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

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.