it becomes more regular and even without rupture as vapour recoil is weakened relative to the Marangoni effect. This suggests that, in the absence of the convection and diffusion of vapour, the destabilizations of vapour recoil and negative gravity could prevail over the stabilizations of thermocapillarity, capillarity, viscous dissipation and mass gain. With an unsaturated initial interface concentration, \(\tilde{x}_{A,I0}\), the 1.5-sided model indicates that the liquid layer can be stabilized to a quasi-hexagon pattern and the Rayleigh-Taylor-driven rupture can be suppressed with the effects of vapour convection and diffusion near the interface. However, the initial dynamics is in contrast to the case with a saturated \(\tilde{x}_{A,I0}\), where transition from weak evaporation to a condensation-dominated regime is seen in the later stage. The viewpoint of stability competition offers vital evidence for an induced Marangoni stabilization, which is a quintessential characteristic of the 1.5-sided model. Comparisons of the theory and simulations with available experiments are included throughout.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.Flow-acoustic resonance in a cavity covered by a perforated plate.https://zbmath.org/1460.766942021-06-15T18:09:00+00:00"Dai, Xiwen"https://zbmath.org/authors/?q=ai:dai.xiwenSummary: To explain the large-scale hydrodynamic instability along a cavity-backed perforated plate in a flow duct, a two-dimensional multimodal analysis of flow disturbances is performed. First, a hole-by-hole description of the perforated plate shows a spatially growing wave with a wavelength close to the plate length, but much larger than the period of perforation. To better understand this problem and also cavity flow oscillations, we then combine the travelling mode and global mode analyses of the flow where the plate is represented by a homogeneous impedance. The spatially growing wave is, from a homogeneous point of view, essentially a Kelvin-Helmholtz instability wave, strongly distorted by evanescent acoustic waves near the cavity downstream edge. The phase difference of the unstable hydrodynamic mode at the two edges is found to be a bit larger than \(2 \pi \), whereas the upstream-travelling evanescent waves reduce the total phase change around the feedback loop, so that the phase condition of the global mode can still be satisfied. This particular case indicates the significant effects of those evanescent waves on both the amplitude and phase of cavity flow disturbances. The criterion of the global instability is discussed: the loop gain being larger or smaller than unity determines whether the global mode is unstable or stable. A global mode in the stable regime, which has so far received little attention, is explored by investigating the system response to external forcing. It is shown that sound can be produced when a lightly damped flow-acoustic resonance is excited by a vortical wave.Scaling of velocity fluctuations in statistically unstable boundary-layer flows.https://zbmath.org/1460.765012021-06-15T18:09:00+00:00"Yang, Xiang I. A."https://zbmath.org/authors/?q=ai:yang.xiang-i-a"Pirozzoli, Sergio"https://zbmath.org/authors/?q=ai:pirozzoli.sergio"Abkar, Mahdi"https://zbmath.org/authors/?q=ai:abkar.mahdiSummary: Much of our theoretical understanding of statistically stable and unstable flows is from the classical Monin-Obukhov similarity theory: the theory predicts the scaling of the mean flow well, but its prediction of the turbulent fluctuation is far from satisfactory. This study builds on Monin-Obukhov similarity theory and Townsend's attached-eddy hypothesis. We present a model that connects the mean flow and the streamwise velocity fluctuations in both neutral and unstable boundary-layer flows at both moderate and high Reynolds numbers. The model predictions are compared to direct numerical simulations of weakly unstable boundary layers at moderate Reynolds numbers, and large-eddy simulations of unstable boundary-layer flows at high Reynolds numbers. The flow is shear dominated. The range of stability parameter considered in this work is \(L/ \delta <-0.1\), where \(L\) is the Monin-Obukhov length, and \(\delta\) is the boundary-layer height. Reasonably good prediction of velocity fluctuations based on knowledge of the mean velocity profile is obtained.Linear stability of katabatic Prandtl slope flows with ambient wind forcing.https://zbmath.org/1460.860302021-06-15T18:09:00+00:00"Xiao, Cheng-Nian"https://zbmath.org/authors/?q=ai:xiao.cheng-nian"Senocak, Inanc"https://zbmath.org/authors/?q=ai:senocak.inancSummary: We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to a downslope uniform ambient wind aloft. We adopt an extension of Prandtl's original model for slope flows [\textit{V. N. Lykosov} and \textit{L. N. Gutman}, ``Turbulent boundary-layer over a sloping underlying surface'', Atmos. Ocean. Phys. 8, No. 8, 799--809 (1972)] to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in [the authors, ``Stability of the Prandtl model for katabatic slope flows'', J. Fluid Mech. 865, R2, 14 p. (2019; \url{doi:10.1017/jfm.2019.132})]. The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and the stabilising effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow's stability is complicated, as the ambient wind can be both stabilising as well as destabilising for a certain range of the parameters. Our results constitute a strong counterevidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.Sorting and bed waves in unidirectional shallow-water flows.https://zbmath.org/1460.763062021-06-15T18:09:00+00:00"Colombini, Marco"https://zbmath.org/authors/?q=ai:colombini.marco"Carbonari, Costanza"https://zbmath.org/authors/?q=ai:carbonari.costanzaSummary: The stability of a uniform flow above an erodible bed composed of a bimodal mixture of sediments is investigated by means of linear analysis. Results show that, for any given set of the flow and sediment parameters, two distinct modes of instability arise, each one characterized by its own wave speed, growth rate and longitudinal wavelength, each one involving spatial variations of both grain size density and bed elevation. Although at a linear level no information on the amplitude of the perturbations is gathered, the analysis of the eigenvectors associated with the two modes of instability allows for an easy classification in terms of the relative amplitudes of the perturbations of bed elevation and size density. One eigenvalue is shown to be associated with the modifications of bed forms induced by the presence of the heterogeneous mixture, such as the local accumulation of finer and coarser material along the unit wavelength, the other with the formation of the low-amplitude sorting waves known as bedload sheets. In the present unidirectional shallow-water framework, only the sorting wave is found to be unstable, since dunes and antidunes, the relevant bed forms for this case, require a more refined rotational flow model in order to become unstable. On the other hand, the simple flow model adopted allows for the formulation of an algebraic eigenvalue problem that can be solved analytically, allowing for a deep insight into the mechanisms that drive both instabilities.Local analysis of absolute instability in plasma jets.https://zbmath.org/1460.769462021-06-15T18:09:00+00:00"Demange, Simon"https://zbmath.org/authors/?q=ai:demange.simon"Chazot, O."https://zbmath.org/authors/?q=ai:chazot.o"Pinna, F."https://zbmath.org/authors/?q=ai:pinna.francesco|pinna.fabioSummary: Stability features of two-stream coaxial plasma jet simulations are investigated using numerical solutions to the spatio-temporal one-dimensional linear stability theory problem. The base states obtained from magneto-hydrodynamic simulations consider the flow as a mixture of gases in local thermodynamic equilibrium (LTE) while stability computations are performed assuming both a calorically perfect gas (CPG) model and LTE. Comparisons with solutions considering a simple CPG model show the non-negligible impact of the LTE on the stability attributes of the plasma jet. For all cases studied, a large region of absolute instability is found for the axisymmetric mode, starting at the jet inlet. The streamwise evolution of the absolute growth rate is found to depend both on the baroclinic torque and the displacement of the maximum shear toward low velocity regions of the jet, combining effects described in the literature. The jet is controlled by means of electric power and static pressure at constant mass flow. The former affects mainly the absolute growth rate through changes of the core-to-bypass stream velocity ratio, while the latter influences mostly the absolute frequency. Finally, the full impulse response reveals a competition mechanism between the absolute mixed modes dominating at low group velocities, and convective shear layer modes at higher group velocities, restricted to the first half of the chamber.Stability of falling liquid films on flexible substrates.https://zbmath.org/1460.760352021-06-15T18:09:00+00:00"Alexander, J. Paul"https://zbmath.org/authors/?q=ai:alexander.j-paul"Kirk, Toby L."https://zbmath.org/authors/?q=ai:kirk.toby-l"Papageorgiou, Demetrios T."https://zbmath.org/authors/?q=ai:papageorgiou.demetrios-tSummary: The linear stability of a liquid film falling down an inclined flexible plane under the influence of gravity is investigated using analytical and computational techniques. A general model for the flexible substrate is used leading to a modified Orr-Sommerfeld problem addressed numerically using a Chebyshev tau decomposition. Asymptotic