A Note on the Conservation of Potential Vorticity Across a Discontinuity in Shallow Water with Application to Theories of Equatorial Dynamics and Rossby Lee Waves

Abstract

It is shown that potential vorticity, as usually defined for slow motions in shallow water, is conserved across a discontinuity in bottom slope if the total depth is continuous, but not across a discontinuity in the depth itself. This is shown to invalidate some published hypotheses concerning possible mechanisms for the generation of strong zonal currents near the equator, and large-amplitude Rossby lee waves in midlatitudes.