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.
Mots-clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {211--234},
publisher = {EDP-Sciences},
volume = {38},
number = {2},
year = {2004},
doi = {10.1051/m2an:2004010},
mrnumber = {2069144},
zbl = {1130.76329},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2004010/}
}
TY - JOUR AU - Ferrari, Stefania AU - Saleri, Fausto TI - A new two-dimensional shallow water model including pressure effects and slow varying bottom topography JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 211 EP - 234 VL - 38 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2004010/ DO - 10.1051/m2an:2004010 LA - en ID - M2AN_2004__38_2_211_0 ER -
%0 Journal Article %A Ferrari, Stefania %A Saleri, Fausto %T A new two-dimensional shallow water model including pressure effects and slow varying bottom topography %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 211-234 %V 38 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2004010/ %R 10.1051/m2an:2004010 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 211-234. doi : 10.1051/m2an:2004010. http://archive.numdam.org/articles/10.1051/m2an:2004010/
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