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

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