From Burgers to Navier-Stokes turbulence

TL;DR

This paper links the origin of Kolmogorov's turbulence law to the stochastic dynamics of shock-separated points, extending 1D results to 3D turbulence and proposing a new method for calculating correlation functions.

Contribution

It introduces a novel approach to understanding turbulence by connecting shock dynamics to Kolmogorov's law and develops a new procedure for correlation function determination in 3D turbulence.

Findings

Kolmogorov's law arises from shock-related stochastic dynamics

Extension of 1D turbulence results to 3D case

Proposed new method for correlation function calculation

Abstract

It is shown that the origin of the Kolmogorov's law of the fully developed turbulence is the result of the joint stochastic dynamics of pair points separated by the shock. The result obtained in 1-d case generalized on 3-d turbulence. A novel procedure of determination of correlation functions in 3-d turbulence is proposed.