Instanton Theory of Burgers Shocks and Intermittency

TL;DR

This paper develops an instanton-based theoretical framework for understanding Burgers turbulence, revealing how shock interactions and background fluctuations lead to intermittency in velocity differences.

Contribution

It introduces a field-theoretical instanton approach to analyze Burgers shocks and intermittency, emphasizing the role of shocks and background fluctuations in turbulence statistics.

Findings

Derived the probability distribution of negative velocity differences.

Identified shocks as instantons responsible for intermittency.

Highlighted the coupling between shocks and background fluctuations.

Abstract

A lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken galilean invariance, the asymptotic form of the probability distribution function of negative velocity-differences. The origin of Burgers intermittency is found to rely on the dynamical coupling between shocks, identified to instantons, and non-coherent background fluctuations, which, then, cannot be discarded in a consistent statistical description of the flow.