Recent zbMATH articles in MSC 76Ehttps://zbmath.org/atom/cc/76E2023-11-13T18:48:18.785376ZWerkzeugSparse Aitken-Schwarz domain decomposition with application to Darcy flowhttps://zbmath.org/1521.651342023-11-13T18:48:18.785376Z"Berenguer, L."https://zbmath.org/authors/?q=ai:berenguer.laurent"Tromeur-Dervout, D."https://zbmath.org/authors/?q=ai:tromeur-dervout.damienSummary: This paper focuses on the acceleration of the Schwarz method by the Aitken's acceleration of the convergence technique by considering the special structure of the Schwarz's error operator between two consecutive iterates on the domain decomposition's interfaces. The new proposed method, called Sparse Aitken-Schwarz method, builds a low-rank space for each subdomain to approximate the true solution on its interfaces instead of building a low-rank space associated to the gathered subdomains' interfaces solution as the Aitken-Schwarz technique does. We show that the resulting method is better than the full GMRES method applied to the global interface problem as the low-rank space generated is a space whose dimension is larger than the size of Krylov space for the same number of local solving. The Sparse Aitken-Schwarz has better robustness to noise than the Aitken-Schwarz. Weak and strong scaling results on a two-level parallel implementation show the improvements of the Sparse Aitken-Schwarz over the Aitken-Schwarz on a 3D Darcy flow application with randomly distributed permeability fields with high contrast values [the first author et al., Comput. Fluids 80, 320--326 (2013; Zbl 1284.76349)].Vortex-wave interaction on the surface of a spherehttps://zbmath.org/1521.760722023-11-13T18:48:18.785376Z"Nelson, Rhodri B."https://zbmath.org/authors/?q=ai:nelson.rhodri-b"McDonald, N. Robb"https://zbmath.org/authors/?q=ai:mcdonald.n-robbSummary: The time-dependent interaction of a point vortex with a vorticity jump separating regions of opposite signed and constant vorticities on the surface of a non-rotating sphere is examined. First, small amplitude interfacial waves are considered where linear theory is applicable. A point vortex in a region of same-signed vorticity will initially move away from the interface and a point vortex in a region of opposite-signed vorticity will move towards it. Weak vortices sufficiently far from the interface then undergo meridional oscillation while precessing about the sphere. The sense of azimuthal precession is determined by the sign of the vorticity jump at the interface. It is demonstrated by both linear and nonlinear theories that a vortex at a pole in a region of same-signed vorticity is a stable equilibrium whereas a vortex at a pole in a region of opposite-signed vorticity is an unstable equilibrium. Numerical computations using contour dynamics confirm these results and the dynamics of more nonlinear cases are examined.Direct and inverse problems on the joint movement of the three viscous liquids in the flat layershttps://zbmath.org/1521.760902023-11-13T18:48:18.785376Z"Lemeshkova, Elena N."https://zbmath.org/authors/?q=ai:lemeshkova.elena-nikolaevnaSummary: The exact stationary decision of the problem about the joint movement of the three viscous liquids in the flat layers has been found. The decision of the direct and inverse non-stationary problem has been given in the form of the final analytical formulas using the method of Laplas transformation. The following statement has been proved: if a gradient of the pressure in one liquid has a final limit, then the decision is located on a stationary mode. Also for a problem about the ``the flooded layer'' movement it has been shown that velocities converge to the different constants with the time growth.On the initial-boundary problem for thermocapillary motion of an emulsion in spacehttps://zbmath.org/1521.760942023-11-13T18:48:18.785376Z"Petrova, Anna G."https://zbmath.org/authors/?q=ai:petrova.anna-georgevnaSummary: The paper is devoted to the study of the initial-boundary problem for thermocapillary motion of an emulsion in closed bounded domain with sufficiently smooth boundary in the absence of gravity. With the use of Tikhonov-Shauder fixed point theorem the local in time solvability to the problem with zero mean volume velocity of the mixture and zero heat flux on the boundary is proved.Correlation between vorticity, Liutex and shear in boundary layer transitionhttps://zbmath.org/1521.761052023-11-13T18:48:18.785376Z"Dong, Xiangrui"https://zbmath.org/authors/?q=ai:dong.xiangrui"Hao, Chunyang"https://zbmath.org/authors/?q=ai:hao.chunyang"Liu, Chaoqun"https://zbmath.org/authors/?q=ai:liu.chaoqunSummary: Correlation analysis on the vorticity, Liutex and the anti-symmetric shear, is discussed in this paper based on the new introduced vortex definition of Liutex, to explore the mechanism of the vortex generation in laminar flow transition and the relation between the fluctuation and the rotation. Compared with the volume vorticity as a good measurement to evaluate the statistical fluctuations, a new concept named volume Liutex is introduced in this study to predict the turbulence, which is an accurate yardstick to quantitatively evaluate the degree of the transition from laminar flow to turbulence. A relatively high correlation between the fluctuation and the rotation is discovered in the transitional flow. It is found that the laminar flow transition must be promoted by transforming the anti-symmetric shear to the rotation; the fluctuation of the flow in transition is mainly caused by the flow rotation, or, the turbulence is caused by Liutex generation and growth. In addition, the Reynolds stress is found concentrated in the surrounding area of the vortex core which has a high Liutex value inside.Stationary flow of three fluids in a flat layer under the influence of thermocapillary forces and pressure differencehttps://zbmath.org/1521.761222023-11-13T18:48:18.785376Z"Lemeshkova, Elena N."https://zbmath.org/authors/?q=ai:lemeshkova.elena-nikolaevnaSummary: The unidirectional movement of the three viscous liquids under the influence of thermocapillary forces and pressure difference in a layer restricted by solid walls was researched. The exact stationary decision of the problem has been found.Spatiotemporal linear stability of viscoelastic subdiffusive channel flows: a fractional calculus frameworkhttps://zbmath.org/1521.761272023-11-13T18:48:18.785376Z"Chauhan, Tanisha"https://zbmath.org/authors/?q=ai:chauhan.tanisha"Bansal, Diksha"https://zbmath.org/authors/?q=ai:bansal.diksha"Sircar, Sarthok"https://zbmath.org/authors/?q=ai:sircar.sarthokSummary: The temporal and spatiotemporal linear stability analyses of viscoelastic, subdiffusive, plane Poiseuille flow obeying the Fractional Upper Convected Maxwell (FUCM) equation in the limit of low to moderate Reynolds number (Re) and Weissenberg number (We) is reported to identify the regions of topological transition of the advancing flow interface. In particular, we demonstrate how the exponent of the power-law scaling \((t^\alpha\), with \(0<\alpha\le 1)\) in viscoelastic microscale models [\textit{T. G. Mason} and \textit{D. A. Weitz}, Phys. Rev. Lett. 74, No. 5, 1250--1253 (1995; \url{doi:10.1103/PhysRevLett.74.1250})] is related to the fractional order of the time derivative, \(\alpha\), of the corresponding non-linear stress constitutive equation in the continuum. The stability studies are limited to two exponents: monomer diffusion in Rouse chain melts, \(\alpha=1/2\), and in Zimm chain