A note on Burgers' turbulence

TL;DR

This paper analyzes the Polyakov equation for velocity-difference PDFs in turbulence with specific forcing correlations, demonstrating solvable cases and extending the method to turbulence models with short-scale correlations relevant to self-organized criticality.

Contribution

It applies and extends Polyakov's method to turbulence with short-scale-correlated forces, providing solvable cases aligned with numerical results.

Findings

Several solvable cases match numerical data

Method applicability to short-scale-correlated turbulence

Extension to models of self-organized criticality

Abstract

In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are considered, which are in a good agreement with available numerical results. Then it is shown how the method developed by A. Polyakov can be applied to turbulence with short-scale-correlated forces, a situation considered in models of self-organized criticality.