On the effects of vertical eddy viscosity on rossby and eady waves in the ocean

The effects of vertical eddy viscosity on simple mesoscale waves in the ocean are studied. The decay of Rossby waves is investigated by one-dimensional depth-dependent linear stability problems which are derived for the interior non-viscous or viscous quasigeostrophic flow using parameterizations of the top and bottom boundary layers corresponding to Ekman suction, no-stress and bottom-stress boundary conditions.The non-slip condition at the bottom yielding an O(E_v^1/2)-Ekman layer causes very short damping times for the 0th Rossby mode. This suggests that this boundary condition is not suitable for mesoscale wave studies, because a Rossby wave fit for the MODE eddy can be done satisfactorily without any damping. Reasonable results for damping times of Rossby waves are obtained by prescribing the bottom stress, resulting from the constant-stress layer at the bottom, and the free-slip condition at the surface. The growth rates of Eady waves are reexamined using this bottom-stress condition.Vertical viscosity in the interior of the ocean, e.g. internal wave induced viscosity, may have a significant influence on the dynamics of the mesoscale motions, comparable to that of the boundary layers in some cases. The results are compatible with the sparse observations available.