Abstract
The motion of an incompressible fluid confined to a shallow basin with avarying bottom topography is considered. We introduce appropriatescalings into a three-dimensional anisotropic eddy viscosity model toderive a two-dimensional shallow water model. The globalregularity of the resulting model is proved. The anisotropic form of thestress tensor in our three-dimensional eddy viscosity model plays acritical role in ensuring that the resulting shallow water model dissipatesenergy.
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