Weak and strong versions of the Kolmogorov 4/5-law for stochastic Burgers equation

TL;DR

This paper establishes two versions of the Kolmogorov 4/5-law for stochastic Burgers equation solutions, revealing the unique universality of the third moment in turbulence statistics.

Contribution

It introduces two versions of the Kolmogorov 4/5-law for stochastic Burgers equations and analyzes the universality of the third moment in turbulence.

Findings

Two asymptotic expansions for third moments of velocity increments.

The third moment uniquely admits a universal asymptotic expansion.

An analogy of Landau's objection to universality in turbulence.

Abstract

For solutions of the space-periodic stochastic 1d Burgers equation we establish two versions of the Kolmogorov 4/5-law which provides an asymptotic expansion for the third moment of increments of turbulent velocity fields. We also prove for this equation an analogy of the Landau objection to possible universality of Kolmogorov's theory of turbulence, and show that the third moment is the only one which admits a universal asymptotic expansion.