New relations for correlation functions in Navier-Stokes turbulence

TL;DR

This paper derives new exact relations for correlation functions in turbulence, extending the classical Kolmogorov flux relation to compressible and incompressible cases, enhancing understanding of turbulence statistics.

Contribution

It introduces a general framework linking current-density correlations to turbulence statistics, providing new exact relations for both compressible and incompressible turbulence.

Findings

Derivation of an analog of the 4/5-law for compressible turbulence

Establishment of a new exact relation for incompressible turbulence

Unification of turbulence correlation relations under a general framework

Abstract

We consider the steady-state statistics of turbulence sustained by a large-scale force. The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current-density correlation function. Using that, we derive an analog of the flux relation for compressible turbulence and a new exact relation for incompressible turbulence.