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M. Oliver and S. Vasylkevych,
Generalized LSG models with varying Coriolis parameter,
Geophys. Astrophys. Fluid Dyn. 107 (2013), 259-276.
Abstract:
In this paper, we derive and study approximate balance models for
nearly geostrophic shallow water flow where the Coriolis parameter is
permitted to vary across the domain so long as it remains
nondegenerate. This situation includes, for example, the
β-plane approximation to the shallow water equations at
mid-latitudes. Our approach is based on changing configuration space
coordinates in the underlying variational principle in such a way that
that consistent asymptotics in the transformed Lagrangian leads to a
degenerate Lagrangian structure. In this article, we restrict our
attention to first order models. We show that the resulting models
can be formulated in terms of an advected potential vorticity with a
nonlinear vorticity inversion relation. We study the associated
solvability conditions and identify a subfamily of models for which
these conditions are satisfied without additional restrictions on the
data. Finally, we provide the link between our framework and the
theory of constrained Hamiltonian systems.
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