solutions, \(\alpha=2/3\). The temporal stability analysis indicates that with decreasing order of the fractional derivative (a) the most unstable mode decreases with decreasing values of \(\alpha\), (b) the peak of the most unstable mode shifts to lower values of Re, and (c) the peak of the most unstable mode, for the Rouse model precipitates towards the limit \(Re\to 0\). The Briggs idea of analytic continuation is deployed to classify regions of temporal stability, absolute and convective instabilities, and evanescent modes. The spatiotemporal phase diagram indicates an abnormal region of temporal stability at high fluid inertia, revealing the presence of a non-homogeneous environment with hindered flow, thus highlighting the potential of the model to effectively capture certain experimentally observed, flow-instability transition in subdiffusive flows.Linear instabilities of pulsatile plane channel flow between compliant wallshttps://zbmath.org/1521.761282023-11-13T18:48:18.785376Z"Lebbal, Smail"https://zbmath.org/authors/?q=ai:lebbal.smail"Alizard, Frédéric"https://zbmath.org/authors/?q=ai:alizard.frederic"Pier, Benoît"https://zbmath.org/authors/?q=ai:pier.benoitSummary: The linear dynamics of perturbations developing in an infinite channel with compliant walls is investigated for pulsatile flow conditions. Two-dimensional modal perturbations are considered for Womersley-type pulsating base flows and the wall motion is only allowed in the normal direction. It is found that the flow dynamics is mainly governed by four control parameters: the Reynolds number \(Re\), the reduced velocity \(V_R\), the Womersley number \(Wo\) and the amplitude of the base-flow modulation \(\tilde{Q}\). Linear stability analyses are carried out within the framework of Floquet theory, implementing an efficient approach for removing spurious eigenmodes. The characteristics of flow-based (Tollmien-Schlichting) and wall-based (both travelling-wave flutter and divergence) modes are investigated over a large control-parameter space. It is shown that travelling-wave flutter (TWF) modes are predominantly influenced by the reduced velocity and that the Reynolds number has only a marginal effect. The critical reduced velocity (corresponding to onset of linear instability) is demonstrated to depend both on the Womersley number and modulation amplitude for a given set of wall parameters. Similarly to the steady flow case, the Tollmien-Schlichting (TS) mode is also found to be only weakly affected by the flexibility of the wall in pulsatile flow conditions. Finally, the classification given by \textit{T. B. Benjamin} [J. Fluid Mech. 16, 436--450 (1963; Zbl 0116.19103)] is found to be too restrictive in the case of pulsatile base flows. In particular, a new type of mode is identified that shares characteristics of two distinct Floquet eigenmodes: TS and TWF modes. Due to coupling of the different Floquet harmonics, a phenomenon specific to time-periodic base flows, this two-wave mode exhibits a beating over the intracyclic dynamics.Relevance of two- and three-dimensional disturbance field explained with linear stability analysis of Orr-Sommerfeld equation by compound matrix methodhttps://zbmath.org/1521.761292023-11-13T18:48:18.785376Z"Maddipati, Raj"https://zbmath.org/authors/?q=ai:maddipati.raj"Sengupta, Tapan K."https://zbmath.org/authors/?q=ai:sengupta.tapan-kumar"Sundaram, Prasannabalaji"https://zbmath.org/authors/?q=ai:sundaram.prasannabalajiSummary: Three-dimensional Orr-Sommerfeld equation is analyzed by compound-matrix method to explain the relevance of two- and three-dimensional wall excitations with respect to three-dimensional direct simulation results presented in
[\textit{P. K. Sharma} and \textit{T. K. Sengupta}, ``Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation'', Phys. Fluids 31, No. 6, Article ID 064107 (2019; \url{doi:10.1063/1.5097272})].
Physical variables are considered in a finite spanwise domain which allows us to consider spanwise wavenumber \(\beta\) as the higher harmonics of fundamental spanwise mode \(\beta_0\) defined by the spanwise domain. Linear stability analysis is performed for various cases with different spanwise wavenumber and neutral curves are generated in both spatial and temporal frameworks. Even though the neutral curves appear different, the critical Reynolds number remains same for all spanwise excitation wavenumbers. The significance of neutral curve in either spatial, or temporal or spatio-temporal frameworks is explained for both modal and non-modal component of the response field. It is shown that as spanwise wavenumber of input excitation increases, the critical Reynolds number increases, while the spatial amplification rate \(\alpha_i\) decreases. Thus, this establishes that increasing three-dimensionality of input excitation will shown enhanced stability of the flow, and helps one to understand the three-dimensional direct simulation of receptivity analysis for wall excitation reported very recently.Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow-thermodynamics interactionshttps://zbmath.org/1521.761302023-11-13T18:48:18.785376Z"Sharma, Bajrang"https://zbmath.org/authors/?q=ai:sharma.bajrang"Girimaji, Sharath S."https://zbmath.org/authors/?q=ai:girimaji.sharath-sSummary: Hydrodynamic stability of compressible boundary layers is strongly influenced by the Mach number (\(M\)), Prandtl number (\(Pr\)) and thermal wall boundary condition. These effects manifest on the flow stability via the flow-thermodynamics interactions. Comprehensive understanding of stability flow physics is of fundamental interest and important for developing predictive tools and closure models for integrated transition-to-turbulence computations. The flow-thermodynamics interactions are examined using linear analysis and direct numerical simulations in the following parameter regime: \(0.5 \leq M \leq 8\); and \(0.5 \leq Pr \leq 1.3\). For the adiabatic wall boundary condition, increasing Prandtl number has a destabilizing effect. In this work, we characterize the behaviour of production, pressure-strain correlation and pressure dilatation as functions of the Mach and Prandtl numbers. First and second instability modes exhibit similar stability trends but the underlying flow physics is shown to be diametrically opposite. The Prandtl number influence on instability is explicated in terms of the base flow profile with respect to the different perturbation mode shapes.Linear inviscid damping in Sobolev and Gevrey spaceshttps://zbmath.org/1521.761312023-11-13T18:48:18.785376Z"Zillinger, Christian"https://zbmath.org/authors/?q=ai:zillinger.christianIn recent years, the asymptotic stability of the two-dimensional incompressible Euler equation
\[\partial_tv+v\cdot\nabla v+\nabla p=0\]
near shear flow solutions \(v = (U(y),0)\) has been an area of very active research.
In [Arch. Ration. Mech. Anal. 235, No. 2, 1327--1355 (2020; Zbl 1434.35079)], \textit{H. Jia} established linear inviscid damping in Gevrey spaces for compactly supported Gevrey regular shear flows in a finite channel. In the present article, the author provides an alternative short proof of stability in Gevrey spaces for those flows which admit an approach by a Fourier-based Lyapunov functional. Furthermore, in the setting of a finite channel, one does not need to assume compact support but only pertubations vanishing to infinite order. The author also establishes Sobolev stability results for perturbations vanishing to finite order.
