Asymptotic Behavior of a Rapidly Rotating Fluid with Random Stationary Surface Stress
Anne-Laure Dalibard · SIAM Journal on Mathematical Analysis · 2009
The goal of this paper is to describe in mathematical terms the effect on ocean circulation of a random stationary wind stress on the surface of the ocean. In order to avoid singular behavior, nonresonance hypotheses are introduced, which ensure that the time frequencies of the wind stress are different from that of the Earth's 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 nonresonant torus.