Buoyancy driven instabilities in rotating layers with parallel axis of rotation

The stability of fluid flow in the gap between two co-axial cylinders kept at different temperatures is considered in the case when the configuration is rotating rigidly about its vertical axis of symmetry. Instabilities in the form of baroclinic waves and thermal convection driven by centrifugal buoyancy have long been studied experimentally and theoretically for this configuration. It is shown that there is still another mechanism of instability which can be isolated in the limit of large Prandtl numbers. Rolls slightly inclined with respect to the axis of rotation convert potential energy into kinetic energy of motion and viscous dissipation. Another simple solution of the stability problem is obtained in the low Prandtl number limit where a shear flow instability akin to the Taylor vortex mechanism is realized.