Zonal flows as statistical equilibria

TL;DR

This paper explores how equilibrium statistical mechanics explains the formation and robustness of zonal jets in geophysical turbulent flows, unifying various dynamical mechanisms under a common theoretical framework.

Contribution

It presents a comprehensive review of how equilibrium statistical mechanics accounts for the emergence and structure of zonal jets across different dynamical regimes.

Findings

Zonal or quasi-zonal states are typical in equilibrium on a beta plane or sphere.

Increasing energy causes bifurcations that break zonal symmetry.

Different dynamical approaches converge to similar jet structures.

Abstract

Zonal jets are striking and beautiful examples of the propensity for geophysical turbulent flows to spontaneously self-organize into robust, large scale coherent structures. There exist many dynamical mechanisms for the formation of zonal jets: statistical theories (kinetic approaches, second order or larger oder closures), deterministic approaches (modulational instability, $\beta$-plumes, radiating instability, zonostrophic turbulence, and so on). A striking remark is that all these different dynamical approaches, each of them possibly relevant in some specific regimes, lead to the same kind of final jet structures. Is it then possible to have a more general explanation of why all these different dynamical regimes, from fully turbulent flows to gentle quasilinear regime, consistently lead to the same jet attractors ? Equilibrium statistical mechanics provides an answer to this general question. Here we we present the salient features of this theory and review applications of this approach to the description of zonal jets. We show that equilibrium states on a beta plane or a sphere are usually zonal or quasi-zonal, and that increasing the energy leads to bifurcations breaking the zonal symmetry.