  We consider the stability of two-dimensional 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) Couette-Taylor flow becomes unstable to two-dimensional
perturbations if one of the cylinders is porous and the normal stress (rather
than normal velocity) is prescribed on that cylinder.
