A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography
MOX, Dipartimento di Matematica , Politecnico di Milano,
via Bonardi 9, 20133 Milano, Italy,
2 MOX, Dipartimento di Matematica , Politecnico di Milano, via Bonardi 9, 20133 Milano Italy, Fausto.Saleri@polimi.it.
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, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional model at the 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 some numerical tests with the aim to validate the proposed model.
Mathematics Subject Classification: 35L65 / 65M60
Key words: Navier-Stokes equations / Saint Venant equations / free surface flows.
© EDP Sciences, SMAI, 2004