Stochastic averaging, jet formation and multistability in geostrophic turbulence

We consider the formation of large scale structures (zonal jets and vortices), in geostrophic turbulence forced by random forces, within the barotropic quasi-geostrophic model. We study the limit of a time scale separation between inertial dynamics on one hand, and the effect of forces and dissipation on the other hand. We prove that stochastic averaging can be performed explicitly in this problem, which is unusual in turbulent systems. It is then possible to integrate out all fast turbulent degrees of freedom, and to get explicitly an equation that describes the slow evolution of zonal jets.