Statistical mechanics and large-scale velocity fluctuations of turbulence

TL;DR

This paper draws an analogy between large-scale velocity fluctuations in turbulence and thermal fluctuations in statistical mechanics, proposing a universal law for their energy distribution validated by experiments.

Contribution

It introduces a formalism linking turbulence large-scale fluctuations to statistical mechanics, providing a universal energy distribution law confirmed experimentally.

Findings

Universal law for turbulence fluctuation energy distribution

Experimental validation across various turbulent flows

Analogy between turbulence fluctuations and thermal fluctuations

Abstract

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.