Velocity distribution functions and intermittency in one-dimensional randomly forced Burgers turbulence

TL;DR

This paper derives an explicit joint distribution function for velocities in one-dimensional Burgers turbulence, revealing strong intermittency at small scales, using replica techniques in the zero-temperature limit.

Contribution

It provides a novel explicit expression for the joint velocity distribution in Burgers turbulence using replica methods, highlighting intermittency phenomena.

Findings

Velocity moments show strong intermittency at small scales.

Explicit joint distribution function derived for velocity separation.

Intermittency behavior confirmed in the zero-temperature limit.

Abstract

The problem of one-dimensional randomly forced Burgers turbulence is considered in terms of (1+1) directed polymers. In the limit of strong turbulence (which corresponds to the zero temperature limit for the directed polymer system) using the replica technique a general explicit expression for the joint distribution function of two velocities separated by a finite distance is derived. In particular, it is shown that at length scales much smaller than the injection length of the Burgers random force the moments of the velocity increment exhibit typical strong intermittency behavior.