Reviewer: Raphaël Danchin (Paris)Stability and dynamics of the flow past a bullet-shaped blunt body moving in a pipehttps://zbmath.org/1521.761322023-11-13T18:48:18.785376Z"Bonnefis, Paul"https://zbmath.org/authors/?q=ai:bonnefis.paul"Fabre, David"https://zbmath.org/authors/?q=ai:fabre.david"Airiau, Christophe"https://zbmath.org/authors/?q=ai:airiau.christopheSummary: The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation. A cartography of the bifurcation curves is provided thanks to LSA, covering the range of parameters corresponding to Reynolds number \(Re = [50\text{--}110]\), confinement ratio \(a/A = [ 0.01\text{--}0.92]\) and length-to-diameter ratio \(L/d = [2\text{--}10]\). Results show that the first bifurcation is always a steady bifurcation associated to a non-oscillating eigenmode with azimuthal wavenumber \(m = \pm1\) leading to a steady state with planar symmetry. For weakly confined cases (\(a/A<0.6\)), the second bifurcation is associated to an oscillating mode with azimuthal wavenumber \(m=\pm 1\), as in the unconfined case. On the other hand, for the strongly confined case (\(a/A>0.8\)), a destabilization of non-oscillating modes with \(|m| = 2,3\) and a restabilization of the \(m = \pm1\) eigenmodes are observed. The aspect ratio \(L/d\) is shown to have a minor influence for weakly confined cases and almost no influence for strongly confined cases. Direct numerical simulation is subsequently used to characterize the nonlinear dynamics. The results confirm the steady bifurcation predicted by LSA with excellent agreement for the threshold Reynolds. For weakly confined cases, the second bifurcation is a Hopf bifurcation leading to a periodic, planar-symmetric state in qualitative accordance with LSA predictions. For more confined cases, more complex dynamics is obtained, including a steady state with \(|m| = 3\) geometry and aperiodic states.Study of the effect of magnetic field characteristics on Rayleigh-Taylor instability with density gradient layershttps://zbmath.org/1521.761332023-11-13T18:48:18.785376Z"Peng, Cheng"https://zbmath.org/authors/?q=ai:peng.cheng"Chu, Mengran"https://zbmath.org/authors/?q=ai:chu.mengran"Song, Youya"https://zbmath.org/authors/?q=ai:song.youya"Deng, Jian"https://zbmath.org/authors/?q=ai:deng.jian"Wu, Jiang"https://zbmath.org/authors/?q=ai:wu.jiang.1Summary: Inertial confinement fusion (ICF) is a possible path of fusion technology for fusion ignition, but during the implosion of a magnetized plasma target by compression, the magnetic Rayleigh-Taylor (R-T) instability similar to that at the interface of the denser and less dense phases can arise when the plasma is subjected to gravitational and magnetic forces, which in turn affect the confinement characteristic and the process of fusion burn. In this study, the R-T instability of two phases in the presence/ absence of a magnetic field in a two-dimensional rectangular duct is simulated based on the MHD model adopted in ANSYS FLUENT. The simulation results show that the R-T instability is substantially weakened for the case with an Atwood number of 0.29 where a constant (DC) magnetic field is imposed in the opposite direction to the gravitational acceleration, meanwhile, a strong countercurrent flow, which occurs near the side walls, enhances the heat and mass transport process, which is related to the M-shape velocity profile formed in the flow channel. Besides, when a DC magnetic field perpendicular to the direction of the gravitational acceleration is introduced, the R-T instability vanishes from the initial moment to the end. When a sinusoidal wave form of varying (AC) magnetic field is introduced, the R-T instability is substantially facilitated. The evolutions of the interface and pressure field distribution are significantly correlated with the change in intensity and direction of the AC magnetic field. After about one cycle of the magnetic field's variation, the density gradient layers in the vertical direction are entirely converted to a density stratification in the horizontal direction with the denser phase occupying the region near the sidewalls of the duct, and ever since then, the R-T instability disappears completely. These findings can provide supports for the design of nuclear fusion devices and magnetic fields.Temporal instability characteristics of Rayleigh-Taylor and Kelvin-Helmholtz mechanisms of an inviscid cylindrical interfacehttps://zbmath.org/1521.761342023-11-13T18:48:18.785376Z"Vadivukkarasan, M."https://zbmath.org/authors/?q=ai:vadivukkarasan.mSummary: The stability characteristics of an inviscid, incompressible and immiscible cylindrical interface are examined using linear temporal theory. The cylindrical interface is subjected to two instability mechanisms, namely Rayleigh-Taylor (R-T) and Kelvin-Helmholtz (K-H) instabilities. The combined action of R-T and K-H in the presence of surface tension is investigated for a hollow jet in an unbounded liquid medium and reported. The problem includes the motion in an axial direction (K-H mechanism) and the radial direction (R-T mechanism) to destabilize the interface. The instability behavior is described by a few operating parameters, namely, Bond number (\(Bo\)), Weber number (\(We\)) and Atwood number (\(A\)). Here, Bond number is attributed to R-T instability whereas Weber number is attributed to K-H instability. The temporal analysis reveals that the Bond number plays a significant role in determining the dominant growth rate, most unstable axial wavenumber and cut-off axial wavenumber. Furthermore, it is also shown through dimensionless energy budget arguments, even a small amount of energy in the radial motion causes the most unstable wavenumber associated with primary atomization to increase significantly.Asymptotic scale-dependent stability of surface quasi-geostrophic vortices: semi-analytic resultshttps://zbmath.org/1521.761352023-11-13T18:48:18.785376Z"Badin, G."https://zbmath.org/authors/?q=ai:badin.gualtiero"Poulin, F. J."https://zbmath.org/authors/?q=ai:poulin.francis-jSummary: The scale-dependent stability of surface quasi-geostrophic (SQG) vortices is studied both analytically and numerically. In particular, we study the sensitivity of the stability of SQG vortices on a nondimensional number \(\sigma\), namely the square root of the Burger number, which sets the transition scale between different dynamical regimes corresponding to local and nonlocal dynamics. We analyse the stability of two different examples. The first example is given by a Rankine vortex, characterised by constant buoyancy. For this case, asymptotic analysis suggests that the frequencies of the perturbations at scales smaller than the transition scale show a \(\sigma^{-1}\) dependence. At scales larger than the transition scale, the frequencies scale instead like \(\sigma^{-2}\). The second example consists of a Rankine vortex shielded by a filament characterised by a different value of constant buoyancy. For this example we study the dispersion relation for the perturbations for the cases in which the inner vortex and the outer filament have different asymptotic properties behaviour.Numerical investigation on the influence of different physical factors on the interface evolution in 3D RTI using CLSVOF