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R. Ford, S.J.A. Malham, and M. Oliver,
A new model for shallow water in the low Rossby-number limit,
J. Fluid Mech. 450 (2002), 287-296.
Abstract:
We revisit Rick Salmon's `Dirac bracket projection' approach to
constructing generalized semi-geostrophic equations. One of the
obstacles to the method's applicability is that it leads to a sign
indefinite energy functional in the computational domain. In some
instances this can cause severe failure of the model. We
demonstrate in the simple context of shallow water semi-geostrophy
that the Hamiltonian remains positive definite when the asymptotic
expansion at the heart of this method is carried to the next order.
The resulting new model can be interpreted in the framework of
regularization by Lagrangian averaging, which is currently receiving
a lot of attention.
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