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A variational derivation of the geostrophic momentum approximation

  • Marcel Oliver (a1)

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.

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Email address for correspondence: oliver@member.ams.org

References

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A variational derivation of the geostrophic momentum approximation

  • Marcel Oliver (a1)

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