methodhttps://zbmath.org/1521.761362023-11-13T18:48:18.785376Z"Li, Y. L."https://zbmath.org/authors/?q=ai:li.yinlin|li.yilun|li.yanling.2|li.yilong|li.yulin|li.yilei|li.yaolong|li.yulan|li.yanlei|li.yanli|li.yile|li.yalin|li.yuanlong|li.yongliang|li.yuliang|li.yuelong|li.yalei|li.yanlong|li.yinglin|li.yanlu|li.yuanlin.2|li.yuelei|li.yalong|li.yelian|li.yulong|li.yunlong|li.yuling|li.yueliang|li.yongle|li.yiliang|li.yueling|li.yilin|li.yuanlu|li.yingli|li.yongling|li.yuelin|li.yanlai|li.yulian|li.yanling|li.yunlei|li.yunliang|li.yili|li.yaling|li.yanglin|li.yalu|li.yonglong|li.yalian|li.yanlun|li.yuan-li|li.yonglin|li.yunliu|li.yinglan|li.yanlin|li.yali|li.yunli|li.yalan|li.yaliang|li.yongli|li.yunlu|li.yinglei|li.ying-le|li.yulu|li.youlin|li.yanheng-li"Wu, T. C."https://zbmath.org/authors/?q=ai:wu.tsu-chen|wu.tzong-chen|wu.tsu-cheng|wu.tiancai|wu.tsui-chou|wu.tzu-chiang|wu.tian-cherng|wu.teng-cao|wu.tu-cheng|wu.tsaur-chin|wu.tsung-cheng|wu.tsu-chin"Ma, C. P."https://zbmath.org/authors/?q=ai:ma.chupeng|ma.chunping"Jiang, D. P."https://zbmath.org/authors/?q=ai:jiang.dongping|jiang.dapeng|jiang.depeng|jiang.dapeiSummary: The three-dimensional (3D) Rayleigh-Taylor instability (RTI) problem is numerically investigated using the coupled level set and volume of fluid (CLSVOF) method. The CLSVOF method combines the level set and volume of fluid methods to ensure good mass conservation performance, enabling the curvature of the interface captured by numerical simulations to be accurately calculated. A classical single-mode RTI (with only one ``mushroom'' generated under the initial setting) is adopted for numerical verification, and the shape of the interface and the penetration depth with respect to time are determined. Based on this initial two-dimensional single-mode RTI problem, the influence of factors such as the surface tension, density ratio, Reynolds number, and viscosity ratio on the 3D effects caused by the velocity gradient on both sides of the interface are thoroughly analyzed. This analysis allows us to obtain the basic laws governing the influence of different physical factors on the 3D effects of the RTI.Role of unstable thermal stratifications on the Rayleigh-Taylor instabilityhttps://zbmath.org/1521.761372023-11-13T18:48:18.785376Z"Sengupta, Aditi"https://zbmath.org/authors/?q=ai:sengupta.aditi"Verma, Atul Kumar"https://zbmath.org/authors/?q=ai:verma.atul-kumar|verma.atul-kumar.1Summary: Three-dimensional simulations of Rayleigh-Taylor instability (RTI) at the interface of two masses of air are performed by solving the compressible Navier-Stokes equation, following the numerical implementation in \textit{Role of non-zero bulk viscosity in three-dimensional Rayleigh-Taylor instability: Beyond Stokes' hypothesis} -- the first author et al. [ibid. 225, Article ID 104995, 15 p. (2021; Zbl 1521.76142)]. The effect of thermal gradients on the RTI is explored by considering two temperature differences between the air masses, \(\Delta T= 21.75K\) and 46.5K, corresponding to Atwood numbers \((A_t)\) of 0.035 and 0.073. The flow is studied in an isolated box with non-periodic walls along three directions. A non-conducting interface, initially separating the two air masses, is removed at the onset of the numerical experiment. The stages in the evolution of the RTI are explored via the enstrophy transport equation (ETE). The contributions from vortex stretching, viscous diffusion and dissipation are quantified for different thermal gradients, showing completely different dynamics. For both \(A_t\) considered, the viscous dissipation term is found to dominate across the stages of RTI evolution, with vortex stretching becoming prominent beyond the development of spikes and bubbles in the mixing layer. For \(A_t = 0.035\), two interpenetrating rows of bubbles are noted, whereas, for \(A_t =0.073\), an alternating row of bubbles and spikes are noted with a 19\% rise in the growth rate of the mixing layer. The present simulations have been experimentally validated for a combined Kelvin-Helmholtz Rayleigh-Taylor instability (KHRTI). It is found that the vortical structures, representative of the KH instability, are stretched and diffused due to the buoyancy-driven RT mechanism.Structural stability of a porous channel of electrical flow affected by periodic velocitieshttps://zbmath.org/1521.761382023-11-13T18:48:18.785376Z"Alkharashi, Sameh A."https://zbmath.org/authors/?q=ai:alkharashi.sameh-a"Alotaibi, Wafa"https://zbmath.org/authors/?q=ai:alotaibi.wafaSummary: This paper investigates the effect of periodic velocity on the stability of two interfacial waves propagating between three layers of immiscible incompressible fluids. The flow propagates saturated in porous media under the influence of an electric field. The viscous potential theory is used to simplify the mathematical procedure, by which viscosity is accumulated on the separating surface rather than in the bulk of fluids. The dispersion relation is shown to be the result of coupled simultaneous Mathieu equations with complex coefficients. The mathematical difficulty in delaying the two Mathieu equations was overcome using the method of multiple time scales. The stability was discussed analytically and numerically by drawing some diagrams and obtaining the transition curves. In the presence and absence of stream periodicity, the linear stage of interface progress is visualized. Depending on the physical quantities used, it has been determined that the upper fluid speed dampens the wave more than the lower and middle velocities. It was discovered that the viscosity ratio of the upper interface, as opposed to the lower viscosity ratio, helps stabilize the liquid sheet. The upper layer porosity has a dual role depending on the sensitivity and significance of the sheet thickness.One-dimensional nonlinear parametric instability of inhomogeneous plasma: time domain problemhttps://zbmath.org/1521.761392023-11-13T18:48:18.785376Z"Gerasimenko, N. V."https://zbmath.org/authors/?q=ai:gerasimenko.n-v"Trukhachev, F. M."https://zbmath.org/authors/?q=ai:trukhachev.f-m"Gusakov, E. Z."https://zbmath.org/authors/?q=ai:gusakov.e-z"Simonchik, L. V."https://zbmath.org/authors/?q=ai:simonchik.l-v"Tomov, A. V."https://zbmath.org/authors/?q=ai:tomov.a-v(no abstract)Interaction ultrasound pulse with ferromagnet plate in magnetoelastic resonance conditionhttps://zbmath.org/1521.761402023-11-13T18:48:18.785376Z"Peĭsakhovich, Yuriĭ G."https://zbmath.org/authors/?q=ai:peisakhovich.yurii-g"Shtygashev, Aleksandr A."https://zbmath.org/authors/?q=ai:shtygashev.aleksandr-aSummary: The scattering of ultrasound wave packet which normally falls on ferromagnetic plate near of magnetoelastic resonance is studied. The spectra of reflection and transmission amplitude contain zeros and poles connected with elastic and spin clockwised polarized waves coupling. Two types of zeros and poles responsibles for evolution of wave field. The quasistationary state connected with quasispin wave poles can be induced in the thin plates. The role of quasiacoustic wave poles arise in the thick plates. The decay times and form are calculated.The effect of initial amplitude and convergence ratio on instability development and deposited fluctuating kinetic energy in the single-mode Richtmyer-Meshkov instability in spherical