The effect of boundary conditions on the stability of two-dimensional flows in an annulus with permeable boundary

Abstract

Our aim is to study the effect of the outflow boundary conditions on the stability of incompressible flows in a domain with a permeable boundary. For this purpose, we examine the stability of the Couette flow with the radial throughflow between permeable cylinders. Most earlier studies of this flow employed the boundary conditions that prescribe all components of the flow velocity on both cylinders. Taking these boundary conditions as a reference point, we investigate the effect of imposing different outflow boundary conditions. These conditions prescribe the normal stress and either the tangential velocity or the tangential stress. It turns out that both sets of boundary conditions make the corresponding steady flows more unstable. In particular, it is shown that even the classical (purely azimuthal) Couette flow becomes unstable to two-dimensional perturbations if one of the cylinders is permeable and the normal stress (rather than normal velocity) is prescribed on that cylinder.