Quasi-hydrostatic primitive equations for ocean global circulation models
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Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.
KeywordsHydrostatic approximation Coriolis force Ocean global circulation models Primitive equations Traditional approximation
2000 MR Subject Classification76M45 76U05 35B40 35Q35 76M20
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- Burger, A. P., The potential vorticity equation: from planetary to small scale, Tellus, 43A, 1991, 191–197.Google Scholar
- Benoit Cushman-Roisin, Introduction to Geophysical Fluid Dynamics, Prentice-Hall, Indiana, 1994.Google Scholar
- Gill, A. E., Atmosphere-Ocean Dynamics, Academic Press, New York, 1982.Google Scholar
- Madec, G., NEMO ocean engine, Note du Pole de Modélisation, 27, Institut Pierre-Simon Laplace (IPSL), France, 2008.Google Scholar
- Madec, G., Delecluse, P, Imbard, M. and Lévy, C., OPA 8.1 Ocean General Circulation Model reference manual, Note du Pole de Modélisation, Institut Pierre-Simon Laplace (IPSL), France, 1999.Google Scholar
- Petcu, M., Temam, R. and Ziane, M., Some mathematical problems in geophysical fluid dynamics, Handbook of Numerical Analysis, Special Volume on Computational Methods for the Oceans and the Atmosphere, P. G. Ciarlet (ed.), Vol. XIV. Elsevier, Amsterdam, 2008.Google Scholar