Turbulence as a problem in non-equilibrium statistical mechanics

TL;DR

This paper reviews recent advances in understanding turbulence through non-equilibrium statistical mechanics, focusing on scaling laws, criticality, and lifetime statistics in turbulent shear flows.

Contribution

It synthesizes findings on turbulent flow scaling laws, critical phenomena, and lifetime statistics, highlighting turbulence as a non-equilibrium statistical mechanics problem.

Findings

Friction factor obeys a two-parameter scaling law.

Power-law scaling of friction factor with Reynolds number.

Super-exponential scaling of turbulence lifetime near transition.

Abstract

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a non-equilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.