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M. Oliver,
A variational derivation of the geostrophic momentum approximation,
J. Fluid Mech. 751 (2014), R2, doi:10.1017/jfm.2014.309.
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 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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