Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects

RésuméConsidering the three-dimensional Navier–Stokes equations with a free moving surface boundary condition and hydrostatic approximation, we study 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 the viscous effects, consistent with a previous one-dimensional analysis, is obtained. Finally, we propose some simple numerical experiments in order to validate the proposed model.