Turbulence: A Nonequilibrium Field Theory

Mahendra Verma

Published 2025-01-31Version 1

Tools of quantum and statistical field theories have ben successfully ported to turbulence. Here, we review the key results of turbulence field theory. Thermalized spectrally-truncated Euler equation is described by \textit{equilibrium field theory}, in which the equipartitioned Fourier modes generate zero energy flux. In contrast, modelling of hydrodynamic turbulence (HDT), which has small viscosity, requires \textit{nonequilibrium field theory}. In HDT, the viscosity is renormalized using field theory that leads to 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, we cover these aspects, along with a brief coverage of weak turbulence and intermittency.