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

Published online by Cambridge University Press:  15 March 2004

Stefania Ferrari  and
Fausto Saleri
Stefania Ferrari
Affiliation:
MOX, Dipartimento di Matematica , Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy, [email protected].
Fausto Saleri
Affiliation:
MOX, Dipartimento di Matematica , Politecnico di Milano, via Bonardi 9, 20133 Milano Italy, [email protected].
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Abstract

The motion of an incompressible fluid confined to a shallow basin witha slightly varying bottom topography is considered. Coriolis force,surface wind and pressure stresses, together with bottom andlateral friction stresses are taken into account. We introduceappropriate scalings into a three-dimensional anisotropic eddyviscosity model; after averaging on the vertical direction andconsidering some asymptotic assumptions, we obtain a two-dimensionalmodel, which approximates the three-dimensional model at the secondorder with respect to the ratio between the vertical scale and thelongitudinal scale. The derived model is shown to be symmetrizablethrough a suitable change of variables. Finally, we propose somenumerical tests with the aim to validate the proposed model.

Keywords

Navier-Stokes equationsSaint Venant equationsfree surface flows.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 211 - 234
Copyright
© EDP Sciences, SMAI, 2004

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