Baroclinic Vortices over a Sloping Bottom

Nonlinear quasigeostrophic flows in two layers over a topographic slope are considered. Scaling the lower layer potential vorticity equation yields two parameters which indicate the degree of nonlinearity in the lower layer. The first, u' (the strength of the deep flow divided by the product of the effective bottom slope and the squared length scale), is related to the advection of relative vorticity, and the second, fU 1 (the product of the inverse square deformation radius of the lower layer and the strength of the surface flow divided by the effective slope), to the advection of vorticity due to interfacial stretching. Two types of isolated vortex are used to examine the parameter dependence. An initially barotropic vortex remains barotropic only when -2 > 1; otherwise f32 L 2 topographic waves are favored at depth, and the vortex separates into a surface vortex and waves. In the latter case, the surface vortex is weakened, consistent with a simple linear theory. An initially surface-trapped vortex which is larger than deformation scale is baroclinically unstable when 9 > 1. If , < 1, radiation of disturbances hinders or even blocks unstable growth, permitting the existence of large, stable surface vortices. Both parameters are also relevant to cascading geostrophic turbulence over a slope. If F2 U1 > 1, a "barotropic cascade" occurs at the deformation radius (Rhines, 1977) and the cascade is arrested at the scale at which =_ 011 O . The resulting flow is dominated by large scale, anisotropic topographic waves. If < 1, layer coupling is hindered and the cascade is arrested at the deformation scale. The flow then is dominated by isotropic surface vortices which continually "leak" energy to topographic waves at a rate proportional to A. In both single vortex and turbulence cases, the distinction between vortices and waves is more 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. ~1~~1-1._^._.._ l~^i_ ~-~ .ii. IU~ I