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A variational derivation of the geostrophic momentum approximation

Published online by Cambridge University Press:  16 June 2014

Marcel Oliver
Marcel Oliver*
Affiliation:
School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
*
†Email address for correspondence: oliver@member.ams.org
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Abstract

This paper demonstrates that the shallow water semigeostrophic equations arise from a degenerate second-order Hamilton principle of very special structure. The associated Euler–Lagrange operator factors into a fast and a slow first-order operator; restricting to the slow part yields the geostrophic momentum approximation as balanced dynamics. While semigeostrophic theory has been considered variationally before, this structure appears to be new. It leads to a straightforward derivation of the geostrophic momentum approximation and its associated potential vorticity law. Our observations further affirm, from a different point of view, the known difficulty in generalizing the semigeostrophic equations to the case of a spatially varying Coriolis parameter.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Shallow water flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , R2
Copyright
© 2014 Cambridge University Press 

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