A shallow water model with eddy viscosity for basins with varying bottom topography

The motion of an incompressible fluid confined to a shallow basin with a va rying bottom topography is considered. We introduce appropriate scalings in to a three-dimensional anisotropic eddy viscosity model to derive a two-dim ensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimension al eddy viscosity model plays a critical role in ensuring that the resultin g shallow water model dissipates energy.