limits of long waves and small Reynolds numbers are addressed analytically and linked to the computations. For long waves, the flexibility has a destabilising effect, where the critical Reynolds number decreases with decreasing stiffness, even destabilising Stokes flow for sufficiently small stiffness. To pursue this further, a Stokes flow approximation was considered, which confirmed the long-wave results, but also revealed a short wave instability not captured by the long-wave expansions. Increasing the surface tension has little effect on these instabilities and so they were characterised as wall modes. Wider exploration revealed mode switching in the dispersion relation, with the wall and surface mode swapping characteristics for higher wavenumbers. The zero-Reynolds-number results demonstrate that the long-wave limit is not sufficient to determine instabilities so the numerical solution for arbitrary wavenumbers was sought. A Chebyshev tau spectral method was implemented and verified against analytical solutions. Short wave wall instabilities persist at larger Reynolds numbers and destabilisation of all Reynolds numbers is achievable by increasing the wall flexibility, however increasing the stiffness reverts back to the rigid wall limit. An energy decomposition analysis is presented and used to identify the salient instability mechanisms and link them to their physical origin.Interfacial instability at a heavy/light interface induced by rarefaction waves.https://zbmath.org/1460.763302021-06-15T18:09:00+00:00"Liang, Yu"https://zbmath.org/authors/?q=ai:liang.yu"Zhai, Zhigang"https://zbmath.org/authors/?q=ai:zhai.zhigang"Luo, Xisheng"https://zbmath.org/authors/?q=ai:luo.xisheng"Wen, Chih-yung"https://zbmath.org/authors/?q=ai:wen.chihyungSummary: The interaction of rarefaction waves and a heavy/light interface is investigated using numerical simulations by solving the compressible Euler equations. An upwind space-time conservation element and solution element (CE/SE) scheme with second-order accuracy in both space and time is adopted. Rarefaction waves are generated by simulating the shock-tube problem. In this work, the \(SF_6\)/air interface evolution under different conditions is considered. First, the gas physical parameters before and after the rarefaction waves impact the interface are calculated using one-dimensional gas dynamics theory. Then, the interaction between the rarefaction waves and a single-mode perturbation interface is investigated, and both the interface evolution and the wave patterns are obtained. Afterwards, the amplitude growth of the interface over time is compared between cases, considering the effects of the interaction period and the strength of the rarefaction waves. During the interaction of the rarefaction waves with the interface, the Rayleigh-Taylor instability induced by the rarefaction waves is well predicted by modifying the nonlinear model proposed by \textit{Q. Zhang} and \textit{W. Guo} [ibid. 786, 47--61 (2016; Zbl 1381.76079)], considering the variable acceleration. After the rarefaction waves leave the interface, the equivalent Richtmyer-Meshkov instability is well depicted by the nonlinear model proposed by \textit{Q. Zhang} et al. [``Quantitative theory for the growth rate and amplitude of the compressible Richtmyer-Meshkov instability at all density ratios'', Phys. Rev. Lett. 121, No. 17, Article ID 174502, 6 p. (2018; \url{doi:10.1103/PhysRevLett.121.174502})], considering the growth rate transition from Rayleigh-Taylor instability to Richtmyer-Meshkov instability. The differences in the heavy/light interface amplitude growth under the rarefaction wave condition and the shock wave condition are compared. The interface perturbation is shown to be more unstable under rarefaction waves than under a shock wave.Stability analysis of deep-water waves on a linear shear current using unsteady conformal mapping.https://zbmath.org/1460.762962021-06-15T18:09:00+00:00"Murashige, Sunao"https://zbmath.org/authors/?q=ai:murashige.sunao"Choi, Wooyoung"https://zbmath.org/authors/?q=ai:choi.wooyoungSummary: This paper describes linear stability analysis of the two-dimensional steady motion of periodic deep-water waves with symmetric non-overhanging profiles propagating on a linear shear current, namely a vertically sheared current with constant vorticity. In order to investigate numerically with high accuracy the stability of large-amplitude waves, we adopt a formulation using conformal mapping, in which the time-varying water surface is always mapped onto the real axis of a complex plane. This formulation allows us to apply numerical methods developed for large-amplitude irrotational waves without a shear current directly to the present problem, and reduces the linear stability problem to a generalized eigenvalue problem. Numerical solutions describe both super- and sub-harmonic instabilities of the periodic waves for a wide range of wave amplitudes and clarify how the behaviours of dominant eigenvalues change with the strength of the shear current. In particular, it is shown that, even in the presence of a linear shear current, the steady periodic waves lose stability due to superharmonic disturbances at the wave amplitude where the wave energy attains an extremum, similarly to the case of irrotational waves without a shear current. It is also found that re-stabilization with an increase in wave amplitude characterizes subharmonic instability for weak shear currents, but the re-stabilization disappears for strong shear currents.Turbulent Rayleigh-Bénard convection in a strong vertical magnetic field.https://zbmath.org/1460.769182021-06-15T18:09:00+00:00"Akhmedagaev, R."https://zbmath.org/authors/?q=ai:akhmedagaev.r"Zikanov, O."https://zbmath.org/authors/?q=ai:zikanov.oleg-yu"Krasnov, D."https://zbmath.org/authors/?q=ai:krasnov.dmitry|krasnov.d-s"Schumacher, J."https://zbmath.org/authors/?q=ai:schumacher.jorgSummary: Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh-Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number \(0.025\) and Rayleigh and Hartmann numbers up to \(10^9\) and \(1400\), respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh-Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.Global instability of wing shock-buffet onset.https://zbmath.org/1460.766282021-06-15T18:09:00+00:00"Timme, Sebastian"https://zbmath.org/authors/?q=ai:timme.sebastianSummary: Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. Its dynamics is revealed through the interaction of spanwise shock-wave oscillations and intermittent turbulent boundary-layer separation. Resulting unsteady aerodynamic loads, and their mutual working with the flexible aircraft structure, need to be accounted for in establishing the safe flight envelope. The question of global instability leading to this flow unsteadiness is addressed herein. It is shown for the first time on an industrially relevant configuration that the dynamics of a single unstable oscillatory eigenmode plays a prominent role in near-onset shock buffet on a quasi-rigid wing. Its three-dimensional spatial structure, previously inferred both from experiment and time-marching simulation, describes a spanwise-localised pocket of shear-layer pulsation synchronised with an outboard-propagating shock oscillation. The results also suggest that the concept of a critical global shock-buffet mode commonly reported for two-dimensional aerofoils also applies to three-dimensional finite and swept wings, albeit different modes at play. Specifically, the modern wing design, NASA Common Research Model, with publicly available geometry and experimental data for code validation is studied at a free-stream Mach number of 0.85 with Reynolds number per reference chord of \(5.0\times 10^6\) and varying angle of attack between \(3. 5^\degree\) and \(4. 0^\degree\) targeting the instability onset. Strouhal number at instability onset just above \(3. 7^\degree\) is approximately 0.39. At the same time, a band of eigenmodes shows reduced decay rate in the Strouhal-number range of 0.3 to 0.7, with additional unstable oscillatory modes appearing beyond onset. Importantly, those emerging modes seem to discretise the continuous band of medium-wavelength modes, as recently reported for infinite swept wings using stability analysis, hence generalising those findings to finite wings. Through conventional time-marching unsteady simulation it is explored how the critical linear eigenmode feeds into the nonlinearly saturated limit-cycle oscillation near instability onset. The established numerical strategy, using an iterative inner-outer Krylov approach with shift-and-invert spectral transformation and sparse iterative linear solver, to solve the arising large-scale eigenvalue problem with an industrial Reynolds-averaged Navier-Stokes flow solver means that such a practical non-canonical test case at a high-Reynolds-number condition can be investigated. The numerical findings can potentially be exploited for more effective unsteady flow analysis in future wing design and inform routes to flow control and model reduction.A probabilistic protocol for the assessment of transition and control.https://zbmath.org/1460.763992021-06-15T18:09:00+00:00"Pershin, Anton"https://zbmath.org/authors/?q=ai:pershin.anton"Beaume, Cédric"https://zbmath.org/authors/?q=ai:beaume.cedric"Tobias, Steven M."https://zbmath.org/authors/?q=ai:tobias.steven-mSummary: Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to turbulence is achieved via the broadening or narrowing of the basin of attraction of the laminar flow. In this paper, a novel methodology to assess the robustness of the laminar flow and