Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem

ISBN-13: 9781470428358 / Angielski

Anne-Laure Dalibard;Laure Saint-Raymond

Opis

This paper is concerned with a complete asymptotic analysis as $E o 0$ of the Munk equation $partial _xpsi -E Delta ^2 psi = au $ in a domain $Omega subset mathbf R^2$, supplemented with boundary conditions for $psi $ and $partial _n psi $. This equation is a simple model for the circulation of currents in closed basins, the variables $x$ and $y$ being respectively the longitude and the latitude. A crude analysis shows that as $E o 0$, the weak limit of $psi $ satisfies the so-called Sverdrup transport equation inside the domain, namely $partial _x psi ^0= au $, while boundary layers appear in the vicinity of the boundary.