# A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

Stefania Ferrari; Fausto Saleri

- Volume: 38, Issue: 2, page 211-234
- ISSN: 0764-583X

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topFerrari, Stefania, and 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 38.2 (2004): 211-234. <http://eudml.org/doc/245994>.

@article{Ferrari2004,

abstract = {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.},

author = {Ferrari, Stefania, Saleri, Fausto},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Navier-Stokes equations; Saint Venant equations; free surface flows},

language = {eng},

number = {2},

pages = {211-234},

publisher = {EDP-Sciences},

title = {A new two-dimensional shallow water model including pressure effects and slow varying bottom topography},

url = {http://eudml.org/doc/245994},

volume = {38},

year = {2004},

}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 2

SP - 211

EP - 234

AB - 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.

LA - eng

KW - Navier-Stokes equations; Saint Venant equations; free surface flows

UR - http://eudml.org/doc/245994

ER -

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