the efficiency of control strategies is introduced. It relies on the statistical sampling of the phase-space neighbourhood around the laminar flow in order to assess the transition probability of perturbations as a function of their energy. This approach is applied to a canonical flow (plane Couette flow) and provides invaluable insight: in the presence of the chosen control, transition is significantly suppressed whereas plausible scalar indicators of the nonlinear stability of the flow, such as the edge-state energy, do not provide conclusive predictions. The methodology presented here in the context of transition to turbulence is applicable to any nonlinear system displaying finite-amplitude instability.Dynamic mobility of surfactant-stabilized nano-drops: unifying equilibrium thermodynamics, electrokinetics and Marangoni effects.https://zbmath.org/1460.760112021-06-15T18:09:00+00:00"Hill, Reghan J."https://zbmath.org/authors/?q=ai:hill.reghan-j"Afuwape, Gbolahan"https://zbmath.org/authors/?q=ai:afuwape.gbolahanSummary: A theoretical analysis of the dynamic electrophoretic mobility of surfactant-stabilized nano-drops is undertaken. Whereas the theory for rigid spherical nanoparticles is well developed, its application to nano-drops is questionable due to fluid mobility of the interface and of the surfactant molecules adsorbed there. At zero frequency, small drops with surface impurities are well known to behave as rigid spheres due to concentration-gradient-induced Marangoni stresses. However, at the megahertz frequencies of electroacoustic (and other spectral-based) diagnostics, the interfacial concentration gradients are dynamic, coupling electromigration, advection and diffusion fluxes. This study addresses a parameter space that is relevant to anionic-surfactant-stabilized oil-water emulsions, using sodium-dodecylsulfate-stabilized hexadecane as a specific example. The drop size is several hundred nanometres, much larger than the diffuse-layer thickness, thus motivating thin-double-layer approximations. The theory demonstrates that fluid mobility and fluctuating Marangoni stresses can have a profound influence on the magnitude and phase of the dynamic mobility. We show that the drop interface transits from a rigid/immobile one at low frequency to a fluid one at high frequency. The model unifies electrokinetics and equilibrium interfacial thermodynamics. Therefore, with knowledge of how the interfacial tension varies with electrolyte composition (oil, surfactant and added salt concentrations), the particle radius might be adopted as the primary fitting parameter (rather than the customary \(\zeta \)-potential) from an experimental measure of the dynamic mobility. This theory is general enough that it might be applied to aerosols and bubbly dispersions (at sufficiently high frequencies).Effects of Atwood and Reynolds numbers on the evolution of buoyancy-driven homogeneous variable-density turbulence.https://zbmath.org/1460.763472021-06-15T18:09:00+00:00"Aslangil, Denis"https://zbmath.org/authors/?q=ai:aslangil.denis"Livescu, Daniel"https://zbmath.org/authors/?q=ai:livescu.daniel"Banerjee, Arindam"https://zbmath.org/authors/?q=ai:banerjee.arindam|banerjee.arindam.1|banerjee.arindam.2Summary: The evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at Atwood numbers up to 0.75 and large Reynolds numbers is studied by using high-resolution direct numerical simulations. To help understand the highly non-equilibrium nature of buoyancy-driven HVDT, the flow evolution is divided into four different regimes based on the behaviour of turbulent kinetic energy derivatives. The results show that each regime has a unique type of dependence on both Atwood and Reynolds numbers. It is found that the local statistics of the flow based on the flow composition are more sensitive to Atwood and Reynolds numbers compared to those based on the entire flow. It is also observed that, at higher Atwood numbers, different flow features reach their asymptotic Reynolds-number behaviour at different times. The energy spectrum defined based on the Favre fluctuations momentum has less large-scale contamination from viscous effects for variable-density flows with constant properties, compared to other forms used previously. The evolution of the energy spectrum highlights distinct dynamical features of the four flow regimes. Thus, the slope of the energy spectrum at intermediate to large scales evolves from \(-7/3\) to \(-1\), as a function of the production-to-dissipation ratio. The classical Kolmogorov spectrum emerges at intermediate to high scales at the highest Reynolds numbers examined, after the turbulence starts to decay. Finally, the similarities and differences between buoyancy-driven HVDT and the more conventional stationary turbulence are discussed and new strategies and tools for analysis are proposed.Convergent Richtmyer-Meshkov instability of heavy gas layer with perturbed inner surface.https://zbmath.org/1460.766262021-06-15T18:09:00+00:00"Sun, Rui"https://zbmath.org/authors/?q=ai:sun.rui"Ding, Juchun"https://zbmath.org/authors/?q=ai:ding.juchun"Zhai, Zhigang"https://zbmath.org/authors/?q=ai:zhai.zhigang"Si, Ting"https://zbmath.org/authors/?q=ai:si.ting"Luo, Xisheng"https://zbmath.org/authors/?q=ai:luo.xishengSummary: The convergent Richtmyer-Meshkov instability (RMI) of an SF\(_6\) layer with a uniform outer surface and a sinusoidal inner surface surrounded by air (generated by a novel soap film technique) is studied in a semiannular convergent shock tube using high-speed schlieren photography. The outer interface initially suffers only a slight deformation over a long period of time, but distorts quickly at late stages when the inner interface is close to it and produces strong coupling effects. The development of the inner interface can be divided into three stages. At stage I, the interface amplitude first drops suddenly to a lower value due to shock compression, then decreases gradually to zero (phase reversal) and later increases sustainedly in the negative direction. After the reshock (stage II), the perturbation amplitude exhibits long-term quasi-linear growth with time. The quasi-linear growth rate depends weakly on the pre-reshock amplitude and wavelength, but strongly on the pre-reshock growth rate. An empirical model for the growth of convergent RMI under reshock is proposed, which reasonably predicts the present results and those in the literature. At stage III, the perturbation growth is promoted by the Rayleigh-Taylor instability caused by a rarefaction wave reflected from the outer interface. It is found that both the Rayleigh-Taylor effect and the interface coupling depend heavily on the layer thickness. Therefore, controlling the layer thickness is an effective way to modulate the late-stage instability growth, which may be useful for the target design.Contribution of viscosity to the circulation deposition in the Richtmyer-Meshkov instability.https://zbmath.org/1460.763232021-06-15T18:09:00+00:00"Liu, Hao-Chen"https://zbmath.org/authors/?q=ai:liu.hao-chen"Yu, Bin"https://zbmath.org/authors/?q=ai:yu.bin.2|yu.bin.1|yu.bin"Chen, Hao"https://zbmath.org/authors/?q=ai:chen.hao.5|chen.hao.2|chen.hao.1|chen.hao.3|chen.hao.4"Zhang, Bin"https://zbmath.org/authors/?q=ai:zhang.bin.4|zhang.bin.1|zhang.bin.2|zhang.bin.3"Xu, Hui"https://zbmath.org/authors/?q=ai:xu.hui"Liu, Hong"https://zbmath.org/authors/?q=ai:liu.hong.1|liu.hongSummary: This study focuses on the process of the circulation deposition in the Richtmyer-Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11\% of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave-turbulence interactions.Flapping dynamics of a flag in the presence of thermal convection.https://zbmath.org/1460.763362021-06-15T18:09:00+00:00"Solano, Tomas"https://zbmath.org/authors/?q=ai:solano.tomas"Ordonez, Juan C."https://zbmath.org/authors/?q=ai:ordonez.juan-c"Shoele, Kourosh"https://zbmath.org/authors/?q=ai:shoele.kouroshSummary: The flow-induced flapping dynamics of a flexible two-dimensional heated flag in the mixed convection regime is studied here. A linear stability analysis is first used to predict the flutter stability using three dimensionless parameters of reduced flow velocity, mass ratio and Richardson number. This is followed by fully coupled computational simulations to investigate the role of flapping motion on the flag's thermal performance. The results show that an increase of Richardson number has a non-monotonic stabilizing effect on the flag response over the range of reduced velocities. The distinct flapping response regimes previously reported in the literature are recovered here and expanded upon by finding new flapping modes within the limit-cycle regime. It is found that mode switching is associated not only with the frequency response of the system but is also highly coupled to the flag's thermal performance. The average Nusselt number over the structure attains the highest value when the flag vibrates in its higher fluttering mode, wherein it shows a higher sensitivity to Richardson number. We also report the correlations for the Nusselt number for the different flapping modes and identify an unexpected dependency of the modes on the flag inertia in the presence of the thermal effects.Ricocheting inclined layer convection states.https://zbmath.org/1460.767292021-06-15T18:09:00+00:00"Tuckerman, Laurette S."https://zbmath.org/authors/?q=ai:tuckerman.laurette-sSummary: Inclining a fluid layer subjected to a temperature gradient introduces a profusion of fascinating patterns and regimes. Previous experimental and computational studies form the starting point for an extensive numerical bifurcation study by \textit{F. Reetz} and \textit{T. M. Schneider} [ibid. 898, Article ID A22, 31 p. (2020; Zbl 1460.76333)] and \textit{F. Reetz} et al. [ibid. 898, Article ID A23, 38 p. (2020; Zbl 1460.76725)]. Intricate trajectories passing through multiple steady and periodic states organize the dynamics. The consequences for chaotic patterns in large geometries is discussed.Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability.https://zbmath.org/1460.763272021-06-15T18:09:00+00:00"Zhu, Lailai"https://zbmath.org/authors/?q=ai:zhu.lailai"Stone, Howard A."https://zbmath.org/authors/?q=ai:stone.howard-aSummary: Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, where the swimming results from a self-oscillatory instability through a Hopf bifurcation. By conducting a linear stability analysis incorporating an elastohydrodynamic model, we theoretically predict the growth rates and critical conditions, which agree well with the numerical counterparts. We also propose a reduced model system consisting of a minimal elastic structure which reproduces the EEH instability. The elasto-viscous response of the composite structure is able to transform the pitchfork bifurcation into a Hopf bifurcation, leading to self-oscillation. Our results imply a new way of harnessing elastic media to engineer self-oscillations, and more generally, to manipulate and diversify the bifurcations and the corresponding instabilities. These ideas will be useful in designing soft, environmentally adaptive machines.Stability of liquid film flow laden with the soluble surfactant sodium dodecyl sulphate: predictions versus experimental data.https://zbmath.org/1460.760502021-06-15T18:09:00+00:00"Katsiavria, A."https://zbmath.org/authors/?q=ai:katsiavria.a"Bontozoglou, V."https://zbmath.org/authors/?q=ai:bontozoglou.vasilisSummary: Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear stability theory. The theory is based on a Frumkin model of adsorption equilibrium, modified by the inclusion of finite compressibility of the adsorbed monolayer. Quantitative comparison between data and theory is first attempted in the limit of infinite wavelength. Though wave characteristics are satisfactorily predicted, the theoretical critical Reynolds number is an order of magnitude below measurements. This discrepancy is understood in terms of the large difference between momentum and mass diffusivities and indicates that the assumption of infinite wavelength is far more restrictive for the mass transfer than for the flow problem. Finite-wavelength effects are taken into account by numerical solution of the Orr-Sommerfeld eigenvalue problem, leading to predictions of maximum stabilization in good agreement with the measurements. Introduction of realistic values of monolayer compressibility improves further the agreement at high surfactant loadings. Finally, a strong stabilizing effect of salinity is confirmed.Viscous and inviscid strato-rotational instability.https://zbmath.org/1460.763052021-06-15T18:09:00+00:00"Robins, Luke J. M."https://zbmath.org/authors/?q=ai:robins.luke-j-m"Kersalé, Evy"https://zbmath.org/authors/?q=ai:kersale.evy"Jones, Chris A."https://zbmath.org/authors/?q=ai:jones.chris-aSummary: We examine the critical viscous mode of the Taylor-Couette strato-rotational instability, concentrating on cases where the buoyancy frequency \(N\) and the inner cylinder rotation rate \(\Omega_{in}\) are comparable, giving a detailed account for \(N= \Omega_{in}\). The ratio of the outer to the inner cylinder rotation rates \(\mu = \Omega_{out}/ \Omega_{in}\) and the ratio of the inner to the outer cylinder radius \(\eta =r_{in}/r_{out}\) satisfy \(0< \mu <1\) and \(0< \eta <1\). We find considerable variation in the structure of the mode, and the critical Reynolds number \(Re_c\) at which the flow becomes unstable. For \(N= \Omega_{in}\), we classify different regions of the \(\eta \mu\)-plane by the critical viscous mode of each region. We find that there is a triple point in the \(\eta \mu\)-plane where three different viscous modes all onset at the same Reynolds number. We also find a discontinuous change in \(Re_c\) along a curve in the \(\eta\mu\)-plane, on one side of which exist closed unstable domains where the flow can restabilise when the Reynolds number is increased. A new form of viscous instability occurring for wide gaps has been detected. We show for the first time that there is a region of the parameter space for which the critical viscous mode at the onset of instability corresponds to the inviscid radiative instability of \textit{S. Le Dizès} and \textit{X. Riedinger} [ibid. 660, 147--161 (2010; Zbl 1205.76110)]. Focusing on small-to-moderate wavenumbers, we demonstrate that the viscous and inviscid systems are not always correlated. We explore which viscous modes relate to inviscid modes and which do not. For asymptotically large vertical wavenumbers, we have extended the inviscid analysis of \textit{J. Park} and \textit{P. Billant} [ibid. 725, 262--280 (2013; Zbl 1287.76107)] to cover the cases where \(N\) and \(\Omega_{in}\) are comparable.Buoyancy-driven unbalanced exchange flow through a horizontal opening.https://zbmath.org/1460.762972021-06-15T18:09:00+00:00"Wise, N. H."https://zbmath.org/authors/?q=ai:wise.n-h"Hunt, G. R."https://zbmath.org/authors/?q=ai:hunt.gary-rSummary: Buoyancy-driven exchange flows occur in a variety of natural and industrial situations, including nuclear and hydraulic engineering, oceanography and building ventilation. Balanced exchange flows, whereby there is simultaneously an equal volume flux transferred vertically upwards and downwards through a horizontal opening, have previously been described theoretically. However, until now there has been no theoretical description of unbalanced exchange flows, whereby the volume flux in one direction through an opening exceeds that in the other. The model developed herein examines the growth of perturbations on the density interface at an opening made in a horizontal plane that connects buoyant fluid below with denser fluid above. By considering the interface as it is advected away from the plane of the opening by a bulk flow imposed in the vertical, we quantify the exchange for the unbalanced case. The model successfully predicts the Froude number criterion, which corresponds directly to the minimum dimensionless flow rate of the imposed flow, for the onset of unbalanced exchange across circular openings found experimentally. Additionally, comparisons made between the exchanges predicted and measured show excellent agreement across the entire range of possible flows, from unidirectional flow, through unbalanced exchange to balanced exchange. Consideration is given to applications of the model to ocean outfall design and to the prediction of building ventilation flows. For natural ventilation, the theoretical model we derive for unbalanced exchange bridges the gap in the prediction of air flow rates between displacement flows, where the flow is unidirectional, and balanced exchange flows.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.Direct numerical simulation of the multimode narrowband Richtmyer-Meshkov instability.https://zbmath.org/1460.765422021-06-15T18:09:00+00:00"Groom, M."https://zbmath.org/authors/?q=ai:groom.michael"Thornber, B."https://zbmath.org/authors/?q=ai:thornber.benSummary: Early to intermediate time behaviour of the planar Richtmyer-Meshkov instability (RMI) is investigated through direct numerical simulation (DNS) of the evolution of a deterministic interfacial perturbation initiated by a \(\mathrm{Ma} = 1.84\) shock. The model problem is the well studied initial condition from the recent \(\theta\)-group collaboration [the second author et al., ``Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: the \(\theta\)-group collaboration'', Phys. Fluids 29, No. 10, Article ID 105107, 24 p. (2017; \url{doi:10.1063/1.4993464})]. A grid convergence study demonstrates that the Kolmogorov microscales are resolved by the finest grid for the entire duration of the simulation, and that both integral and spectral quantities of interest are converged. Comparisons are made with implicit large eddy simulation (ILES) results from the \(\theta\)-group collaboration, generated using the same numerical algorithm. The total amount of turbulent kinetic energy (TKE) is shown to be decreased in the DNS compared to the ILES, particularly in the transverse directions, giving rise to a greater level of anisotropy in the flow (70\% vs. 40\% more TKE in the shock parallel direction at the latest time considered). This decrease in transfer of TKE to the transverse components is shown to be due to the viscous suppression of secondary instabilities. Overall the agreement in the large scales between the DNS and ILES is very good and hence the mixing width and growth rate exponent \(\theta\) are very similar. There are substantial differences in the small scale behaviour however, with a 38\% difference observed in the minimum values obtained for the mixing fractions \(\Theta\) and \(\Xi\). Differences in the late time decay of TKE are also observed, with decay rates calculated to be \(\tau^{-1.41}\) and \(\tau^{-1.25}\) for the DNS and ILES respectively.Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness.https://zbmath.org/1460.763922021-06-15T18:09:00+00:00"Liu, Yinhui"https://zbmath.org/authors/?q=ai:liu.yinhui"Dong, Ming"https://zbmath.org/authors/?q=ai:dong.ming"Wu, Xuesong"https://zbmath.org/authors/?q=ai:wu.xuesongSummary: This paper investigates the receptivity of a supersonic boundary layer to slow acoustic waves whose characteristic frequency and wavelength are on the triple-deck scales, and the phase speed is thus asymptotically small. Acoustic waves on these scales are of special importance as they have the interesting property that a perturbation with a magnitude of \(O( \epsilon_u)\) in the free stream generates much larger, \(O( \varepsilon_u R^{1/8})\), velocity fluctuations inside the boundary layer, where \(R\) is the Reynolds number based on the distance to the leading edge. Their interaction with streamwise localized roughness elements, leading to stronger receptivity, is studied using triple-deck theory and direct numerical simulations (DNS). The receptivity coefficient, defined as the ratio of the streamwise-velocity amplitude of the instability mode excited to that of the incident free-stream acoustic wave, serves to characterize receptivity efficiency. Its dependence on the roughness width, the Reynolds number \(R\), the free-stream Mach number \(M\) and the incident angle of the acoustic wave is examined. The theoretical predictions, obtained assuming \(R\gg 1\), are found to be in quantitative agreement with the DNS results at moderate values of \(R\) when the roughness elements are located near the lower branch of the instability. The receptivity is sensitive to the incident angle (or the phase speed) of the acoustic wave, being highly effective within a small range of angles close to \(\cos^{-1}(1/M)\) and \(\pi +\cos^{-1}(1/M)\) for downstream and upstream propagating sound waves, respectively. The amplitude of the instability mode excited is proportional to the streamwise-velocity amplitude of the acoustic signature inside the boundary layer, and scales with the roughness height \(h^*\) as \((h^*/ \delta^*) R^{1/4}\), where \(\delta^*\) is the boundary-layer thickness.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.Coherent structures in the turbulent channel flow of an elastoviscoplastic fluid.https://zbmath.org/1460.764762021-06-15T18:09:00+00:00"Le Clainche, Soledad"https://zbmath.org/authors/?q=ai:le-clainche.soledad"Izbassarov, D."https://zbmath.org/authors/?q=ai:izbassarov.daulet"Rosti, M."https://zbmath.org/authors/?q=ai:rosti.marco-edoardo"Brandt, L."https://zbmath.org/authors/?q=ai:brandt.luca"Tammisola, O."https://zbmath.org/authors/?q=ai:tammisola.outiSummary: In this numerical and theoretical work, we study the turbulent channel flow of Newtonian and elastoviscoplastic fluids. The coherent structures in these flows are identified by means of higher order dynamic mode decomposition (HODMD), applied to a set of data non-equidistant in time, to reveal the role of the near-wall streaks and their breakdown, and the interplay between turbulent dynamics and non-Newtonian effects. HODMD identifies six different high-amplitude modes, which either describe the yielded flow or the yielded-unyielded flow interaction. The structure of the low- and high-frequency modes suggests that the interaction between high- and low-speed streamwise velocity structures is one of the mechanisms triggering the streak breakdown, dominant in Newtonian turbulence where we observe shorter near-wall streaks and a more chaotic dynamics. As the influence of elasticity and plasticity increases, the flow becomes more correlated in the streamwise direction, with long streaks disrupted for short times by localised perturbations, reflected in reduced drag. Finally, we present streamwise-periodic dynamic mode decomposition modes as a viable tool to describe the highly complex turbulent flows, and identify simple well-organised groups of travelling waves.Nonlinear dynamics of two-layer channel flow with soluble surfactant below or above the critical micelle concentration.https://zbmath.org/1460.760482021-06-15T18:09:00+00:00"Kalogirou, A."https://zbmath.org/authors/?q=ai:kalogirou.anna"Blyth, M. G."https://zbmath.org/authors/?q=ai:blyth.mark-gSummary: The nonlinear stability of an inertialess two-layer surfactant-laden Couette flow is considered. The two fluids are immiscible and have different thicknesses, viscosities and densities. One of the fluids is contaminated with a soluble surfactant whose concentration may be above the critical micelle concentration, in which case micelles are formed in the bulk of the fluid. A surfactant kinetic model is adopted that includes the adsorption and desorption of molecules to and from the interface, and the formation and breakup of micelles in the bulk. The lubrication approximation is applied and a strongly nonlinear system of equations is derived for the evolution of the interface and surfactant concentration at the interface, as well as the vertically averaged monomer and micelle concentrations in the bulk (as a result of fast vertical diffusion). The primary aim of this study is to determine the influence of surfactant solubility on the nonlinear dynamics. The nonlinear lubrication model is solved numerically in periodic domains and saturated travelling waves are obtained at large times. It is found that a sufficiently soluble surfactant can either destabilise or stabilise the interface depending on certain fluid properties. The stability behaviour of the system depends crucially on the values of the fluid viscosity ratio \(m\) and thickness ratio \(n\) in reference to the boundary \(m=n^2\). If the surfactant exists at large concentrations that exceed the critical micelle concentration, then long waves are stable at large times, unless density stratification effects overcome the stabilising influence of micelles. Travelling wave bifurcation branches are also calculated and the impact of various parameters (such as the domain length or fluid thickness ratio) on the wave shapes, amplitudes and speeds is examined. The mechanism responsible for interfacial (in)stability is explained in terms of the phase difference between the interface deformation and concentration waves, which is shifted according to the sign of the crucial factor \((m-n^2)\) and the strength of the surfactant solubility.Invariant states in inclined layer convection. I: Temporal transitions along dynamical connections between invariant states.https://zbmath.org/1460.763332021-06-15T18:09:00+00:00"Reetz, Florian"https://zbmath.org/authors/?q=ai:reetz.florian"Schneider, Tobias M."https://zbmath.org/authors/?q=ai:schneider.tobias-mSummary: Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number \(Pr=1.07\). Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of self-organized spatio-temporal convection patterns. Close to onset, these patterns have been explained in terms of linear stability analysis of primary and secondary flow states. At a larger temperature difference, far beyond onset, experiments and simulations show complex, dynamically evolving patterns that are not described by stability analysis and remain to be explained. Here we employ a dynamical systems approach. We construct stable and unstable exact invariant states, including equilibria and periodic orbits of the fully nonlinear three-dimensional Oberbeck-Boussinesq equations. These invariant states underlie the observed convection patterns beyond their onset. We identify state space trajectories that, starting from the unstable laminar flow, follow a sequence of dynamical connections between unstable invariant states until the dynamics approaches a stable attractor. Together, the network of dynamically connected invariant states mediates temporal transitions between coexisting invariant states and thereby supports the observed complex time-dependent dynamics in inclined layer convection.Taylor-Couette flow of polymer solutions with shear-thinning and viscoelastic rheology.https://zbmath.org/1460.760192021-06-15T18:09:00+00:00"Cagney, Neil"https://zbmath.org/authors/?q=ai:cagney.neil"Lacassagne, Tom"https://zbmath.org/authors/?q=ai:lacassagne.tom"Balabani, Stavroula"https://zbmath.org/authors/?q=ai:balabani.stavroulaSummary: We study Taylor-Couette flow of a glycerol-water mixture containing a wide range of concentration (0--2000 ppm) of xanthan gum, which induces both shear-thinning and viscoelasticity, in order to assess the effect of the changes in rheology on various flow instabilities. For each suspension, the Reynolds number (the ratio of inertial to viscous forces) is slowly increased to a peak value of around 1000, and the flow is monitored continuously using flow visualisation. Shear-thinning is found to suppress many elasticity-controlled instabilities that have been observed in previous studies of viscoelastic Taylor-Couette flow, such as diwhirls and disordered oscillations. The addition of polymers is found to reduce the critical Reynolds number for the formation of Taylor vortices, but delay the onset of wavy flow. However, in the viscoelastic regime \((\geq 1000\,\text{ppm}\) concentration), the flow becomes highly unsteady soon after the formation of Taylor vortices, with substantial changes in the waviness with Reynolds number, which are shown to be highly repeatable. Vortices are found to suddenly merge as the Reynolds number increases, with the number of mergers increasing with polymer concentration. These abrupt changes in wavelength are highly hysteretic and can occur in both steady and wavy regimes. Finally, the vortices in moderate and dense polymer solutions are shown to undergo a gradual drift in both their size and position, which appears to be closely linked to the splitting and merger of vortices.Linear, nonlinear and transitional regimes of second-mode instability.https://zbmath.org/1460.766722021-06-15T18:09:00+00:00"Unnikrishnan, S."https://zbmath.org/authors/?q=ai:unnikrishnan.sanil"Gaitonde, Datta V."https://zbmath.org/authors/?q=ai:gaitonde.datta-vSummary: