Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence

TL;DR

This paper derives exact two-time velocity distribution functions in Gaussian Burgers turbulence using a replica approach applied to a directed polymer model, providing new insights into the statistical behavior of turbulent flows.

Contribution

It introduces an explicit calculation of two-time four-point free energy distributions in a Gaussian model, enabling exact results for velocity distributions in Burgulence.

Findings

Exact two-time velocity distribution functions derived

Explicit two-time four-point free energy distribution obtained

Provides a new analytical approach to Burgers turbulence

Abstract

The problem of randomly forced Burgers turbulence ("Burgulence") is considered in terms of the toy Gaussian Larkin model of directed polymers. In terms of the replica technique the explicit expressions for the two-time four-point free energy distribution function is obtained which makes possible to derive the exact result for the two-time velocity distribution function in the corresponding Burgulence problem.