The Effect of a Bottom Boundary Layer on the Stability of a Baroclinic Zonal Current

Abstract

The effect of a depth-limited bottom boundary layer on the stability of a baroclinic zonal current is investigated. The model is of a two-layer quasi-geostrophic flow. Limiting the height of the boundary layer introduces a shear between the advection velocities within the boundary layer and the geostrophic flow above. This can induce a new type of instability, the unstable mode being a barotropic Rossby wave, a baroclinic Rossby wave or a bottom wave, or a mixture of all three. The system can be unstable outside the regions predicted by conventional inviscid baroclinic instability theory, in particular when there is zero shear in the mean zonal flow. The energy source for the growth of the disturbance is the kinetic energy of the mean zonal flow of the lower layer and this acts as a type of topographic drag on the mean flow. When applied to the ocean the theory gives an e-folding time of 3 months for this unstable mode.