A new two-dimensional shallow water model including pressure effects and slow varying bottom topography
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 211-234

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.

DOI : https://doi.org/10.1051/m2an:2004010
Classification:  35L65,  65M60
Keywords: Navier-Stokes equations, Saint Venant equations, free surface flows
@article{M2AN_2004__38_2_211_0,
     author = {Ferrari, Stefania and Saleri, Fausto},
     title = {A new two-dimensional shallow water model including pressure effects and slow varying bottom topography},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {2},
     year = {2004},
     pages = {211-234},
     doi = {10.1051/m2an:2004010},
     zbl = {1130.76329},
     mrnumber = {2069144},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_2_211_0}
}
Ferrari, Stefania; Saleri, Fausto. A new two-dimensional shallow water model including pressure effects and slow varying bottom topography. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 211-234. doi : 10.1051/m2an:2004010. http://www.numdam.org/item/M2AN_2004__38_2_211_0/

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