Turbulence: A Nonequilibrium Field Theory

Tools of quantum and statistical field theories have been successfully ported to turbulence. Here, we review the key results of turbulence field theory. $\mathit{\text{Equilibrium}}\mathit{\text{field}}\mathit{\text{theory}}$ describes thermalized spectrally-truncated Euler equation, where the equipartitioned Fourier modes generate zero energy flux. In contrast, $\mathit{\text{nonequilibrium}}\mathit{\text{field}}\mathit{\text{theory}}$ 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.