implosionshttps://zbmath.org/1521.761412023-11-13T18:48:18.785376Z"Heidt, Liam"https://zbmath.org/authors/?q=ai:heidt.liam"Flaig, M."https://zbmath.org/authors/?q=ai:flaig.m"Thornber, B."https://zbmath.org/authors/?q=ai:thornber.ben|thornber.b-j-rSummary: This paper investigates the growth of perturbations on the inner surface of a dense imploding spherical shell due to hydrodynamic instabilities. The perturbations change in amplitude due to Richtmyer-Meshkov instability and Rayleigh-Taylor instability, geometric convergence, and compressibility. Two mode numbers \(( \ell = 5 , 50)\) and three different perturbation amplitudes \(( a_0 = 0.1 \lambda , 0.01 \lambda , 0.001 \lambda )\) are applied to the surface of the dense inner shell. Two independent codes were used to perform simulations with these six perturbation profiles at four convergence ratios, ranging from 3.6 to 7.3, for a total of 48 cases. The mixing layer amplitudes show good agreement between the two simulation codes across the range of convergence ratios, mode numbers, and initial amplitudes. The growth of the mixing layer is employed to validate an extension of a recently proposed Bell-Plesset model, showing good agreement across the range of convergence ratios. Persistent and substantial shock-deposited fluctuating kinetic energy is observed within the light core, away from the perturbed interface. Temporal evolution of fluctuating kinetic energy indicates a time delay between the peak radial and theta directions, consistent with a build-up of vortical motion. A ``jet'' like phenomena is observed at the peaks and troughs of the initial perturbations in both simulation codes across a variety of cases. It is postulated that these occur due to the shape singularity shown to develop in spatially periodic perturbed planar shock waves in ideal gas dynamics. Significant anisotropy of kinetic energy components is present at all times.Role of non-zero bulk viscosity in three-dimensional Rayleigh-Taylor instability: beyond Stokes' hypothesishttps://zbmath.org/1521.761422023-11-13T18:48:18.785376Z"Sengupta, Aditi"https://zbmath.org/authors/?q=ai:sengupta.aditi"Samuel, Roshan J."https://zbmath.org/authors/?q=ai:samuel.roshan-j"Sundaram, Prasannabalaji"https://zbmath.org/authors/?q=ai:sundaram.prasannabalaji"Sengupta, Tapan K."https://zbmath.org/authors/?q=ai:sengupta.tapan-kumarSummary: Three-dimensional direct numerical simulations (DNS) of Rayleigh-Taylor instability (RTI) at the interface of two masses of air with a sharp temperature gradient of 149 K are performed by solving the compressible Navier-Stokes equation (NSE). The flow is studied in an isolated box with non-periodic walls along the three directions. A non-conducting interface separating the two air masses is impulsively removed at the onset of the instability. No external perturbation has been used at the interface to instigate the instability at the onset, corresponding to practical scenarios in experiments. Computations have been carried out for the two configurations reported by
\textit{K. I. Read} [``Experimental investigation of turbulent mixing by Rayleigh-Taylor instability'', Physica D 12, No. 1--3, 45--58 (1984; \url{doi:10.1016/0167-2789(84)90513-X})]. The compressible formulation is free from the Boussinesq approximation commonly used for solving the incompressible NSE. The role of non-zero bulk viscosity is quantified by using a model from acoustic attenuation measurements for the bulk viscosity of air. Effects of Stokes' hypothesis on the onset of RTI and the growth of mixing layer are reported. The incipient stage is shown to have a strong dependence on the constitutive relation used. The small-scale billowing motion is only observed for non-zero bulk viscosities. Following this stage, the growth rates for bubbles and spikes in the mixing layer are found to be underpredicted by 12\% with the use of Stokes' hypothesis. The results imply that the evolution of RTI from the onset to the fully turbulent regime is best captured by using non-zero values of the bulk viscosity.Non-local hydrodynamics as a slow manifold for the one-dimensional kinetic equationhttps://zbmath.org/1521.761432023-11-13T18:48:18.785376Z"Kogelbauer, Florian"https://zbmath.org/authors/?q=ai:kogelbauer.florianSummary: We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the Chapman-Enskog expansion for small relaxation times. Our results rely on the spectral theory of Jacobi operators with rank-one perturbations.Effect of waveform on turbulence transition in pulsatile pipe flowhttps://zbmath.org/1521.761512023-11-13T18:48:18.785376Z"Morón, Daniel"https://zbmath.org/authors/?q=ai:moron.daniel"Feldmann, Daniel"https://zbmath.org/authors/?q=ai:feldmann.daniel"Avila, Marc"https://zbmath.org/authors/?q=ai:avila.marcSummary: Pulsatile flow in a straight pipe is a model system for unsteady internal flows in industrial engineering and physiology. In some parameter regimes, the laminar flow is susceptible to helical perturbations, whose transient energy growth scales exponentially with the Reynolds number (\textit{Re}). In this paper, we link the transient growth of these perturbations to the instantaneous linear instability of the laminar flow. We exploit this link to study the effect of the waveform on turbulence transition by performing linear stability and transient growth analyses of flows driven with different waveforms. We find a higher-energy growth in flows driven with longer low-velocity phases as well as with steeper deceleration and acceleration phases. Finally, we perform direct numerical simulations and show that cases with larger transient growth transition faster to turbulence and exhibit larger turbulence intensities. However, these same cases are also more prone to relaminarisation once turbulence has been established. This highlights that, in pulsatile flows, the linear mechanisms responsible for turbulence transition are distinctly different from the nonlinear mechanisms sustaining turbulence.Numerical investigations of Rayleigh-Taylor instability with a density gradient layerhttps://zbmath.org/1521.762512023-11-13T18:48:18.785376Z"Song, Yang"https://zbmath.org/authors/?q=ai:song.yang"Wang, Pei"https://zbmath.org/authors/?q=ai:wang.pei.3"Wang, Lili"https://zbmath.org/authors/?q=ai:wang.lili.9Summary: The Rayleigh-Taylor instability (RTI) with a density gradient layer was investigated by implicit large eddy simulations (ILES) in a framework of three dimensional compressible multiphase flow with the single fluid approximation. The simulations are firstly initialized by multi-mode random perturbations in classic RTI and the associated case with a premixed layer. It is found that the late time behaviours of the turbulent mixing layer in classic and premixed cases are similar although an initial premixed layer slows down the growth of the turbulent mixing layer significantly. A variety of flow quantities for different cases are compared and studied at different time. In addition, the turbulent mixing caused by RTI with a single-mode dominated perturbation is investigated in classic and premixed cases. Different stages are identified for the time evolution of turbulent mixing layer. The dynamics of bubble-spike structures at early time, and the production and transfer of turbulent kinetic energy at late time are expatiated. Typical quantities of turbulent