Mathematical Study of Degenerate Boundary Layers - A Large Scale ...

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

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English | May 1, 2018 | ISBN-10: 1470428350 | 111 pages| PDF (True) | 1.3 MB

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 $Omega subset mathbf R2$, 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.