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Cosine Effect on Shallow Water Equations and Mathematical Properties

Carine Lucas 1 
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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 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 mathematical properties of these equations.
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Submitted on : Friday, November 9, 2007 - 4:57:30 PM
Last modification on : Thursday, January 20, 2022 - 5:28:01 PM
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Carine Lucas. Cosine Effect on Shallow Water Equations and Mathematical Properties. Quarterly of Applied Mathematics, 2009, 67 (2), pp.283-310. ⟨10.1090/S0033-569X-09-01113-0⟩. ⟨inria-00186560⟩



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