Related papers: On Instability and Stability of Three-Dimensional …
We are concerned with the instability of a generic compressible two-fluid model in the whole space $\mathbb{R}^3$, where the capillary pressure $f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account. For the case that the capillary…
In this paper, we study the nonlinear stability of a steady circular flow created between two rotating concentric cylinders. The dynamics of the viscous fluid are described by 2D Navier-Stokes equations. We adopt scaling variables. For the…
How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=\rho v_0^2/2\sigma_a$, where $\rho$ is the suspension…
We study the displacement of three immiscible Stokes fluids with constant viscosities in a porous medium. The middle-layer fluid is contained in a bounded region. We give an analysis of the linear stability of this process. This stability…
This paper investigates the nonlinear stability of Taylor-Couette (TC) flows incorporating the thermal buoyancy within an annular domain characterized by small viscosity $\nu$ and thermal diffusivity $\mu$. It is well established that the…
Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work is…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
We consider the linear stability to three-dimensional perturbations of two-dimensional nonlinear magnetohydrodynamic basic states obtained from a specified forcing function in the presence of an imposed initially uniform magnetic field of…
In this paper, we study the instability effect of viscous dissipation in a domain without boundaries. We construct a shear flow that is initially spectrally stable but evolves into a spectrally unstable state under the influence of viscous…
This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in…
This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal…
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important…
This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability…
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier--Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source)…
A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially…
The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modelled as an exponential function of…
We study miscible Rayleigh-Taylor (RT) fingering instability in two-dimensional homogeneous porous media, in which the fluid density varies non-monotonically as a function of the solute concentration such that the maximum density lies in…
A plane non-parallel vortex flow in a square fluid domain is examined. The energy dissipation of the flow is dominated by viscosity and linear friction effect of a Hartmann layer. This is a traditional Navier-Stokes flow when the linear…
We prove the existence of weak solutions to the steady compressible Navier-Stokes system in the barotropic case for a class of pressure laws singular at vacuum. We consider the problem in a bounded domain in R^2 with slip boundary…
The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation and biglobal stability analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This study…