Statistical mechanics of two-dimensional and geophysical flows

TL;DR

This paper reviews the application of statistical mechanics to understand the self-organization and equilibrium states of two-dimensional and geophysical turbulent flows, with examples from planetary atmospheres and ocean dynamics.

Contribution

It provides a comprehensive, self-contained overview of classical and recent statistical mechanics approaches to geophysical flows, including applications to real-world phenomena like Jupiter's vortices and ocean jets.

Findings

Predicts long-term behavior of turbulent flows as statistical equilibria.

Models specific phenomena such as Jupiter's Great Red Spot and ocean jets.

Discusses non-equilibrium steady states and relaxation processes.

Abstract

The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter's troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. The equilibrium microcanonical measure is built from the Liouville theorem. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states.