On nonlinear stability of baroclinic fronts

We study the nonlinear stability of baroclinic fronts in a channel with variable bottom topography in the framework of the model proposed by Swaters and Flierl (1991). Sufficient conditions for nonlinear stability of steady flows in a channel with arbitrary bottom topography are obtained. We consider quite general perturbations which include non-zero perturbations of the circulations of the velocity along the rigid boundaries. The special case of zonal (x-independent) topography is treated in more detail. Here we make use of an additional invariant of the governing equations (the momentum). This allows us to obtain a less restrictive (than in the general situation) sufficient condition for nonlinear stability.