On turbulence-mean-flow interactions in two dimensions
Anna Frishman, Technion
Earths jet streams, Jupiters Great Red Spot and its zonal winds are all examples of persistent large scale flows, whose dynamics is to a good approximation two-dimensional. These flows are also highly turbulent, and a first-principles theory for the interaction between turbulence and these coherent structures remains a challenge. Such interactions take a different character in 2D compared to 3D. In 2D, energy is transferred to progressively larger scales, and in a finite domain small scale turbulence eventually self organizes into a large scale coherent structure, a so called condensate, on top of small scale fluctuations. Here I will present a self-consistent theoretical framework for turbulence-mean-flow interactions in an idealized simplest setting, along with its numerical validation. The framework is quasi-linear and yields the coherent mean flow profile and that of large scale turbulent fluctuations, namely the mean momentum flux and mean turbulent energy. I will mainly focus on 2D Navier-Stokes (in a doubly periodic domain), where the theory relies on a scale-separation for the forcing and mean flow. I will discuss the role played by symmetries and the universality of the results with respect to forcing. I will also show results for the Asymptotic Model---a 2D model obtained as a limit of the quasi-geostrophic shallow water equations, where the requirement for scale separation can be relaxed.