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

This paper is concerned with a complete asymptotic analysis as $E to 0$ of the Munk equation $partial _xpsi -E Delta ^2 psi = tau $ 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 $E to 0$, the weak limit of $psi $ satisfies the so-called Sverdrup transport equation inside the domain, namely $partial _x psi ^0=tau $, while boundary layers appear in the vicinity of the boundary.