The instability of baroclinic Rossby waves over two-dimensional topography is examined using a nonlinear model, a linear stability calculation and wave triads. In all cases, the Rossby waves are unstable, as seen previously over a flat bottom. But topography decreases the growth rates and changes the structure of the unstable waves. When the topographic height (or slope) exceeds a critical value, the instability is ‘locked’ to topography, in that the most unstable mode, particularly in the lower layer, resembles the bathymetry. In this limit, the growth rate becomes independent of topographic height. A triad calculation suggests that the growth rates in the locked state should depend on the lateral scale of the bathymetry but not its height, and that locking does not occur for topographic scales smaller than the surface deformation radius. The results suggest an alternate way that topographically locked flow can be generated, and indicate that baroclinic instability can be much different over steep bathymetry.
LaCasce et al. (Wed,) studied this question.