Relevance of instantons in Burgers turbulence

TL;DR

This paper demonstrates that instanton calculations accurately predict the tails of the velocity gradient PDF in Burgers turbulence, aligning well with numerical simulations across various regimes, thus confirming the approach's relevance.

Contribution

It establishes the validity of instanton methods for predicting velocity gradient PDFs in Burgers turbulence beyond previously studied limiting cases.

Findings

Instanton predictions agree with DNS results across multiple regimes.

The approach confirms the relevance of instantons for velocity gradient tail exponents.

Results suggest potential applicability to other turbulence contexts.

Abstract

Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These results are then compared to those obtained from massive direct numerical simulations (DNS) of the randomly forced Burgers equation. The instanton predictions are shown to agree with the DNS in a wide range of regimes, including those that are far from the limiting cases previously considered in the literature. These results settle the controversy of the relevance of the instanton approach for the prediction of the velocity gradient PDF tail exponents. They also demonstrate the usefulness of the instanton formalism in Burgers turbulence, and suggest that this approach may be applicable in other contexts, such as 2D and 3D turbulence in compressible and incompressible flows.