Stability of a two-layer quasigeostrophic vortex over axisymmetric localized topography

The stability of a quasigeostrophic vortex over a radially symmetric topographic feature (elevation or depression) in a two-layer ocean on the f plane is examined. This article's concern is with compensated vortices, that is, those in which the lower layer is at rest (the disturbances, however, are present in both layers). Through numerical solution of the linear normal-mode problem, it is demonstrated that a bottom elevation is a stabilizing influence for a cyclone and a destabilizing influence for an anticyclone, whereas a bottom depression acts in the opposite way. These conclusions are interpreted using an asymptotic theory developed for the case of a thin upper layer. It is demonstrated that an elevation moves the critical level of an unstable mode toward the periphery of the cyclone, which leads to its stabilization. Estimates based on realistic oceanic parameters show that stabilization occurs for relatively small topography (5%-15% of the lower layer's depth).