A Shallow Water Model of the Winter Stratosphere

Abstract

The shallow water equations are used to investigate the interaction of planetary wave-breaking with a “diabatic” forcing. The numerical integrations demonstrate the formation of a sharp gradient in potential vorticity at the edge of the polar vortex, despite “diabatic relaxation” towards a smooth gradient. Successive cycles of Rossby wave-breaking accentuate the distinction between the vortex and the surf-zone. Persistent easterly acceleration in the tropics eventually produces a flow regime of little relevance to the atmosphere. For the period when the flow has some qualitative resemblance to the middle stratosphere diffusion coefficients are calculated from the meridional fluxes of potential vorticity and of passive tracers. It is found that the unique dynamical nature of potential vorticity among tracers is not reflected in its diffusion coefficient.