Modelling geophysical flows in the equatorial zone

Laure Saint-Raymond[1]

  • [1] Laboratoire J.-L. Lions UMR 7598 Université Paris VI 175, rue du Chevaleret 75013 Paris FRANCE

Journées Équations aux dérivées partielles (2005)

  • page 1-18
  • ISSN: 0752-0360

Abstract

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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.

How to cite

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Saint-Raymond, Laure. "Modelling geophysical flows in the equatorial zone." Journées Équations aux dérivées partielles (2005): 1-18. <http://eudml.org/doc/10604>.

@article{Saint2005,
abstract = {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.},
affiliation = {Laboratoire J.-L. Lions UMR 7598 Université Paris VI 175, rue du Chevaleret 75013 Paris FRANCE},
author = {Saint-Raymond, Laure},
journal = {Journées Équations aux dérivées partielles},
keywords = {geophysical flows; equatorial zone; earth rotation; Coriolis penalization; oscillations; rotation; Saint-Venant model},
language = {eng},
month = {6},
pages = {1-18},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Modelling geophysical flows in the equatorial zone},
url = {http://eudml.org/doc/10604},
year = {2005},
}

TY - JOUR
AU - Saint-Raymond, Laure
TI - Modelling geophysical flows in the equatorial zone
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 18
AB - 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.
LA - eng
KW - geophysical flows; equatorial zone; earth rotation; Coriolis penalization; oscillations; rotation; Saint-Venant model
UR - http://eudml.org/doc/10604
ER -

References

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  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 211 - 223 . Zbl1037.76012MR1989675
  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. Zbl1034.35107MR1935994
  3. I. Gallagher & L. Saint-Raymond, Weak convergence results for inhomogeneous rotating fluid equations. to appear in Journal d’Analyse Mathématique, (2005). Zbl1044.76067
  4. I. Gallagher & L. Saint-Raymond, On pressureless gases driven by a strong inhomogeneous magnetic field. SIAM Journal on Mathematical Analysis,36(4), (2005). Zbl1145.35095MR2139205
  5. I. Gallagher & L. Saint-Raymond, Study of equatorial waves for the β -plane model. In preparation. Zbl1151.35070
  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. Zbl0884.35183MR1459589
  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 476 - 512 . Zbl0838.35071MR1303036

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