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We consider the stability of two-dimensional viscous flows in an annulus withpermeable boundary. In the basic flow, the velocity has nonzero azimuthal andradial components, and the direction of the radial flow can be from the innercylinder to the outer one or vice versa. In most earlier studies, allcomponents of the velocity were assumed to be given on the entire boundary ofthe flow domain. Our aim is to study the effect of different boundaryconditions on the stability of such flows. We focus on the following boundaryconditions: at the inflow part if the boundary (which may be either inner orouter cylinder) all components of the velocity are known; at the outflow partof the boundary (the other cylinder), the normal stress and either thetangential velocity or the tangential stress are prescribed. Both types ofboundary conditions are relevant to certain real flows: the first one - toporous cylinders, the second - to flows, where the fluid leaves the flow domainto an ambient fluid which is at rest. It turns out that both sets of boundaryconditions make the corresponding steady flows more unstable (compared withearlier works where all components of the velocity are prescribed on the entireboundary). In particular, it is demonstrated that even the classical (purelyazimuthal) Couette-Taylor flow becomes unstable to two-dimensionalperturbations if one of the cylinders is porous and the normal stress (ratherthan normal velocity) is prescribed on that cylinder.

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