Mathematical Problems in Mechanics
Resonant wind-driven oceanic motions
Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 451-456.

We are interested here in describing the linear response of a rapidly rotating fluid to some surface stress, possibly due to the wind. The distinctive feature of the model considered here lies in the fact that the stress admits fast time oscillations and may be resonant with the Coriolis force. In addition to the usual Ekman layer, the model exhibits another – much larger – boundary layer, and some global vertical profile. We prove, in particular, that for large times, the wind effect is no longer localized in the vicinity of the surface.

Cette Note est consacrée à la description des effets d'un forçage surfacique, par exemple dû au vent, sur des fluides en rotation rapide dont l'évolution est régie par une équation linéaire. La particularité de l'analyse menée ici réside dans le caractère fortement oscillant en temps du vent, qui peut alors entrer en résonance avec la force de Coriolis. En particulier, la taille des couches limites dûes au forçage résonnant est beaucoup plus grande que celle des couches d'Ekman habituelles, et il apparaît un profil vertical singulier, qui, en temps grand, n'est pas localisé dans un voisinage de la surface.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.01.025
Dalibard, Anne-Laure 1, 2; Saint-Raymond, Laure 3

1 Université Paris-Dauphine, Ceremade, F-75016 Paris, France
2 CNRS, UMR 7534, F-75016 Paris, France
3 Université Paris 6 & École normale supérieure, DMA-UMR CNRS 8553, F-75005 Paris, France
@article{CRMATH_2009__347_7-8_451_0,
     author = {Dalibard, Anne-Laure and Saint-Raymond, Laure},
     title = {Resonant wind-driven oceanic motions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {451--456},
     publisher = {Elsevier},
     volume = {347},
     number = {7-8},
     year = {2009},
     doi = {10.1016/j.crma.2009.01.025},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.025/}
}
TY  - JOUR
AU  - Dalibard, Anne-Laure
AU  - Saint-Raymond, Laure
TI  - Resonant wind-driven oceanic motions
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 451
EP  - 456
VL  - 347
IS  - 7-8
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.01.025/
DO  - 10.1016/j.crma.2009.01.025
LA  - en
ID  - CRMATH_2009__347_7-8_451_0
ER  - 
%0 Journal Article
%A Dalibard, Anne-Laure
%A Saint-Raymond, Laure
%T Resonant wind-driven oceanic motions
%J Comptes Rendus. Mathématique
%D 2009
%P 451-456
%V 347
%N 7-8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.01.025/
%R 10.1016/j.crma.2009.01.025
%G en
%F CRMATH_2009__347_7-8_451_0
Dalibard, Anne-Laure; Saint-Raymond, Laure. Resonant wind-driven oceanic motions. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 451-456. doi : 10.1016/j.crma.2009.01.025. http://www.numdam.org/articles/10.1016/j.crma.2009.01.025/

[1] Chemin, J.-Y.; Desjardins, B.; Gallagher, I.; Grenier, E. Mathematical Geophysics, Oxford Lecture Series in Mathematics and its Applications, vol. 32, Oxford University Press, 2006

[2] A.-L. Dalibard, L. Saint-Raymond, Mathematical study of rotating fluids with resonant surface stress, Journal of Differential Equations (2009), submitted for publication

[3] Desjardins, B.; Grenier, E. On the homogeneous model of wind-driven ocean circulation, SIAM Journal on Applied Mathematics, Volume 60 (1999), pp. 43-60

[4] Grenier, E. Oscillatory perturbations of the Navier–Stokes equations, Journal de Mathématiques Pures et Appliquées, Volume 76 (1997), pp. 477-498

[5] Masmoudi, N. Ekman layers of rotating fluids: the case of general initial data, Communications in Pure and Applied Mathematics, Volume 53 (2000), pp. 432-483

[6] Schochet, S. Fast singular limits of hyperbolic PDEs, Journal of Differential Equations, Volume 114 (1994), pp. 476-512

Cited by Sources: