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

TL;DR

This paper mathematically analyzes how a random stationary surface wind stress influences ocean circulation, demonstrating convergence of the Navier-Stokes-Coriolis system under rapid rotation and deriving an average limit system.

Contribution

It introduces non-resonance hypotheses to avoid singularities and proves convergence results for a 3D Navier-Stokes-Coriolis system with random boundary conditions.

Findings

Convergence of the Navier-Stokes-Coriolis system in the asymptotic limit.

Existence of random stationary boundary layer profiles.

Derivation of an average equation for the limit system.

Abstract

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.