On présente ici une série de travaux dont le but est de décrire les flots géophysiques dans la zone équatoriale, en tenant compte de l’influence prédominante de la rotation de la terre. Pour cela, on procède par approximations successives, en calculant pour chaque modèle la réponse du fluide à la pénalisation par la force de Coriolis. La principale difficulté provient des variations spatiales de l’accélération de Coriolis : en particulier, comme elle s’annule à l’équateur, les oscillations rapides sont piégées dans une fine bande de latitudes.
We present here a series of works which aims at describing geophysical flows in the equatorial zone, taking into account the dominating influence of the earth rotation. We actually proceed by successive approximations computing for each model the response of the fluid to the strong Coriolis penalisation. The main difficulty is due to the spatial variations of the Coriolis acceleration : in particular, as it vanishes at the equator, fast oscillations are trapped in a thin strip of latitudes.
@article{JEDP_2005____A13_0,
author = {Saint-Raymond, Laure},
title = {Modelling geophysical flows in the equatorial zone},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {13},
pages = {1--18},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2005},
doi = {10.5802/jedp.24},
mrnumber = {2352780},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jedp.24/}
}
TY - JOUR AU - Saint-Raymond, Laure TI - Modelling geophysical flows in the equatorial zone JO - Journées équations aux dérivées partielles PY - 2005 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://archive.numdam.org/articles/10.5802/jedp.24/ DO - 10.5802/jedp.24 LA - en ID - JEDP_2005____A13_0 ER -
%0 Journal Article %A Saint-Raymond, Laure %T Modelling geophysical flows in the equatorial zone %J Journées équations aux dérivées partielles %D 2005 %P 1-18 %I Groupement de recherche 2434 du CNRS %U http://archive.numdam.org/articles/10.5802/jedp.24/ %R 10.5802/jedp.24 %G en %F JEDP_2005____A13_0
Saint-Raymond, Laure. Modelling geophysical flows in the equatorial zone. Journées équations aux dérivées partielles (2005), article no. 13, 18 p. doi : 10.5802/jedp.24. http://archive.numdam.org/articles/10.5802/jedp.24/
[1] D. Bresch & B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equation and convergence to the quasi-geostrophic model. Commun. Math. Phys. 238, 2003, pages . | MR | Zbl
[2] J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids, Nonlinear Partial Differential Equations and their applications, Collège de France Seminar, Studies in Mathematics and its Applications, 31, (2002), pages 171–191. | MR | Zbl
[3] I. Gallagher & L. Saint-Raymond, Weak convergence results for inhomogeneous rotating fluid equations. to appear in Journal d’Analyse Mathématique, (2005).
[4] I. Gallagher & L. Saint-Raymond, On pressureless gases driven by a strong inhomogeneous magnetic field. SIAM Journal on Mathematical Analysis, 36(4), (2005). | MR | Zbl
[5] I. Gallagher & L. Saint-Raymond, Study of equatorial waves for the -plane model. In preparation.
[6] I. Gallagher & L. Saint-Raymond, About the influence of earth’s rotation on geophysical flows. Handbook of Mathematical Fluid Dynamics, S. Friedlander & D. Serre eds, Vol. 4, In preparation.
[7] A. E. Gill, Atmosphere-Ocean Dynamics, International Geophysics Series, Vol. 30, 1982.
[8] E. Grenier, Pseudo-differential energy estimates of singular perturbations. Comm. Pure Appl. Math. 50, 1997, pages 821-865. | MR | Zbl
[9] R. Klein & A. Majda, Systematic multi-scale models for the tropics. Journal of Atmospheric Sciences,
[10] S. Philander, El Nino, la nina, and the southern oscillation, Academic Press, 1990.
[11] S. Schochet, Fast singular limits of hyperbolic PDEs. J. Diff. Equ. 114, 1994, pages . | MR | Zbl
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