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Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects. (English) Zbl 1105.76021
Summary: Considering the three-dimensional Navier-Stokes equations under a free moving surface boundary condition and hydrostatic approximation, we perform the derivation, with asymptotic analysis, of a new two-dimensional viscous shallow water model in rotating framework, with irregular topography, linear and quadratic bottom friction terms and capillary effects. A new formulation of viscous effects, consistent with a previous one-dimensional analysis, is obtained. Finally, we describe some simple numerical experiments in order to validate the proposed model.

MSC:
76D33 Waves for incompressible viscous fluids
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
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