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.