The evolution of the potent second-mode instability in hypersonic boundary layers (HBLs) is examined holistically, by tracking its linear and nonlinear evolution, followed by its role in initiating transition and eventual breakdown of the HBL into a fully turbulent state. Linear stability theory is utilized to first identify the features of the second-mode wave after \(FS\)-synchronization. These are then employed in separate linearly and nonlinearly forced two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations (DNS). The nonlinear 2-D DNS shows saturation of the fundamental frequency, and the resulting superharmonics induce tightly braided `rope-like' patterns near the generalized inflection point (GIP). The instability exhibits a second region of growth constituted by the fundamental frequency downstream of the primary envelope, which is absent in the linear scenario. Subsequent fully 3-D DNS identify this region as crucial in amplifying oblique instabilities riding on the 2-D second-mode `rollers'. This results in lambda vortices below the GIP, which are detached from the rollers in the inner boundary layer. Streamwise vortex-stretching results in a localized peak in length scales inside the HBL, eventually forming hairpin vortices. Spectral analyses track the transformation of harmonic peaks into a turbulent spectrum. The appearance of oblique modes at the fundamental frequency suggests that fundamental resonance is the most dominant mechanism of transition. The bispectrum reveals coupled nonlinear interactions between the fundamental and its superharmonics leading to spectral broadening, as well as traces of subharmonic resonance. The global forms of the fundamental and subharmonic modes show that the former disintegrate at the location of spanwise breakdown, beyond which the latter amplify. Statistical analyses of the near-wall flow field indicate an increase in large-scale `splatting' motions immediately following transition, resulting in extreme skin-friction events, which equilibrate as turbulence sets in. Fundamental resonance results in complete breakdown of streamwise streaks in the lower log-layer, ultimately resulting in a fully turbulent HBL.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.Stability of fluid flows coupled by a deformable solid layer.https://zbmath.org/1460.763092021-06-15T18:09:00+00:00"Patne, Ramkarn"https://zbmath.org/authors/?q=ai:patne.ramkarn"Ramon, Guy Z."https://zbmath.org/authors/?q=ai:ramon.guy-zSummary: Fluid flows coupled by a deformable solid layer (DS) may be found in both natural and industrial settings. To analyse the stability of such systems, we consider plane Couette flows coupled by a DS. The shear stress exerted by the flowing fluids on the DS leads to its deformation, coupling the motion in each fluid. We demonstrate that, as a consequence of the coupling and irrespective of the thickness of the DS, a viscous instability exists, which can lead to absolute instability at sufficiently high dimensionless speed of the lower plate. The predicted instability apparently arises due to the energy exchange between the fluids and DS via the tangential velocities at the interface. A linear elasticity model for the DS is employed, removing the non-physical growth rate predicted by previous models. A spatio-temporal analysis further reveals the existence of an absolute instability. Insight on this instability could be potentially utilised in manipulating mixing in microfluidic systems and membrane separation as well as for understanding morphologies evolving during membrane formation via interfacial polymerisation.Stability of hexagonal pattern in Rayleigh-Bénard convection for thermodependent shear-thinning fluids.https://zbmath.org/1460.760162021-06-15T18:09:00+00:00"Varé, T."https://zbmath.org/authors/?q=ai:vare.t"Nouar, Chérif"https://zbmath.org/authors/?q=ai:nouar.cherif"Métivier, C."https://zbmath.org/authors/?q=ai:metivier.christel"Bouteraa, M."https://zbmath.org/authors/?q=ai:bouteraa.mSummary: Stability of hexagonal patterns in Rayleigh-Bénard convection for shear-thinning fluids with temperature-dependent viscosity is studied in the framework of amplitude equations. The rheological behaviour of the fluid is described by the Carreau model and the relationship between the viscosity and the temperature is of exponential type. Ginzburg-Landau equations including non-variational quadratic spatial terms are derived explicitly from the basic hydrodynamic equations using a multiple scale expansion. The stability of hexagonal patterns towards spatially uniform disturbances (amplitude instabilities) and to long wavelength perturbations (phase instabilities) is analysed for different values of the shear-thinning degree \(\alpha\) of the fluid and the ratio \(r\) of the viscosities between the top and bottom walls. It is shown that the amplitude stability domain shrinks with increasing shear-thinning effects and increases with increasing the viscosity ratio \(r\). Concerning the phase stability domain which confines the range of stable wavenumbers, it is shown that it is closed for low values of \(r\) and becomes open and asymmetric for moderate values of \(r\). With increasing shear-thinning effects, the phase stability domain becomes more decentred towards higher values of the wavenumber. Beyond the stability limits, two different modes go unstable: longitudinal and transverse modes. For the parameters considered here, the longitudinal mode is relevant only in a small region close to the onset. The nonlinear evolution of the transverse phase instability is investigated by numerical integration of amplitude equations. The hexagon-roll transition triggered by the transverse phase instability for sufficiently large reduced Rayleigh number \(\epsilon\) is illustrated.Electrohydrodynamic droplet formation in a T-junction microfluidic device.https://zbmath.org/1460.769372021-06-15T18:09:00+00:00"Singh, R."https://zbmath.org/authors/?q=ai:singh.roshani|singh.rishi-pal|singh.robin-vikram|singh.ravindra-pratap|singh.ranveer|singh.rita|singh.rajrupa|singh.ripudaman|singh.rattan|singh.rana-p|singh.raj-narain|singh.rayman-preet|singh.rajwinder|singh.rishi-n|singh.ram-sakal|singh.ramanpreet|singh.rajiv-kumar|singh.ram-nandan-p|singh.rajnish-kumar|singh.ram-mehar|singh.rama-krishna|singh.ram-binoy|singh.ramkaran|singh.ram-nawal|singh.ram-gopal|singh.rajinder-pal|singh.rishi-ranjan|singh.raj-narayan|singh.renu|singh.ram-naresh|singh.ran-vir|singh.ritesh-k|singh.robby|singh.raghavendra|singh.rajeshwar-prasad|singh.rajdeep|singh.ramendra-p|singh.raghu-nath|singh.ramanand|singh.rajesh-pratap|singh.ramji|singh.rajiv-r-p|singh.rajkumar-brojen|singh.randheer|singh.ramesh-kumar|singh.radhey-s|singh.rupen-pratap|singh.rajmeet|singh.rattandeep|singh.ram-narayan|singh.ravinder.2|singh.ravi-p|singh.rameshwar|singh.ramandeep|singh.rakeshwar|singh.rajat-kumar|singh.rajpal|singh.raushan|singh.raj-kishor|singh.r-t|singh.richa|singh.raghvendra|singh.rajesh-kumar|singh.rajindar|singh.ram-veer|singh.ratna|singh.reshma|singh.r-k-tarachand|singh.rohit-r|singh.rajendra-prasad|singh.raman-p|singh.rituraj|singh.rajkeshar|singh.r-a|singh.rishi-ram-h-n|singh.rekha|singh.ravendra|singh.ranbir|singh.ritambhara|singh.rashmi|singh.roli|singh.ranjit-j|singh.rajvir|singh.randhir|singh.rahul-kumar|singh.ruchi|singh.rasphal|singh.ram-kishore|singh.rishabh|singh.rakhi|singh.ram-chandra|singh.r-k-p|singh.rajeev-kumar|singh.rajani|singh.ranjeet-k|singh.ranveer-kumar|singh.rajneesh-kumar|singh.r-d|singh.raghuraj|singh.raghuvansh-p|singh.rajbir|singh.rangi|singh.reen-nripjeet"Bahga, S. S."https://zbmath.org/authors/?q=ai:bahga.supreet-s"Gupta, A."https://zbmath.org/authors/?q=ai:gupta.anubhav|gupta.asish|gupta.archana|gupta.alakananda|gupta.ashutosh|gupta.abhinav|gupta.abhishek-kr|gupta.anupama|gupta.amit-kumar|gupta.anubha|gupta.anu|gupta.amitabha|gupta.asit-kumar|gupta.akanksha|gupta.abha|gupta.abhijit-kar|gupta.awadhesh-chandra|gupta.arnab|gupta.ankur|gupta.arvind-kumar|gupta.anil-kumar|gupta.anoop-k|gupta.arushi|gupta.ansraj|gupta.anurag-p|gupta.ashu|gupta.amritava|gupta.anindita-sen|gupta.akshat|gupta.alok-kumar|gupta.anirudh|gupta.ashim-das|gupta.ankita|gupta.anadi-shankar|gupta.akshya-kumar|gupta.arobinda|gupta.alpana|gupta.anuradha|gupta.arpan|gupta.arindam|gupta.anshuman|gupta.at|gupta.animesh|gupta.aastha|gupta.ashok-ji|gupta.ashish|gupta.anuj|gupta.arun-kumar|gupta.asha|gupta.anand-p|gupta.anupam|gupta.ashok-kumar|gupta.anita|gupta.abhineet|gupta.ankit.2|dasgupta.anirban|gupta.abhimanyu|gupta.anant|gupta.anjali|gupta.akhilesh-kumar|gupta.anila|gupta.alka|gupta.ajaya-kumar|gupta.anindya|gupta.ayush|gupta.amar|gupta.a-n|gupta.amitava|gupta.a-datta|gupta.ananya|gupta.anupam.1|gupta.aniket|gupta.anjana|gupta.aparna|gupta.ajaykumar|gupta.aarti|gupta.anshu|gupta.amarnath|gupta.apurv|gupta.ashan|gupta.atual|gupta.anshul|gupta.anju-rani|gupta.ankit.1|gupta.anjulika|gupta.arjun-k|gupta.ajay-k|gupta.atul|gupta.aman|gupta.anjanSummary: An experimental investigation of droplet formation induced by an external electric field in a T-shaped microfluidic device is presented. The effect of electric field is reported for scenarios where the hydrodynamics is known to be governed by the cumulative effect of hydrodynamic pressure and interfacial tension acting on the liquid-liquid interface. Experiments reveal that the electrohydrodynamic phenomena transforms the droplet formation mechanism by inducing pinning of the dispersed phase to the channel wall, leading to a significant decrease in the droplet filling time and hence a decrease in the size of droplets generated. The experimental observations are used to formulate