Turbulence: A Nonequilibrium Field Theory

TL;DR

This paper reviews how quantum and statistical field theories are applied to turbulence, highlighting the differences between equilibrium and nonequilibrium approaches and their implications for modeling turbulent flows.

Contribution

It provides a comprehensive overview of turbulence field theory, emphasizing the application of nonequilibrium field theory to hydrodynamic turbulence and related systems.

Findings

Equilibrium field theory describes thermalized spectral states with zero energy flux.

Nonequilibrium field theory models turbulence with wavenumber-dependent viscosity and nonzero energy flux.

Field theory methods extend to passive scalar and magnetohydrodynamics systems.

Abstract

Tools of quantum and statistical field theories have been successfully ported to turbulence. Here, we review the key results of turbulence field theory. \textit{Equilibrium field theory} describes thermalized spectrally-truncated Euler equation, where the equipartitioned Fourier modes generate zero energy flux. In contrast, \textit{nonequilibrium field theory} is employed for modelling of hydrodynamic turbulence (HDT), which has small viscosity. In HDT, viscosity renormalization yields wavenumber-dependent viscosity and energy spectrum. Field theory calculations also yields nonzero energy flux for HDT. These field theory computations have been generalized to other systems, e.g., passive scalar and magnetohydrodynamics. In this review, I cover these aspects, along with a brief coverage of weak turbulence and intermittency.