Velocity fluctuations in forced Burgers turbulence

TL;DR

This paper introduces a straightforward method to analyze velocity difference statistics in forced Burgers turbulence across dimensions, revealing a specific inverse square decay in the distribution tail, consistent with numerical data.

Contribution

It presents a new simple approach to compute velocity difference statistics in Burgers turbulence, connecting shock dynamics with distribution tail behavior.

Findings

Left tail of velocity difference distribution decays as inverse square

Method aligns with numerical data on shock nucleation and coalescence

Results compare favorably with instanton and operator product expansion approaches

Abstract

We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the `left' tail of the distribution decays as an inverse square power, which is compatible with numerical data. Our results are compared to those of various recent approaches: instantons, operator product expansion, replicas.