Hamilton's principle for quasigeostrophic motion

Darryl D. Holm; Vladimir Zeitlin

doi:10.1063/1.869623

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arXiv · chao-dyn/9801018

Hamilton's principle for quasigeostrophic motion

Darryl D. Holm·Vladimir Zeitlin

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Abstract

We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its prolongation in the beta-plane case. This implies a new momentum equation and an associated Kelvin circulation theorem for QG motion. We treat the barotropic and two-layer baroclinic cases, as well as the continuously stratified case.

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Darryl D. Holm, Vladimir Zeitlin. 1998-01-13. Hamilton's principle for quasigeostrophic motion. https://doi.org/10.1063/1.869623

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