A Shallow Water Model with Eddy Viscosity for Basins with Varying Bottom Topography
Friday, February 15, 2002 - 9:30am - 10:30am
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three dimensional anisotropic eddy viscosity model to derive derive a two dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three dimensional eddy viscosity model plays a critical role in ensuring the resulting shallow water model dissipates energy.