相关论文: Transition and Stability of 3D MHD Around Couette …
This study seeks to characterise the breakdown of the steady 2D solution in the flow around a 180-degree sharp bend to infinitesimal 3D disturbances using a linear stability analysis. The stability analysis predicts that 3D transition is…
In this paper, we investigate linear stability properties of the 2D isentropic compressible Euler equations linearized around a shear flow given by a monotone profile, close to the Couette flow, with constant density, in the domain…
Inspired by the experiment from Moresco \& Alboussi\`ere (2004, J. Fluid Mech.), we study the stability of a liquid metal flow in a rectangular, electrically insulating duct with a steady homogeneous transverse magnetic field. The Lorentz…
The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of infinite vertical extension is considered. For flows with a resting outer cylinder there is a well-known characteristic Reynolds number even without magnetic…
In this paper, we prove the non-uniform continuity of the data-to-solution map for the incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion in Sobolev spaces $H^s(\mathbb{R}^d)$ for all $s>0$ and $d=2,3$. Our…
We report the results of a complete modal and nonmodal linear stability analysis of the electrohydrodynamic flow (EHD) for the problem of electroconvection in the strong injection region. Convective cells are formed by Coulomb force in an…
Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\_in = B\_out has been considered. For high…
We investigate the Kelvin-Helmholtz instability occuring at the interface of a shear flow configuration in 2D compressible magnetohydrodynamics (MHD). The linear growth and the subsequent non-linear saturation of the instability are studied…
This paper concerns with the stability of the plane Couette flow resulted from the motions of boundaries that the top boundary $\Sigma_1$ and the bottom one $\Sigma_0$ move with constant velocities $(a,0)$ and $(b,0)$, respectively. If one…
Rotating waves (RW) bifurcating from the axisymmetric basic magnetized spherical Couette (MSC) flow are computed by means of Newton-Krylov continuation techniques for periodic orbits. In addition, their stability is analysed in the…
We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. In this work, we show that there is constant $0…
In this paper, we investigate the nonlinear stability and transition threshold for the 3D Boussinesq system in Sobolev space under the high Reynolds number and small thermal diffusion in $\mathbb{T}\times\mathbb{R}\times\mathbb{T} $. It is…
This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal…
This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an external magnetic field. A particular focus is…
We study the monotone nonlinear energy stability of \textit{magnetohydrodynamics plane shear flows, Couette and Hartmann flows}. We prove that the least stabilizing perturbations, in the energy norm, are the two-dimensional spanwise…
We study a new rheological model describing flows of melts and solutions of incompressible viscoelastic polymeric media in an external uniform magnetic field in the presence of a temperature drop and a conduction current. We find an…
We study the stability of Couette flow in the 3d Navier-Stokes equations with rotation, as given by the Coriolis force. Hereby, the nature of linearized dynamics near Couette flow depends crucially on the force balance between background…