a correlation between the droplet size, applied electric field, fluid properties and flow parameters. A mechanistic explanation of droplet formation process using a mathematical model is also presented. Simulations reveal that the droplets are formed primarily due to normal electric stress acting on the liquid-liquid interface. The electric stress results in a distinct feature of pinning and early onset of neck formation of the emerging dispersed phase, leading to a reduction in the size of the droplet formed for the same hydrodynamic conditions. The findings reported demonstrate that an applied electric field has the potential to produce relatively smaller-sized droplets than that possible through hydrodynamics alone.Steady Rayleigh-Bénard convection between stress-free boundaries.https://zbmath.org/1460.763222021-06-15T18:09:00+00:00"Wen, Baole"https://zbmath.org/authors/?q=ai:wen.baole"Goluskin, David"https://zbmath.org/authors/?q=ai:goluskin.david"Leduc, Matthew"https://zbmath.org/authors/?q=ai:leduc.matthew"Chini, Gregory P."https://zbmath.org/authors/?q=ai:chini.gregory-p"Doering, Charles R."https://zbmath.org/authors/?q=ai:doering.charles-rSummary: Steady two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios \(\pi /5\leqslant \Gamma \leqslant 4\pi\), where \(\Gamma\) is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, \(10^3\leqslant Ra\leqslant 10^{11}\), and four orders of magnitude in the Prandtl number, \(10^{-2}\leqslant Pr\leqslant 10^2\). At large \(Ra\) where steady rolls are dynamically unstable, the computed rolls display \(Ra \rightarrow \infty\) asymptotic scaling. In this regime, the Nusselt number \(Nu\) that measures heat transport scales as \(Ra^{1/3}\) uniformly in \(Pr\). The prefactor of this scaling depends on \(\varGamma\) and is largest at \(\Gamma \approx 1.9\). The Reynolds number \(Re\) for large-\(Ra\) rolls scales as \(Pr^{-1} Ra^{2/3}\) with a prefactor that is largest at \(\Gamma \approx 4.5\). All of these large-\(Ra\) features agree quantitatively with the semi-analytical asymptotic solutions constructed by \textit{G. P. Chini} and \textit{S. M. Cox} [Phys. Fluids 21, No. 8, Paper No. 083603, 15 p. (2009; Zbl 1183.76148)]. Convergence of \(Nu\) and \(Re\) to their asymptotic scalings occurs more slowly when \(Pr\) is larger and when \(\Gamma\) is smaller.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}.On the effect of free-stream turbulence on boundary-layer transition.https://zbmath.org/1460.763832021-06-15T18:09:00+00:00"Fransson, Jens H. M."https://zbmath.org/authors/?q=ai:fransson.jens-h-m"Shahinfar, Shahab"https://zbmath.org/authors/?q=ai:shahinfar.shahabSummary: Free-stream turbulence (FST) and its effect on boundary-layer transition is an intricate problem. Elongated unsteady streamwise streaks of low and high speed are created inside the boundary layer and their amplitude and spanwise wavelength are believed to be important for the onset of transition. The transitional Reynolds number is often simply correlated with the turbulence intensity \((Tu)\), and the characteristic length scales of the FST are often considered to have a small to negligible influence on the transition location. Here, we present new results from a large experimental measurement campaign, where both the \(Tu\) and the integral length scale \((\Lambda_x)\) are varied \((1.8\% <Tu<6.2\%; 16 \text{mm}< \Lambda_x < 26\text{mm})\). In the current experiments it has been noted that on the one hand, for small \(Tu\), an increase in \(\Lambda_x\) advances transition, which is in agreement with established results. On the other hand, for large \(Tu\), an increase in \(\Lambda_x\) postpones transition. This trend can be explained by the fact that an optimal ratio between FST length scale and boundary-layer thickness at transition onset exists. Furthermore, our results strengthen the fact that the streaks play a key role in the transition process by showing a clear dependence of the FST characteristics on their spanwise scale. Our measurements show that the aspect ratio of the streaky structures correlates with an FST Reynolds number and that the aspect ratio can change by a factor of two at the location of transition. Finally, we derive a semi-empirical transition prediction model, which is able to predict the influence of \(\Lambda_x\) for both small and high values of \(Tu\).The magnetised Richtmyer-Meshkov instability in two-fluid plasmas.https://zbmath.org/1460.769452021-06-15T18:09:00+00:00"Bond, Daryl"https://zbmath.org/authors/?q=ai:bond.daryl"Wheatley, V."https://zbmath.org/authors/?q=ai:wheatley.v"Li, Y."https://zbmath.org/authors/?q=ai:li.yuanman|li.yueru|li.yezhen|li.yuanjiang|li.yanqiao|li.yiwen|li.yetong|li.yicheng|li.yuanchao|li.yingcheng|li.youcheng|li.yanchu|li.yincan|li.yuanchuan|li.yaochong|li.youcai|li.yuanchun|li.yuchao|li.yuechen|li.yanchao|li.yingchun|li.yanchun|li.yuancheng|li.yongci|li.yichen|li.youchao|li.yucheng|li.yuechao|li.yichao|li.yuchen|li.yingchen|li.yancang|li.yichuan|li.yingchuan|li.yichu|li.yachao|li.yachen|li.yance|li.yancai|li.yingchao|li.yangchun|li.yuchun|li.yuancen|li.yachun|li.yancheng|li.yongchao|li.yuncheng|li.yunchuan|li.yuqiao|li.yongqin|li.yongjie|li.yuguang|li.yuzhou|li.yunhui|li.yongzhe|li.yi|li.yaqian|li.yumao|li.yingguang|li.yugao|li.yuying|li.yemo|li.yuze|li.yungao|li.yongfu|li.yajie|li.yibiao|li.yafeng|li.yutian|li.yuning|li.yiqin|li.yang.4|li.yonghong|li.yiyun|li.yanqing|li.yuping|li.yanyan.1|li.yuyuan|li.yanzhe|li.yadong|li.yezhou|li.yan.2|li.yongfan|li.yanzhao|li.yunxian|li.yanting|li.yunlu|li.yingjun|li.yiming|li.youfa|li.yaofei|li.yaoxian|li.yingkun|li.yanming|li.yunshan|li.yiquan|li.yazhou|li.yude|li.yanhua|li.yanan|li.yangmin|li.yi.5|li.yabei|li.yusha|li.yingfa|li.yuye|li.yibin|li.yannan|li.yuanmei|li.youkui|li.yameng|li.yanwu|li.yinxing|li.yingguo|li.yongzhuang|li.yixing|li.yalian|li.yunzhang|li.yunze|li.yimin|li.yongle|li.yongmin|li.yingxiong|li.yan.4|li.yunhe|li.yan.5|li.yafei|li.yunhua|li.yadan|li.yanpo|li.yutong|li.yibing|li.yihua|li.yuanbo|li.yuzhu|li.yan|li.yanbiao|li.yile|li.yanfang|li.yuji|li.yiguo|li.youtang|li.youfeng|li.yuelong|li.yanmin|li.yuqian|li.yinghai|li.yongfei|li.yushan|li.yueshuang|li.yanbao|li.yijie|li.yao|li.yuannan|li.yungui|li.yanlai|li.yuan|li.yongqun|li.yaning|li.yuansheng|li.yannian|li.yufen|li.yongxun|li.yejun|li.yangsheng|li.yongwu|li.yangda|li.yaotong|li.yuanlong|li.ying|li.y-charles|li.yingqiu|li.yaching|li.yanwen|li.yonglong|li.youde|li.yuanjun|li.yunmeng|li.yu|li.yangjia|li.yanbo|li.yonglin|li.yejia|li.yong.6|li.yunke|li.yanglin|li.yinshi|li.yongchi|li.yongyue|li.yanfeng|li.yanghui|li.yingxing|li.yehua|li.yalin|li.yusheng|li.yuesheng|li.ye.4|li.yubao|li.yilong|li.yiting|li.yuanzheng|li.yaokuang|li.yaxiang|li.yinsheng|li.yong.9|li.yunyu|li.yuzhi|li.yintang|li.yuanzhen|li.yinwan|li.yunli|li.yuanjian|li.yulan|li.yuexian|li.yajuan|li.yuanping|li.youning|li.yueheng|li.yiyi|li.yinghong|li.yanzhong|li.yazhi|li.yunyang|li.yong.5|li.yayun|li.yuanqunig|li.yoksheung|li.yugang|li.yibei|li.youqin|li.yongxing|li.yajian|li.yingzi|li.yukun|li.yilin|li.yushuang|li.yanling.1|li.youbao|li.yewen|li.yanxiong|li.youming|li.yufan|li.youai|li.yanda|li.yonbing|li.yujiao|li.yongxin|li.yingxiang|li.yinhua|li.yuejuan|li.yeqing|li.yunfeng|li.yuanlu|li.yingshu|li.yingzhen|li.yihu|li.yingbo|li.yunqun|li.yingfu|li.yinting|li.yuwen|li.ye.3|li.yaqiong|li.yongtao|li.yanbing|li.yuming|li.youyun|li.yifei|li.yuejiao|li.yunzhao|li.yusi|li.yanli|li.yaguang|li.yongmei|li.yuxiu|li.yongsen|li.yongming.2|li.yingqing|li.yuanzhi|li.yong.7|li.yuhan|li.yaoyao|li.yixin|li.yhilin|li.yinping|li.yunqing|li.yubai|li.yixun|li.yaoguo|li.yonggang|li.yinzhen|li.yuexin|li.yanlin|li.yuanmin|li.yufei.2|li.youmei|li.yun|li.yanbin|li.yuheng|li.yaoting|li.yanxia|li.yin|li.yaliang|li.yulong|li.yuxiang.1|li.yongping|li.yuzhe|li.yanpeng|li.yingjiu|li.youwen|li.yuqiang|li.yuhong|li.yongquan|li.yaowu|li.yinjie|li.yingxue|li.yourun|li.yansheng|li.yong.4|li.yanlu|li.yunfei|li.yi.2|li.ya|li.yudong|li.yiyong|li.youping|li.yining|li.yongkun.1|li.yongqing|li.yinian|li.yanzhi|li.yanhui|li.yuquan|li.yunghua|li.yuyu|li.yan.6|li.yapeng|li.yingke|li.yongzhong|li.yuke|li.yongzhi|li.yujia|li.yangming|li.yongming|li.yunyun|li.yi.4|li.yamei|li.yuewu|li.yanxi|li.yanjuan|li.yonggong|li.yuanzhang|li.yuanke|li.yuliang|li.yunxiang|li.yanning|li.yiqing|li.yelian|li.yitong|li.yishhen|li.yuandan|li.yina|li.yaling|li.yingxu|li.yuan.1|li.yingping|li.yongxiong|li.yang.2|li.yongxiang|li.yonghua|li.yongfang|li.yuqin|li.yuanyou|li.yongjian|li.yaxian|li.yangxi|li.yuling|li.yongfeng|li.yuqing|li.youlin|li.yuwei|li.youguang|li.yinglin|li.yuexia|li.yuenan|li.youyu|li.yingzhe|li.yibao|li.yueqiu|li.yongku|li.yufei.1|li.yalei|li.yongdong|li.yantao|li.yan.3|li.yalan|li.yinshan|li.yamin|li.yitian|li.yuepeng|li.yuebo|li.yingkui|li.yijiang|li.yuanxi|li.you|li.yanlei|li.yiwei|li.yueting|li.yinxin|li.yunzhi|li.yongkun|li.yingkai|li.yaqin|li.yipin|li.yonghui|li.yurong|li.yipeng|li.yonqing|li.yongwei|li.yishun|li.yikang|li.yiren|li.yongliang|li.yingzhi|li.yingda|li.yan.8|li.yiteng|li.yongsun|li.yuefeng|li.yizeng|li.yongnian|li.yinqiu|li.yuanxing|li.yunzhang.1|li.yawen|li.yuezhi|li.yanping|li.yinglei|li.yantong|li.yijing|li.yongxiang.1|li.ying.2|li.yaolong|li.yinguo|li.yeting|li.yuanxiao|li.yinghua|li.yangming.1|li.yongshan|li.yujuan|li.youwei|li.yuxia|li.yifeng|li.yahong|li.yue|li.yongbo|li.yongqiu|li.yingnan|li.yukui|li.yinguang|li.yaqiao|li.yuehua|li.yuru|li.yunpeng|li.yangrong|li.yunliang|li.youhu|li.yulian|li.yongzhen|li.yuting|li.yunxia|li.yifu|li.yingjian|li.youmou|li.yaoyi|li.yongjun|li.yanjing|li.yangfan|li.yugui|li.yugi|li.yufang|li.yinya|li.yuyan|li.yongzhao|li.yixuan|li.yuxiong|li.yunqiang|li.yuanxia|li