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Large scale ocean models beyond the traditional approximation. (English. French summary) Zbl 1390.35276

Summary: This work corresponds to classes given by A. Rousseau in February 2014 in Toulouse, in the framework of the CIMI labex. The objective is to describe and question the models that are traditionally used for large scale oceanography, whether in 2D or 3D. Starting from fundamental equations (mass and momentum conservation), it is explained how (thanks to approximations for which we provide justifications) one can build simpler models that allow a realistic numerical implementation. We particularly focus on the so-called traditional approximation that neglects part of the Coriolis force.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q86 PDEs in connection with geophysics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76U05 General theory of rotating fluids
76B65 Rossby waves (MSC2010)
35L20 Initial-boundary value problems for second-order hyperbolic equations
86A10 Meteorology and atmospheric physics

Keywords:

oceanography
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References:

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