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Shallow water equations with a complete Coriolis force and topography

P. J. Dellar and R. Salmon (2005) *Shallow water equations
with a complete Coriolis force and topography *Phys. Fluids** 17**,
106601* * doi:10.1063/1.2116747

Preprint available as Adobe PDF ( CompleteCoriolis.pdf
304K)

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Abstract

This paper derives a set of two dimensional equations describing a thin
inviscid fluid layer flowing over topography in a frame rotating about
an arbitrary axis. These equations retain various terms involving the
locally horizontal components of the angular velocity vector that are
discarded in the usual shallow water equations. The obliquely rotating
shallow water equations are derived both by averaging the three
dimensional equations, and from an averaged Lagrangian describing
columnar motion using Hamilton's principle. They share the same
conservation properties as the usual shallow water equations, for the
same energy and modified forms of the momentum and potential vorticity.
They may also be expressed in noncanonical Hamiltonian form using the
usual shallow water Hamiltonian and Poisson bracket. The conserved
potential vorticity takes the standard shallow water form, but with the
vertical component of the rotation vector replaced by the component
locally normal to the surface midway between the upper and lower
boundaries.

@article{DellarSalmon05,

Author =
{Dellar, P. J. and Salmon, R.},

Title = {Shallow water equations with a
complete Coriolis force and topography},

Journal =
{Phys. Fluids},

Year = {2005},

Volume =
{17},

Pages = {106601--19},

DOI = {doi:10.1063/1.2116747},

URL = {http://link.aip.org/link/?PHF/17/106601/1}

}