A new two-dimensional Shallow Water model including pressure effects
Thursday 5th December 2002
Ferrari, Stefania; Saleri, Fausto
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, togheter with bottom and lateral friction stresses are taken into account. We introduce appropriatescalings into a three-dimensional anisotropic eddy viscosity model: after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional modl, which approximates the three-dimensional model at second order with respect to the ratio between the vertical scale and the longitudinal scale. The derived model is shown to be symmetrizable through a suitable change of variables. Finally, we propose sone numerical tests with the aim to validate the proposed model.