.yahui|li.yawei|li.youzhi|li.yiqun|li.yujian|li.yongjiang|li.yisheng|li.yaya|li.yujun|li.yuzhuo|li.yongyu|li.yanshen|li.yinbo|li.yishen|li.yudan|li.yansu|li.yuanming|li.ye|li.yanhai|li.yunhong|li.yefeng|li.yajing|li.yaxin|li.yixue|li.yuxi|li.yaohang|li.yankai|li.yizhe|li.yunan|li.yunzhou|li.yinkui|li.yifang|li.yuanzhou|li.yang.5|li.yongyin|li.yongning|li.yixia|li.yunyi|li.yaotang|li.yongxian|li.yanying|li.yaoqiang|li.yatao|li.yang|li.yalu|li.yaxu|li.yaxing|li.yueping|li.yajun|li.yabo|li.yanling|li.yangang|li.youquan|li.yuanqin|li.yuanfu|li.yongli|li.yinbin|li.yanlong|li.yuanxuan|li.yueyang|li.yinshen|li.yukai|li.yunxin|li.yangbo|li.yupeng|li.yuntong|li.yingmin|li.yizhong|li.yangjun|li.yongbin|li.yongming.1|li.yueqiao|li.yizhou|li.yuanzhong|li.ying.3|li.yueliang|li.yuan.3|li.yi.3|li.yonghe|li.yuren|li.yubo|li.yanjiang|li.yanqin|li.yaochen|li.yidong|li.yixiao|li.yunxiao|li.yiyang|li.yifan|li.yichun|li.yuanhua|li.yong.3|li.yongyao|li.yeping|li.yimei|li.yingming|li.yunkai|li.yinghui|li.yongqian|li.yongjiu|li.yinxue|li.yanmeng|li.yifa|li.yaowen|li.yunnan|li.yongyan|li.yuxiao|li.yuhuan|li.yanni|li.yuanshu|li.yanran|li.yanjiao|li.yanjun|li.yongjiao|li.yingtai|li.yunfan|li.yanrui|li.yiyu|li.yishan|li.yingfang|li.yan.1|li.yexue|li.yansong|li.yushu|li.yaping|li.yongnan|li.yuntao|li.yaochang|li.yongling|li.yunsong|li.yuelin|li.yunlong|li.yingmei|li.yumeng|li.yanyin|li.yuanxin|li.yanru|li.yinxiang|li.yinong|li.yemei|li.yonghai|li.yang.3|li.yikai|li.yongqiang|li.yongbing|li.yiqian|li.yingying|li.yingwei|li.yingshan|li.you-rong|li.yan.9|li.yiqiong|li.yongshu|li.yaohong|li.yongjing|li.yingjie|li.yuanyuan|li.yiping|li.yuxin|li.yiqiang.1|li.yarun|li.yunxi|li.yanjie|li.yan.7|li.yineng|li.yongan|li.yingyi|li.yizheng|li.yuqi|li.yanmei|li.yinfei|li.yaojun|li.yangcheng|li.yuexiang|li.yuhang|li.yunyan|li.yesong|li.yali|li.yongkai|li.yunlei|li.yunbo|li.yongtong|li.yingqi|li.ye.1|li.yinhong|li.yumei|li.yanyun|li.yanhong|li.yuhua|li.yinfan|li.yongjin|li.yueqing|li.youyan|li.yanxin|li.yanta|li.yuanfei|li.yanheng|li.yanzhen|li.yanshu|li.yong.8|li.yaan|li.yuanxu|li.yihuan|li.yaduan|li.youjuan|li.yinan|li.yuanxie|li.yan.10|li.yulin|li.yaohui|li.yingsong|li.yingqin|li.yuanhong|li.yafang|li.yanqiu|li.yujie|li.yuanqing|li.yusong|li.yanyan|li.yuhui|li.yumiao|li.yihlang|li.yiou|li.yaoyiran|li.yijun|li.yiqiang|li.yuntu|li.yueming|li.yueyue|li.yanshuo|li.yueling|li.yuxuan|li.yanxiao|li.yongsheng|li.yongge|li.yongkui|li.yili|li.yaoyong|li.yaming|li.yunde|li.ying.1|li.yuang|li.yuxiang|li.yongshun|li.yaoxing|li.youfu|li.yi.1|li.yuguo|li.yuanxiang|li.yanzhang|li.yaowei|li.yexin|li.yongqi|li.yihong|li.yonggan|li.yinquan|li.yanlun|li.yuanlin|li.yangyang|li.yiran|li.yuanjie|li.yingli|li.yundong|li.yiqi|li.yingde|li.yuanhan|li.yiliang|li.yanzhou|li.yih|li.yuankai|li.yangxue|li.yueying|li.yuewen|li.yufeng|li.yaxun|li.yakun|li.yadai|li.yazhe|li.yinglan|li.yaqing.1|li.yihao"Samtaney, R."https://zbmath.org/authors/?q=ai:samtaney.ravi"Pullin, D. I."https://zbmath.org/authors/?q=ai:pullin.dale-iSummary: We investigate the effects of magnetisation on the two-fluid plasma Richtmyer-Meshkov instability of a single-mode thermal interface using a computational approach. The initial magnetic field is normal to the mean interface location. Results are presented for a magnetic interaction parameter of 0.1 and plasma skin depths ranging from 0.1 to 10 perturbation wavelengths. These are compared to initially unmagnetised and neutral fluid cases. The electron flow is found to be constrained to lie along the magnetic field lines resulting in significant longitudinal flow features that interact strongly with the ion fluid. The presence of an initial magnetic field is shown to suppress the growth of the initial interface perturbation with effectiveness determined by plasma length scale. Suppression of the instability is attributed to the magnetic field's contribution to the Lorentz force. This acts to rotate the vorticity vector in each fluid about the local magnetic-field vector leading to cyclic inversion and transport of the out-of-plane vorticity that drives perturbation growth. The transport of vorticity along field lines increases with decreasing plasma length scales and the wave packets responsible for vorticity transport begin to coalesce. In general, the two-fluid plasma Richtmyer-Meshkov instability is found to be suppressed through the action of the imposed magnetic field with increasing effectiveness as plasma length scale is decreased. For the conditions investigated, a critical skin depth for instability suppression is estimated.Linear stability and saddle-node bifurcation of electromagnetically driven electrolyte flow in an annular layer.https://zbmath.org/1460.763262021-06-15T18:09:00+00:00"McCloughan, John"https://zbmath.org/authors/?q=ai:mccloughan.john"Suslov, Sergey A."https://zbmath.org/authors/?q=ai:suslov.sergey-aSummary: Comprehensive linear stability study of flow in an annular layer of electrolyte driven by the action of the Lorentz force is conducted following the analysis of steady axisymmetric solutions of \textit{S. A. Suslov} et al. [ibid. 828, 573--600 (2017; Zbl 1460.76939)]. It is shown that an experimentally observed instability in the form of anticyclonic moving vortices reported in [\textit{J. Pérez-Barrera} et al., ``Instability of electrolyte flow driven by an azimuthal Lorentz force'', Magnetohydrodynamics 51, No. 2, 203--213 (2015), \url{http://mhd.sal.lv/contents/2015/2/MG.51.2.4.R.html}] develops on a background of the basic flow consisting of two tori with the opposite azimuthal vorticity components. It is found that, while the background flow is driven electromagnetically, the appearance of vortices is purely due to hydrodynamic effects: shear of the flow and centrifugal inertial forcing. The current study has also revealed that the unstable two-torus basic flow has a stable single-torus counterpart, both emanating from a saddle-node bifurcation of steady states when the Lorentz force is sufficiently strong. The transition from a one-torus to two-torus flow at weaker forcing is abrupt and leads to the appearance of vortices as soon as it occurs. The ranges of layer depths and Reynolds numbers for which vortices develop on a steady background are determined. Subsequently, weakly nonlinear amplitude expansion is used to find an approximate unsteady solution beyond the saddle-node bifurcation.Marangoni instabilities associated with heated surfactant-laden falling films.https://zbmath.org/1460.760422021-06-15T18:09:00+00:00"D'Alessio, S. J. D."https://zbmath.org/authors/?q=ai:dalessio.s-j-d"Pascal, J. P."https://zbmath.org/authors/?q=ai:pascal.j-p"Ellaban, E."https://zbmath.org/authors/?q=ai:ellaban.e"Ruyer-Quil, C."https://zbmath.org/authors/?q=ai:ruyer-quil.christianSummary: Investigated in this paper is the stability of the gravity-driven flow of a liquid layer laden with soluble surfactant down a heated incline. A mathematical model incorporating variations in surface tension with surfactant concentration and temperature has been formulated. A linear stability analysis is carried out both asymptotically for small wavenumbers and numerically for arbitrary wavenumbers. An expression for the critical Reynolds number has been derived which accounts for thermocapillary and solutocapillary effects, and reduces to known documented results for special cases. Also, a nonlinear reduced model has been derived using weighted residuals, and solved numerically to simulate the instability of the equilibrium flow and the development of permanent surface waves that arise. The nonlinear simulations were found to be in good agreement with the linear stability analysis.A new instability for Boussinesq-type equations.https://zbmath.org/1460.763292021-06-15T18:09:00+00:00"Kirby, James T."https://zbmath.org/authors/?q=ai:kirby.james-tSummary: A wide class of problems for free-surface gravity waves fall into a weakly dispersive regime, in which wavelength is large compared to water depth, and wave phase speed differs by a small amount from the speed \(c_0=\sqrt{gh}\) of shallow-water waves. The resulting problem is treated naturally using Taylor series expansions of dependent variables in the vertical coordinate, leading to a class of models that are collectively referred to here as Boussinesq-type models. \textit{P. A. Madsen} and \textit{D. R. Fuhrman} [ibid. 889, Article ID A38, 25 p. (2020; Zbl 1460.76102)] have recently shown that certain members of this broad class of models are subject to a high-wavenumber instability, which can grow rapidly when the elevation of the wave trough is sufficiently depressed below the mean water surface. This newly revealed instability may provide an explanation for the modelling community's frequent observations of noisy behaviour in Boussinesq-type model calculations.On the linear stability of vortex columns in the energy space.https://zbmath.org/1460.763402021-06-15T18:09:00+00:00"Gallay, Thierry"https://zbmath.org/authors/?q=ai:gallay.thierry"Smets, Didier"https://zbmath.org/authors/?q=ai:smets.didierSummary: We investigate the linear stability of inviscid columnar vortices with respect to finite energy perturbations. For a large class of vortex profiles, we show that the linearized evolution group has a sub-exponential growth in time, which means that the associated growth bound is equal to zero. This implies in particular that the spectrum of the linearized operator is entirely contained in the imaginary axis. This contribution complements the results of our previous work [Anal. PDE 13, No. 6, 1777--1832 (2020; Zbl 1454.35267)], where spectral stability was established for the linearized operator in the enstrophy space.