Renormalization Analysis of Magnetohydrodynamics: Two-Loop Approximation

Abstract

We investigate the stochastic version of the paradigmatic model of magnetohydrodynamic turbulence. The model can be interpreted as an active vector admixture subject to advective processes governed by turbulent flow. The back influence on fluid dynamics is explicitly taken into account. The velocity field is generated through a fully developed turbulent flow taking into account the violation of spatial parity, which is introduced through the helicity parameter ρ. We consider a generalized setup in which parameter A is introduced in model formulation, which is associated with the interaction part of the model, and its actual value represents different physical systems. The model is analyzed by means of the field-theoretic renormalization group. The calculation is performed using ε-expansion, where ε is the deviation from the Kolmogorov scaling. Two-loop numerical calculations of the renormalization constant associated with the renormalization of the magnetic field are presented.

Keywords

• magnetohydrodynamics
• fully developed turbulence
• field-theoretic renormalization group
• parity symmetry breaking
• helicity