Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Cosine effect on shallow water equations and mathematical properties

Author: Carine Lucas
Journal: Quart. Appl. Math. 67 (2009), 283-310
MSC (2000): Primary 76M45, 76U05; Secondary 35B40, 35Q35, 46E35
DOI: https://doi.org/10.1090/S0033-569X-09-01113-0
Published electronically: March 20, 2009
MathSciNet review: 2514636
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Abstract: This paper presents a viscous Shallow Water type model with new Coriolis terms, and some limits according to the values of the Rossby and Froude numbers. We prove that the extension to the bidimensional case of the unidimensional results given by [J.-F. GERBEAU, B. PERTHAME. Discrete Continuous Dynamical Systems, (2001)] including the Coriolis force has to add new terms, omitted up to now, depending on the latitude cosine, when the viscosity is assumed to be of the order of the aspect ratio.

We show that the expressions for the waves are modified, particularly at the equator, as well as the Quasi-Geostrophic and the Lake equations. To conclude, we also study the mathematical properties of these equations.

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Additional Information

Carine Lucas
Affiliation: Laboratoire MAPMO, Université d’Orléans–UFR Sciences, Bât. de Mathématiques–Route de Chartres, BP. 6759, 45067 Orléans cedex 2, France
Email: Carine.Lucas@univ-orleans.fr

DOI: https://doi.org/10.1090/S0033-569X-09-01113-0
Keywords: Shallow Water equations, viscosity, Coriolis force, asymptotics, waves, {\it a priori} estimates, existence of solutions.
Received by editor(s): November 1, 2007
Published electronically: March 20, 2009
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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