Related papers: A viscous instability in axially symmetric laminar…
We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. When the steady density is heavier with…
This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational…
The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics,…
A certain appeal to the alpha model for turbulence and related viscosity in accretion disks was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence driven by a certain mechanism will attain a…
In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the…
First results from a high-resolution three-dimensional nonlinear numerical study of the kink oscillation are presented. We show in detail the development of a shear instability in an untwisted line-tied magnetic flux tube. The instability…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
In this paper, we prove the nonlinear instability of a given vertical shear of velocity between two rigid plane for the 3-D inviscid, non-conducting Boussinesq equations with rotation. When the Rossby number is zero, this rotating inviscid…
The stability of buoyant flows occurring in the mixed convection regime for a viscous fluid in a horizontal plane-parallel channel with adiabatic walls is investigated. The basic flow features a parallel velocity field under stationary…
We investigate the 2D instability recently discussed by Gallet et al. (2010) and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed on a centrifugally-stable swirling flow. By finding a simpler rectilinear example of…
The perturbations of weakly-viscous, barotropic, non-self-gravitating, Newtonian rotating fluids are analyzed via a single partial differential equation. The results are then used to find an expression for the viscosity-induced normal-mode…
It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate, or the flow in a Taylor-Couette geometry, can become unstable to a…
We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear $q=2.1, 4.2$ ($q = - d\ln\Omega / d\ln r$) and compare it with the…
This paper investigates the generation of free-surface waves in a liquid layer driven by linear instabilities in Couette-Poiseuille (quadratic) shear flows. The base velocity profiles are characterized by a curvature parameter, and…
Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the…
In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations.…
The present study investigates the linear stability of Riemann ellipsoids in both the inviscid limit and in the presence of weak viscosity. In the inviscid regime, we derive a generalised Poincare equation governing small fluid oscillations…
In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $\mathbb{T}\times \mathbb{R}$. In the inviscid case there is a generic…
According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the…