P. Alewyn and . Burger, The potential vorticity equation: from planetary to small scale, pp.191-197, 1991.

. Benoit-cushman-roisin, Introduction to Geophysical Fluid Dynamics, 1994.

C. Cao and E. S. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics, Annals of Mathematics, vol.166, issue.1, pp.245-267, 2007.
DOI : 10.4007/annals.2007.166.245

J. Paul, R. Dellar, and . Salmon, Shallow water equations with a complete coriolis force and topography, Physics of Fluids, vol.17, issue.10, p.106601, 2005.

A. E. Gill, Atmosphere-Ocean Dynamics, 1982.

M. Georgij and . Kobelkov, Existence of a solution " in the large " for ocean dynamics equations, J. Math. Fluid Mech, vol.9, issue.4, pp.588-610, 2007.

I. Kukavica and M. Ziane, On the regularity of the primitive equations of the ocean, Nonlinearity, vol.20, issue.12, pp.2739-2753, 2007.
DOI : 10.1088/0951-7715/20/12/001

C. Lucas and A. Rousseau, New Developments and Cosine Effect in the Viscous Shallow Water and Quasi-geostrophic Equations, Multiscale Modeling & Simulation, vol.7, issue.2, pp.793-813, 2008.
DOI : 10.1137/070705453
URL : https://hal.archives-ouvertes.fr/inria-00392886

C. Lucas and A. Rousseau, Cosine effect in ocean models, Discrete and Continuous Dynamical Systems - Series B, vol.13, issue.4, pp.841-857, 2010.
DOI : 10.3934/dcdsb.2010.13.841
URL : https://hal.archives-ouvertes.fr/inria-00428977

J. Lions, R. Temam, and S. Wang, New formulations of the primitive equations of atmosphere and applications, Nonlinearity, vol.5, issue.2, pp.237-288, 1992.
DOI : 10.1088/0951-7715/5/2/001

J. Lions, R. Temam, and S. Wang, On the equations of the large-scale ocean, Nonlinearity, vol.5, issue.5, pp.1007-1053, 1992.
DOI : 10.1088/0951-7715/5/5/002

G. Madec, NEMO ocean engine Note du Pole de modélisation, 2008.

G. Madec, P. Delecluse, M. Imbard, and C. Lévy, OPA 8.1 Ocean General Circulation Model reference manual. Note du Pole de modélisation, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00154217

J. Pedlosky, Geophysical fluid dynamics, 1987.

A. Norman and . Phillips, The equations of motion for a shallow rotating atmosphere and the " traditional approximation, Journal of the atmospheric sciences, vol.23, pp.626-628, 1966.

A. Norman and . Phillips, Reply (to George Veronis) Journal of the atmospheric sciences, pp.1155-1157, 1968.

M. Petcu, R. Temam, and M. Ziane, Some Mathematical Problems in Geophysical Fluid Dynamics, Handbook of Numerical Analysis. Special volume on Computational Methods for the Oceans and the Atmosphere, 2008.
DOI : 10.1016/S1570-8659(08)00212-3

F. Alexander, J. C. Shchepetkin, and . Mcwilliams, The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modelling, pp.347-404, 2005.

G. Veronis, Comments on Phillips' Proposed Simplification of the Equations of Motion for a Shallow Rotating Atmosphere, Journal of the Atmospheric Sciences, vol.25, issue.6, pp.1154-1155, 1968.
DOI : 10.1175/1520-0469(1968)025<1154:COPPSO>2.0.CO;2

K. Roald and . Wangsness, Comments on " the equations of motion for a shallow rotating atmosphere and the 'traditionnal approximation, Journal of the atmospheric sciences, vol.27, pp.504-506, 1970.

A. A. White and R. A. Bromley, Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force, Quarterly Journal of the Royal Meteorological Society, vol.115, issue.522, pp.399-418, 1995.
DOI : 10.1002/qj.49712152208

A. A. White, B. J. Hoskins, I. Roulstone, and A. Staniforth, Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic, Quarterly Journal of the Royal Meteorological Society, vol.130, issue.609, pp.2081-2107, 2005.
DOI : 10.1256/qj.04.49