Asymptotic behaviour of a rapidly rotating fluid with random stationary surface stress

Anne-Laure Dalibard (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The goal of this paper is to describe in mathematical terms the effect on the ocean circulation of a random stationary wind stress at the surface of the ocean. In order to avoid singular behaviour, non-resonance hypotheses are introduced, which ensure that the time frequencies of the wind-stress are different from that of the Earth rotation. We prove a convergence result for a three-dimensional Navier-Stokes-Coriolis system in a bounded domain, in the asymptotic of fast rotation and vanishing vertical viscosity, and we exhibit some random and stationary boundary layer profiles. At last, an average equation is derived for the limit system in the case of the non-resonant torus.

Mots clés: Rotating fluids; Oceanic circulation; Stationary setting; Boundary layer

Domaines: Equations aux dérivées partielles [math.AP]

Anne-Laure Dalibard. Asymptotic behaviour of a rapidly rotating fluid with random stationary surface stress. SIAM Journal on Mathematical Analysis, 2009, 41 (2), pp.511-563. ⟨10.1137/080718139⟩. ⟨hal-00260396v3⟩