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Submesoscale potential vorticity
  • Christian Buckingham
Christian Buckingham
Université de Bretagne Occidentale

Corresponding Author:[email protected]

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Ertel’s potential vorticity theorem is essentially a clever combination of two conservation principles. The result is a conserved scalar q that accurately reflects vorticity values that fluid parcels can possess and acts as a tracer for fluid flow. While true at large horizontal scales in the ocean and atmosphere, at increasingly smaller scales and in sharply curved fronts, its accuracy breaks down. This is because Earth’s rotation imparts angular momentum to fluid parcels and the conservation of absolute angular momentum L restricts the range of centripetal accelerations possible in balanced flow; this correspondingly restricts vorticity. To address this discrepancy, we revisit Ertel’s derivation and obtain a new conserved scalar Lq that more properly reflects the vorticity of fluid parcels at these small horizontal scales. Although limited to flows on the f plane, this theorem nevertheless highlights a fundamental principle applicable to all geophysical fluids: at sufficiently small horizontal scales such that L can appropriately be conserved, centripetal accelerations-or curvature-can modify the vorticity of fluid parcels observed on the sphere.