Symmetries of the Burgers Turbulence without Pressure

TL;DR

This paper explores the local symmetries and anomalies in Burgers turbulence driven by random forces, linking these symmetries to fundamental turbulence laws using a path integral approach.

Contribution

It reveals the presence of local symmetries and anomalies in Burgers turbulence and connects a local invariance of the effective action to Kolmogorov's second law.

Findings

Identification of local symmetries and anomalies in Burgers turbulence

Connection between local invariance and Kolmogorov's self-similarity law

Insights into the physics of the Jacobian in turbulence

Abstract

We investigate local symmetries of the Burgers turbulence driven by an external random force. By using a path integral formalism, we show that the Jacobian has physics in it; local symmetries and an anomaly. We also study a local invariance of the effective action and show it is related to Kolmogorov's second law of self-similarity.