Baroclinic vortices over a sloping bottom

Abstract

Nonlinear quasigeostrophic flows in two layers over a topographic slope are considered. The evolution depends on the size of two parameters which indicate the degree of nonlinearity at depth. The first measures the importance of relative vorticity advection and the second of stretching vorticity. Two types of isolated vortex are used to examine the parameter dependence. An initially barotropic vortex remains barotropic only when the first parameter is large, otherwise topographic waves dominate at depth. An Initially surface-trapped vortex larger than deformation scale is baroclinically unstable when the second is large, but is stabilized by the slope otherwise. Both parameters are also relevant to cascading geostrophic turbulence. If the stretching parameter is large, a "barotropic cascade" occurs at the deformation radius (Rhines, 1977) and the cascade "arrests" when the relative vorticity parameter is order unity. If small, layer coupling is hindered and the cascade is arrested at the deformation scale, with the flow dominated by isotropic surface vortices. In both cases, the distinction between vortices and waves is transparent when viewing potential vorticity. It is more difficult to identify waves and vortices from the streamfunction fields, because the waves are present in both layers.