Shock statistics in higher-dimensional Burgers turbulence

TL;DR

This paper conjectures the exact shock statistics in higher-dimensional Burgers turbulence with correlated initial velocities, supported by field-theory arguments and numerical calculations, revealing uncorrelated shocks along any direction.

Contribution

It introduces a conjecture for shock statistics in higher-dimensional Burgers turbulence with correlated initial velocities, extending previous one-dimensional results.

Findings

Shock sizes and locations are uncorrelated along any given direction.

The conjecture is supported by numerical calculations.

The approach uses a field-theory argument.

Abstract

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.