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Gravity driven shallow water models for arbitrary topography. (English) Zbl 1084.76012
Summary: We derive new models for gravity driven shallow water flows in several space dimensions over a general topography. The first model is valid for small slope variation, i.e. small curvature, and the second model is valid for arbitrary topography. In both cases no particular assumption is made on velocity profile in the material layer. The models are written for an arbitrary coordinate system, and several formulations are provided. A Coulomb friction term is derived within the same framework, relevant in particular for debris avalanches. All our models are invariant under rotation, admit a conservative energy equation, and preserve the steady state of a lake at rest.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35 PDEs in connection with fluid mechanics
86A05 Hydrology, hydrography, oceanography
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