Navier-Stokes equation: irreversibility turbulence and ensembles equivalence

TL;DR

This paper explores the statistical properties of the Navier-Stokes equations under fixed forcing, proposing an analogy with thermodynamic ensemble equivalence to understand turbulence and irreversibility.

Contribution

It introduces a novel perspective linking turbulence in Navier-Stokes equations to ensemble equivalence concepts from statistical mechanics.

Findings

Stationary states form a family of probability distributions depending on Reynolds number

Proposes that different equations can produce identical distributions through an ensemble analogy

Links the removal of UV cut-off to thermodynamic limits in statistical mechanics

Abstract

The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fields depending on a parameter R (Reynolds number). It is proposed that other equations could lead to -- exactly -- the same distributions via a mechanism closely analogous to the coincidence of the canonical and microcanonical averages of local observables in the statistical mechanics thermodynamic limit (proposed, here, to correspond to the limit in which the UV cut-off N, regularizing the equations, is removed to infinity).