On some homogenization problems from shallow water theory

This note is devoted to the effect of topography on geophysical flows. We consider two models derived from shallow water theory: the quasigeostrophic equation and the lake equation. Small scale variations of topography appear in these models through a periodic function, of small wavelength ε. The asymptotic limit as ε goes to zero reveals homogenization problems in which the cell and averaged equations are both nonlinear. In the spirit of article [P.-L. Lions, N. Masmoudi, Homogenization of the Euler system in a 2D porous medium, J. Math. Pures Appl. (9) 84 (1) (2005) 1–20], we derive rigorously the limit systems, through the notion of two-scale convergence. c 2006 Elsevier Ltd. All rights reserved.

• Type: Journal
• Year: 2007
• Where: APPML
• Authors: Didier Bresch, David Gérard-Varet
• Keywords: APPML 2007, Quasigeostrophic Equation, Shallow Water Theory, Small Scale Variations