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

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  • 1 Department of Environmental Sciences, Tel Aviv University, Ramat-Aviv, Tel-Aviv, Israel
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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.

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.

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