Equivalence of nonequilibrium ensembles: Two-dimensional turbulence with a dual cascade

TL;DR

This study demonstrates that a time-reversible 2D Navier-Stokes model can replicate the statistical features of standard turbulence, supporting the equivalence of nonequilibrium ensembles in dual-cascade turbulent flows.

Contribution

It constructs a time-reversible 2D Navier-Stokes system with conserved energy and enstrophy and shows it reproduces key turbulence features of the standard system.

Findings

Excellent agreement in statistical properties between reversible and standard systems.

The equivalence holds at finite Reynolds numbers for 2D turbulence.

Supports the conjecture beyond the original 3D turbulence context.

Abstract

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equations clearly show that a formally time-reversible system is able to reproduce the features of a 2D turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems, for the inverse- and direct cascade regions. Moreover, we find that the conjecture holds very well for 2D turbulent flows with both conserved energy and enstrophy at finite Reynolds number, which goes beyond the original conjecture for three-dimensional turbulence in the limit of infinite Reynolds number.