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A new two-dimensional shallow water model including pressure effects and slow varying bottom topography. (English) Zbl 1130.76329
Summary: 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.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
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FreeFem++
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