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, INPG - Institut National Polytechnique de Grenoble
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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/inria-00186560
Contributor : Carine Lucas <>
Submitted on : Friday, November 9, 2007 - 4:57:30 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:34 AM
Long-term archiving on : Monday, April 12, 2010 - 1:45:53 AM

File

CosineEffect.pdf
Files produced by the author(s)

Identifiers

Citation

Carine Lucas. Cosine Effect on Shallow Water Equations and Mathematical Properties. Quarterly of Applied Mathematics, American Mathematical Society, 2009, 67 (2), pp.283-310. ⟨10.1090/S0033-569X-09-01113-0⟩. ⟨inria-00186560⟩

Share

Metrics

Record views

344

Files downloads

354