Statistical theory of reversals in two-dimensional confined turbulent flows

TL;DR

This paper demonstrates that a finite set of equations can accurately model the complex reversal dynamics of large-scale circulation in confined 2D turbulent flows, revealing bifurcations and ergodicity breaking.

Contribution

It introduces a minimal 13-mode Truncated Euler model that captures the statistical reversals and bifurcations in 2D turbulence with bottom friction and periodic forcing.

Findings

Reversals involve bifurcations in the probability distribution of circulation velocity.

The microcanonical distribution describes transitions from Gaussian to bimodal states.

A 13-mode model reproduces the observed reversal dynamics.

Abstract

It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined 2D Navier-Stokes flow with bottom friction and a spatially periodic forcing. In particular, the random reversals of the large scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation velocity that are described by the related microcanonical distribution which displays transitions from gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.