Dynamical Scaling in Dissipative Burgers Turbulence

TL;DR

This paper provides an exact analysis of two-point correlation functions in dissipative Burgers turbulence, revealing the presence of two distinct dynamic scales and discussing implications for scaling theories across arbitrary dimensions.

Contribution

It introduces a novel exact analysis showing two dynamic scales in dissipative Burgers turbulence, challenging the single-scale scaling hypothesis.

Findings

Identification of diffusive and super-diffusive scales in turbulence

Derivation of the super-diffusive scale exponent a = (d+1)/(d+2)

Discussion of implications for conventional scaling theory

Abstract

An exact analysis is performed for the two-point correlation function C(r,t) in dissipative Burgers turbulence with bounded initial data, in arbitrary spatial dimension d. Contrary to the usual scaling hypothesis of a single dynamic length scale, it is found that C contains two dynamic scales: a diffusive scale l_{D} \sim t^{1/2} for very large r, and a super-diffusive scale L(t) \sim t^{a} for r \ll l_{D}, where a = (d+1)/(d+2). The consequences for conventional scaling theory are discussed. Finally, some simple scaling arguments are presented within the `toy model' of disordered systems theory, which may be exactly mapped onto the current problem.