Field Theory and the Phenomenon of Turbulence

TL;DR

This paper applies statistical physics to turbulence, introducing a turbulent partition function, developing a perturbative approach with Feynman diagrams, and exploring implications for different turbulence types.

Contribution

It presents a novel statistical physics framework for turbulence, including a turbulent partition function and perturbative methods using Feynman diagrams.

Findings

Turbulent states differ from thermodynamic equilibrium.

A turbulent analog of the partition function is constructed.

Perturbative computation of turbulent correlation functions is demonstrated.

Abstract

We study the phenomenon of turbulence from the point of view of statistical physics. We discuss what makes the turbulent states different from the thermodynamic equilibrium and give the turbulent analog of the partition function. Then, using the soluble theory of turbulence of waves as an example, we construct the turbulent action and show how one can compute the turbulent correlation functions perturbatively thus developing the turbulent Feynman diagrams. And at last, we discuss which part of what we learnt from the turbulence of waves can be used in other types of turbulence, in particular, the hydrodynamic turbulence of fluids. This paper is based on the talk delivered at SMQFT (1993) conference at the University of Southern California.