mixing are also summarized. It is found that there is an inactive stage before the fast growth of bubble-spike structures with an initial premixed layer and the spectra need more time to adjust until the flow turns to a self-similar regime.The early-time dynamics of Rayleigh-Taylor mixing with a premixed layerhttps://zbmath.org/1521.762522023-11-13T18:48:18.785376Z"Song, Yang"https://zbmath.org/authors/?q=ai:song.yang"Wang, Pei"https://zbmath.org/authors/?q=ai:wang.pei.3"Wang, Lili"https://zbmath.org/authors/?q=ai:wang.lili.9"Ma, Dongjun"https://zbmath.org/authors/?q=ai:ma.dongjun"He, Anmin"https://zbmath.org/authors/?q=ai:he.anmin"Chen, Dawei"https://zbmath.org/authors/?q=ai:chen.dawei.1"Fan, Zhengfeng"https://zbmath.org/authors/?q=ai:fan.zhengfeng"Ma, Zongqiang"https://zbmath.org/authors/?q=ai:ma.zongqiang"Wang, Jianguo"https://zbmath.org/authors/?q=ai:wang.jianguo|wang.jianguo.1Summary: The early-time dynamics of Rayleigh-Taylor instability with a premixed density gradient layer was investigated by three-dimensional implicit large eddy simulation. Compared with the classic Rayleigh-Taylor instability, it was found that the mixing layer undergoes an inactive stage when the mixing width of the layer is nearly unchanged. The development of hydrodynamic instability with a premixed layer was studied. Energy transfer and vortex generation at the early time show that span-wise vortices predominate at this stage. Afterwards, initial conditions including the parameters of initial perturbations and the mixing width of premixed layer were investigated in detail. In our study, it was found that the amplitude of initial perturbations and the width of premixed layer are important for determining the characteristic time scale of the inactive stage while the wave number has less effect. The influence of initial conditions on the early-time dynamics of mixing layer was also analysed.Corrigendum to: ``Linear stability analysis on the most unstable frequencies of supersonic flat-plate boundary layers''https://zbmath.org/1521.762942023-11-13T18:48:18.785376Z"Guo, Peixu"https://zbmath.org/authors/?q=ai:guo.peixu"Gao, Zhenxun"https://zbmath.org/authors/?q=ai:gao.zhenxun"Jiang, Chongwen"https://zbmath.org/authors/?q=ai:jiang.chongwen"Lee, Chun-Hian"https://zbmath.org/authors/?q=ai:lee.chunhianCorrects a typo in the first paragraph of Section 4.4, p. 5 in the authors' paper [Comput. Fluids 197, Article ID 104394, 16 p. (2020; Zbl 1519.76117)].Cell-centered Lagrangian scheme for multi-material flows with pressure equilibrationhttps://zbmath.org/1521.764512023-11-13T18:48:18.785376Z"Manach-Pérennou, B."https://zbmath.org/authors/?q=ai:manach-perennou.b"Chauvin, R."https://zbmath.org/authors/?q=ai:chauvin.remi"Guisset, S."https://zbmath.org/authors/?q=ai:guisset.sebastien"Llor, A."https://zbmath.org/authors/?q=ai:llor.antoineSummary: A cell-centered Lagrangian scheme is presented for a multi-material hydrodynamics model with equilibrated material pressures. The scheme is conservative in mass, momentum, and total energy while being entropic per material. This last point is critical for various engineering applications but is seldom addressed. The entropy production in each material is taken as an arbitrary part of the global entropy production hence mimicking different viscosity operators and the underlying vanishing viscosity solution. The scheme is applied to various 1 or 2-dimensional test cases where materials have highly contrasted equations of state. These challenging test cases confirm the robustness of the scheme and show that pressures are kept equal up to the scheme order or even strictly if an additional equilibration procedure is added.Investigation on shear layer instabilities and generation of vortices during shock wave and boundary layer interactionhttps://zbmath.org/1521.765522023-11-13T18:48:18.785376Z"Kundu, Abhishek"https://zbmath.org/authors/?q=ai:kundu.abhishek"Thangadurai, Murugan"https://zbmath.org/authors/?q=ai:thangadurai.murugan"Biswas, Gautam"https://zbmath.org/authors/?q=ai:biswas.gautamSummary: The interaction of a reflected shock with the boundary layer inside the shock tubes is an important engineering problem. Studies related to shock wave mitigation and attenuation are performed inside the shock tubes. A proper understanding of the flow behind the reflected shock and the separated zone involving multiple vortical structures is highly essential for estimating the effectiveness of the shock wave mitigation/ attenuation. Such complex flows consist of Lambda shock, shear layer originating from the triple point, multiple shocklets, Mach stems, and vortices. Experimentally the shock structures are obtained through optical techniques. The vortices present in the compressible flow can be obtained through numerical simulations. The complex flows consisting of the above- mentioned features have been simulated numerically so far for the Reynolds numbers up to 1000
[\textit{G. Zhou} et al., ``Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube'', Phys. Fluids 30, No. 1, Article ID 016102, 21 p. (2018; \url{doi:10.1063/1.4998300})]. In the present investigation, the shock-wave boundary-layer interaction is simulated for the Reynolds numbers of 1000 and 2500 using a 13th order hybrid scheme to discern the distinct flow features. First, the solver
[\textit{A. Kundu} and \textit{S. De}, Comput. Fluids 157, 131--145 (2017; Zbl 1390.76587)]
was validated with the benchmark wall density data for a Reynolds number of 1000. Next, the simulations were performed using 50 and 109.5 million cells for the Reynolds number of 2500. The density gradients, vorticity, wall density, and Fourier spectra were used for comparing the flow field for the Reynolds numbers of interest. The Lambda shock, Kelvin-Helmholtz (K-H) vortices in the shear layer, shocklets, the height of lambda shock, and Mach stems were obtained using a grid-mesh of 109.5 million cells. It is observed that the number of vortices generated inside the separated flow region increased with the increase in Reynolds number from 1000 to 2500. Furthermore, the triple point height and the number of K-H vortices generated at the shear layer also increase with an increase in Reynolds number. The present simulations revealed the formation of vortices close to the wall at a Reynolds number of 2500. Such flow structures have an important role in shock / blast wave mitigation and the associated aeroacoustics.Global spectral analysis of the Lax-Wendroff-central difference scheme applied to convection-diffusion equationhttps://zbmath.org/1521.765852023-11-13T18:48:18.785376Z"Sengupta, Soumyo"https://zbmath.org/authors/?q=ai:sengupta.soumyo"N. A., Sreejith"https://zbmath.org/authors/?q=ai:n-a.sreejith"Mohanamuraly, Pavanakumar"https://zbmath.org/authors/?q=ai:mohanamuraly.pavanakumar"Staffelbach, Gabriel"https://zbmath.org/authors/?q=ai:staffelbach.gabriel"Gicquel, Laurent"https://zbmath.org/authors/?q=ai:gicquel.laurent-yves-marcelSummary: In this work, the Global Spectral Analysis (GSA) is applied to the convective Lax-Wendroff based discretization of linear convection-diffusion problem in both 1D and 2D. Contrary to standard numerical analysis approaches, two important physical processes (convection and diffusion) are treated together, thus making GSA a function of multiple