The effect of boundary conditions on the stability of twodimensional flows in an annulus with permeable boundary
Abstract
We consider the stability of twodimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner cylinder to the outer one or vice versa. In most earlier studies, all components of the velocity were assumed to be given on the entire boundary of the flow domain. Our aim is to study the effect of different boundary conditions on the stability of such flows. We focus on the following boundary conditions: at the inflow part if the boundary (which may be either inner or outer cylinder) all components of the velocity are known; at the outflow part of the boundary (the other cylinder), the normal stress and either the tangential velocity or the tangential stress are prescribed. Both types of boundary conditions are relevant to certain real flows: the first one  to porous cylinders, the second  to flows, where the fluid leaves the flow domain to an ambient fluid which is at rest. It turns out that both sets of boundary conditions make the corresponding steady flows more unstable (compared with earlier works where all components of the velocity are prescribed on the entire boundary). In particular, it is demonstrated that even the classical (purely azimuthal) CouetteTaylor flow becomes unstable to twodimensional perturbations if one of the cylinders is porous and the normal stress (rather than normal velocity) is prescribed on that cylinder.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12150
 Bibcode:
 2021arXiv210912150I
 Keywords:

 Physics  Fluid Dynamics;
 Mathematical Physics;
 76D05;
 76E07