On Deep Quasi-geostrophic Theory

Abstract

Deep quasi-geostrophic theory applies to large-scale flow whose vertical depth scale is comparable to the potential temperature scale height. The appropriate expression for the potential vorticity equation is derived from the general formulation due to Ertel. It is further shown that the potential temperature field on a lower boundary acts as a surface charge of potential vorticity. Deep equivalent barotropic Rossby waves in the presence of a mean zonal wind exhibit an enhanced beta effect but a reduced phase speed. This behavior, analogous to that displayed in shallow water theory, arises due to the inclusion of compressibility effects in the deep theory. These results help clarify the applicability of shallow water theory to barotropic atmospheric flows. A conceptual model of the role of a surface charge of potential vorticity gradient in generating a change in the relative vorticity of a fluid parcel is described.