title: Statistical theory of reversals in two-dimensional confined turbulent flows.
abstract: It is shown that the truncated Euler equation (TEE), 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 two-dimensional flow obeying Navier-Stokes equation (NSE) with bottom friction and a spatially periodic forcing. The random reversals of the NSE large-scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation. We demonstrate that these NSE bifurcations are described by the related TEE microcanonical distribution which displays transitions from Gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.
authors.affiliation: Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University; UPMC Univ Paris 06, Sorbonne Universités; Université Paris Diderot, Sorbonne Paris-Cité; and CNRS, 24 Rue Lhomond, 75005 Paris, France.
authors.forename: Vishwanath
authors.initials: V
authors.lastname: Shukla
authors.affiliation: Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University; UPMC Univ Paris 06, Sorbonne Universités; Université Paris Diderot, Sorbonne Paris-Cité; and CNRS, 24 Rue Lhomond, 75005 Paris, France.
authors.forename: Stephan
authors.initials: S
authors.lastname: Fauve
authors.affiliation: Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University; UPMC Univ Paris 06, Sorbonne Universités; Université Paris Diderot, Sorbonne Paris-Cité; and CNRS, 24 Rue Lhomond, 75005 Paris, France.
authors.forename: Marc
authors.initials: M
authors.lastname: Brachet