Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere

TL;DR

This paper applies statistical mechanics to a simplified atmospheric model, revealing a phase transition between different flow structures and exploring ensemble equivalence through Goldstone modes.

Contribution

It introduces a novel application of statistical mechanics to a quasi-geostrophic model, identifying phase transitions and symmetry-breaking in planetary flows.

Findings

Identification of a second order phase transition between flow states

Demonstration of spontaneous symmetry-breaking in the dipole phase

Extension of ensemble equivalence theory via Goldstone modes

Abstract

The large-scale circulation of planetary atmospheres like that of the Earth is traditionally thought of in a dynamical framework. Here, we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasi-geostrophic model, leading to non-trivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole. A second order phase transition occurs between these two phases, with associated spontaneous symmetry-breaking in the dipole phase. This model allows us to go beyond the general theory of marginal ensemble equivalence through the notion of Goldstone modes.