Renormalization group analysis of turbulent magnetohydrodynamics

Abstract

The properties of quasi-neutral fluids governed by stochastic magnetohydrodynamic (MHD) equations are investigated with a method based on the diagrammatic representation of the Martin-Siggia-Rose field-theoretic formulation of stochastic dynamics. We carry out a Wilson-Kadanoff momentum-shell renormalization-group (RG) analysis and identify an infinite set of diagrams which are marginal in the RG sense. We show, in agreement with previous work, that the same problem arises for the randomly stirred Navier-Stokes equation. The marginal variables can be suppressed by working near equilibrium, where stochastic forcing represents thermal fluctuations. In a similar manner, we consider regimes where the MHD equations are subject either to kinetic or magnetic forcing only. In such models the macroscopic limit can be taken such that all marginal terms are irrelevant and the dynamics is governed by linear equations. Non-trivial fixed points are identified and limiting values of either the kinematic viscosity or magnetic diffusivity are derived. A consistent description of MHD far from equilibrium is still absent, though we highlight several aspects of the functional integral formulation with regard to the symmetries of the system and propose possible ways to study this system non-perturbatively.