A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari; Fausto Saleri

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Ferrari, 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 38.2 (2010): 211-234. <http://eudml.org/doc/194211>.

@article{Ferrari2010,
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},
keywords = {Navier-Stokes equations; Saint Venant equations; free surface flows.},
language = {eng},
month = {3},
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/194211},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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/194211
ER -

References

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Citations in EuDML Documents

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  1. Emmanuel Audusse, Marie-Odile Bristeau, Finite-volume solvers for a multilayer Saint-Venant system
  2. Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame, Jacques Sainte-Marie, A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
  3. Emmanuel Audusse, Marie-Odile Bristeau, Benoît Perthame, Jacques Sainte-Marie, A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation

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