non-dimensional numerical parameters, namely, the non-dimensional wavenumber (kh), the Courant-Friedrich-Lewy number (Nc) and the Peclet number (Pe). All the three quantities impact the stability of the numerical scheme by affecting both numerical amplification factor as well as numerical diffusion. Likewise, numerical phase speed and numerical group velocity all become expressions of all three non-dimensional parameters. Leveraging the GSA, an accurate map (property charts) of acceptable range of parameter space is evidenced to obtain the spatio-temporal numerical solution that is stable as well as Dispersion Relation Preserving (DRP). The numerical property charts are shown to be useful to calibrate numerical solutions of both \(1D\) and the \(2D\) convection-diffusion equations on uniform meshes. Finally, as demonstrated while solving the Navier-Stokes equation for a Taylor-Green vortex problem, property charts allow to explain numerical behaviors often observed with real complex flow problems.On small perturbations of thermocapillary stationary two-layer flow in plane layer with movable boundaryhttps://zbmath.org/1521.767842023-11-13T18:48:18.785376Z"Andreev, Viktor K."https://zbmath.org/authors/?q=ai:andreev.viktor-konstantinovich"Bekezhanova, Viktoriya B."https://zbmath.org/authors/?q=ai:bekezhanova.viktoriya-bSummary: Problem on plane unidirectional two-layer flow of viscous heat-conducting fluid in microgravity is studied. There is a situation in which the flow is generated by Marangoni forces and motion of one of channel's walls only. Using the linearization method the stability of the regime is investigated. The flow crisis is induced by thermal oscillatory or monotonic waves for different wavenumber.Numerical simulations of Richtmyer-Meshkov instability of \(\mathrm{SF}_6\) square bubble in diatomic and polyatomic gaseshttps://zbmath.org/1521.767972023-11-13T18:48:18.785376Z"Singh, Satyvir"https://zbmath.org/authors/?q=ai:singh.satyvir"Battiato, Marco"https://zbmath.org/authors/?q=ai:battiato.marcoSummary: The Richtmyer-Meshkov instability of a shock-driven \(\mathrm{SF}_6\) square bubble in monatomic, diatomic, and polyatomic gases is investigated numerically. The focus was placed on presenting more intuitive details of the flow-fields visualizations, vorticity production, degree of thermal non-equilibrium, enstrophy and dissipation rate evolutions, and interface structures. A mixed-type modal discontinuous Galerkin method is employed for solving the two-dimensional system of physical conservation laws derived from the Boltzmann-Curtiss kinetic equation of diatomic and polyatomic gases. For validation, the numerical results were compared with the existing experimental results. The results revealed that diatomic and polyatomic gases provoke considerable changes in the flow-fields, resulting in complex wave patterns, bubble deformation, and outward \(\mathrm{SF}_6\) jets formation in contrast to monatomic gas. A detailed investigation on the effects of diatomic and polyatomic gases is carried out through the vorticity production, degree of nonequilibrium, and evolution of enstrophy as well as dissipation rate. Moreover, the length and height of the interface structures are investigated quantitatively. Finally, the effects of thermal non-equilibrium parameters, such as inverse power-law index and bulk viscosity ratio are examined. The present work attempts to enhance the understanding of the RM instability studies in monatomic, diatomic, and polyatomic gases.Wave patterns of stationary gravity-capillary waves from a moving obstacle in a magnetic fluidhttps://zbmath.org/1521.769072023-11-13T18:48:18.785376Z"Krakov, M. S."https://zbmath.org/authors/?q=ai:krakov.mikhail-s|krakov.m-s"Khokhryakova, C. A."https://zbmath.org/authors/?q=ai:khokhryakova.c-a"Kolesnichenko, E. V."https://zbmath.org/authors/?q=ai:kolesnichenko.e-vSummary: The influence of a magnetic field on the pattern of stationary waves formed on the surface of a magnetic fluid (ferrofluid) when an obstacle moves has been studied both theoretically and experimentally. It is found that a vertical magnetic field narrows the cone of stationary waves and increases their amplitude. In the wake region, the peaks of the Rosensweig instability appear in a magnetic field that is smaller than the critical field that determines this instability occurrence. A horizontal magnetic field parallel to the obstacle velocity expands the cone of waves but reduces their amplitude up to the suppression of stationary waves. A horizontal field perpendicular to the obstacle velocity also expands the cone of waves and stabilizes their amplitude.Effects of boundary conditions on the onset of convection with tilted magnetic field and rotation vectorshttps://zbmath.org/1521.769122023-11-13T18:48:18.785376Z"Proctor, M. R. E."https://zbmath.org/authors/?q=ai:proctor.michael-r-e"Weiss, N. O."https://zbmath.org/authors/?q=ai:weiss.nigel-o"Thompson, S. D."https://zbmath.org/authors/?q=ai:thompson.s-d"Roxburgh, N. T."https://zbmath.org/authors/?q=ai:roxburgh.n-tSummary: The problem of the onset of thermal convection is considered, firstly when a uniform tilted magnetic field is present, and secondly in a frame rotating about an oblique axis. If up-down symmetry is broken we expect to find only bifurcations that lead to travelling waves. Numerical studies show, however, that in a Boussinesq fluid the spectrum of eigenvalues can be symmetrical about the real axis, even when the boundary conditions are asymmetrical. Here we show analytically that this symmetry property indeed holds for a wide range of boundary conditions and hence that both steady solutions and standing waves are allowed.Patterns of convection in solidifying binary solutionshttps://zbmath.org/1521.800172023-11-13T18:48:18.785376Z"Keating, Shane R."https://zbmath.org/authors/?q=ai:keating.shane-r"Spiegel, E. A."https://zbmath.org/authors/?q=ai:spiegel.edward-a"Worster, M. G."https://zbmath.org/authors/?q=ai:worster.m-graeSummary: During the solidification of two-component solutions a two-phase mushy layer often forms consisting of solid dendritic crystals and solution in thermal equilibrium. Here, we extend previous weakly nonlinear analyses of convection in mushy layers to the derivation and study of a pattern equation by including a continuous spectrum of horizontal wave vectors in the development. The resulting equation is of the Swift-Hohenberg form with an additional quadratic term that destroys the up-down symmetry of the pattern as in other studies of non-Boussinesq convective pattern formation. In this case, the loss of symmetry is rooted in a non-Boussinesq dependence of the permeability on the solid-fraction of the mushy layer. We also study the motion of localized chimney structures that results from their interactions in a simplified one-dimensional approximation of the full pattern equation.Relativistic liquids: GENERIC or EIT?https://zbmath.org/1521.830042023-11-13T18:48:18.785376Z"Gavassino, L."https://zbmath.org/authors/?q=ai:gavassino.lorenzo"Antonelli, M."https://zbmath.org/authors/?q=ai:antonelli.melissa|antonelli.michela|antonelli.miranda-j|antonelli.mattia|antonelli.michele|antonelli.massimo|antonelli.marcoSummary: We study the GENERIC hydrodynamic theory for relativistic liquids formulated by