Dynamical Anomalies and Intermittency in Burgers Turbulence

TL;DR

This paper investigates the field theory of Burgers turbulence, focusing on shock fields, intermittency, and dynamical anomalies, revealing their interconnected roles in turbulence behavior.

Contribution

It introduces a detailed operator product expansion for shock fields and links dynamical anomalies to intermittency in Burgers turbulence.

Findings

Shock fields characterize velocity singularities.

Intermittency is constrained by dynamical anomalies.

Finite dissipation persists in the inviscid limit.

Abstract

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing intermittency. The latter is found to be constrained by dynamical anomalies expressing finite dissipation in the inviscid limit. The link between dynamical anomalies and intermittency is argued to be important in a wider context of turbulence.