Nonstationary models for shallow lakes

Article type: Research Article

Authors: Bresch, Didier | Lemoine, Jérôme | Simon, Jacques^;

Affiliations: Laboratoire de Mathématiques Appliquées, CNRS (UMR 6620), Université Blaise Pascal (Clermont‐Ferrand 2), 63177 Aubière Cedex, France

Note: [] Corresponding author. E‐mail: simon@ucfma.univ‐bpclermont.fr.

Abstract: In this paper we study the behaviour of solutions of Navier–Stokes equations with adherence to the bottom and traction by wind at the surface when the aspect ratio \delta=\hbox{depth}/\hbox{lenght} of the domain tends to 0. Precisely, we prove that when wind is moderate, a variational solution converges to the solution of a vertical diffusion model. This model is either quasistationary or nonstationary, according to the characteristic time.

Keywords: Navier–Stokes equations, wind driven, Coriolis force, asymptotic model, shallow water

Journal: Asymptotic Analysis, vol. 22, no. 1, pp. 15-38, 2000