Öttinger and collaborators. We use the maximum entropy principle to derive its conditions for linear stability (in an arbitrary reference frame) and for relativistic causality. In addition, we show that, in the linear regime, its field equations can be recast into a symmetric-hyperbolic form. Once rewritten in this way, the linearised field equations turn out to be a particular realisation of the Israel-Stewart theory, where some of the Israel-Stewart free parameters are constrained. This also allows us to reinterpret the GENERIC framework in view of the principles of extended irreversible thermodynamics and to discuss its physical relevance to model (possibly viscoelastic) fluids.Wind instability of gravitation waves on liquid surface in finite poolhttps://zbmath.org/1521.830252023-11-13T18:48:18.785376Z"Gestrin, S. G."https://zbmath.org/authors/?q=ai:gestrin.s-g"Staravoytova, E. V."https://zbmath.org/authors/?q=ai:staravoytova.e-v(no abstract)Inflationary cosmology with rotation and chaotic inflationhttps://zbmath.org/1521.832162023-11-13T18:48:18.785376Z"Panov, V. F."https://zbmath.org/authors/?q=ai:panov.v-f"Sandakova, O. V."https://zbmath.org/authors/?q=ai:sandakova.o-v"Kuvshinova, E. V."https://zbmath.org/authors/?q=ai:kuvshinova.e-v(no abstract)High order instabilities of the Poincaré solution for precessionally driven flowhttps://zbmath.org/1521.860012023-11-13T18:48:18.785376Z"Wu, Cheng-Chin"https://zbmath.org/authors/?q=ai:wu.cheng-chin"Roberts, Paul H."https://zbmath.org/authors/?q=ai:roberts.paul-hSummary: Sloudsky in 1895 and Poincaré in 1910 were the first to derive solutions for the flow driven in the Earth's fluid core by the luni-solar precession. In 1993, Kerswell investigated the stability of this so-called ``Poincaré flow'' by applying a method devised in 1992 by Ponomarev and Gledzer to study the instability of flows with elliptical streamlines. They represented the components of the perturbed flow by sums of polynomials. Kerswell restricted attention to the linear and quadratic cases. Here cubic, quartic, quintic, and sextic generalizations are developed. Instabilities are located in new areas of parameter space, including some that verge on the small oblateness of the Earth's coreOcean circulations driven by meridional density gradientshttps://zbmath.org/1521.860052023-11-13T18:48:18.785376Z"Bell, Michael J."https://zbmath.org/authors/?q=ai:bell.michael-jSummary: State-of-the-art ocean models spinning up from realistic density fields rapidly develop deep western boundary currents and meridional overturning circulations (MOCs). \textit{R. Wajsowicz} and \textit{A. E. Gill} [Adjustment of the ocean under buoyancy forces, Part I: The role of Kelvin waves. J. Phys. Oceanogr. 16, 2097--2114 (1986)] found that the initial spin-up of a flat-bottomed ocean model from a meridionally varying density field is well described by the shallow water equations for a two-layer fluid and that the initial evolution on a \(\beta\)-plane could be understood in terms of \(f\)-plane dynamics: Kelvin waves propagate rapidly round the ocean boundaries establishing eastern and western boundary currents. The time-mean baroclinic motion of a two-layer fluid in a closed basin on an \(f\)-plane which spins up from an initial state of rest with a meridionally sloping interface is derived here and compared with Gill's steady-state solution [\textit{A. E. Gill}, Adjustment under gravity in a rotating channel, J. Fluid Mech. 77, 603--621 (1977)] for an open channel. These solutions are used to illustrate the constraints imposed by the no normal flow inviscid boundary conditions which also apply to solutions on a sphere or \(\beta\)-plane. Miles' solution [\textit{J. W. Miles}, Kelvin waves on oceanic boundaries.
J. Fluid Mech. 55, 113--127 (1972; Zbl 0244.76006)] for Kelvin waves on a sphere is used to analyse the initial spin-up on a \(\beta\)-plane. Motivated by the slow speed of the geostrophic adjustment by the planetary waves at mid- to high-latitudes and the influence of the inviscid boundary conditions, simple, analytical steady-state solutions driven by relaxation of the internal interface towards a meridionally varying reference field and closed by dissipative boundary layers are derived using the planetary geostrophic equations for the baroclinic motion in a two-layer fluid. The solutions can be applied to basins which span the equator and derived using the full nonlinear continuity equation for any shape of basin. The depth of the internal interface is constant along the eastern boundaries and the equator but its east-west variations can be a large fraction of the pole to equator difference at high latitudes. The solutions support significant MOCs and, when periodic east-west boundary conditions are imposed at the southern boundary, can be shown to have a significant cross-equatorial baroclinic flow in the western boundary layer with greater southward flow in the lower layer than the surface layer.Linear baroclinic and parametric instabilities of boundary currentshttps://zbmath.org/1521.860062023-11-13T18:48:18.785376Z"Carton, Xavier"https://zbmath.org/authors/?q=ai:carton.xavier-j"Poulin, FrancisJ."https://zbmath.org/authors/?q=ai:poulin.francisj"Pavec, Marc"https://zbmath.org/authors/?q=ai:pavec.marcSummary: The linear baroclinic and parametric instabilities of boundary currents with piecewise-constant potential vorticity are studied in a two-layer quasi-geostrophic model. The growth rates of both the exponential modes and of the optimal perturbations are calculated for the baroclinic instability of steady coastal currents. We show that the growth rates of the exponential modes are maximal for a vertically symmetric flow. Furthermore, the vertical asymmetries induced by different layer thicknesses, the presence of a barotropic potential vorticity or bottom topography, all act to dampen the growth rates and favor growth at shorter wavelengths. It is shown that this behavior can be predicted from the conditions for vertical resonance of Rossby waves on the two potential vorticity fronts. Also, the baroclinic instability of the optimal perturbations has larger growth rates at shorter wavelengths and shorter time scales. As well, the presence of a sloping bottom of moderate amplitude favors the growth of these optimal perturbations. Finally, we compute the growth rates of parametric instability of oscillatory coastal flows. We show that subharmonic resonance is the most unstable mode of growth. In addition, a second region of parametric instability is found (for the first time) away from marginality of exponential-mode baroclinic instability. It is shown that the functional dependency of the growth rates of parametric instability, for optimal excitation, are similar to that of the optimal perturbations of baroclinic instability. To explain this a mechanism for parametric instability, involving the rapid growth of short-wave optimal perturbations, is proposed.Improved bounds on linear instability of barotropic zonal flow within the shallow water equationshttps://zbmath.org/1521.860082023-11-13T18:48:18.785376Z"Clark, A. D."https://zbmath.org/authors/?q=ai:clark.antwan-d|clark.allan-derek"Herron, I. H."https://zbmath.org/authors/?q=ai:herron.isom-h-junSummary: Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water.