Field theoretic calculation of renormalized-viscosity, renormalized-resistivity, and energy fluxes of magnetohydrodynamic turbulence

Abstract

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with zero cross helicity. Kolmogorov's 5/3 powerlaw has been shown to be a consistent solution for $d \ge d_c \approx 2.2$. For Kolmogorov's solution, both renormalized viscosity and resistivity are positive for the whole range of parameters. Various cascade rate and Kolmogorov's constant for MHD turbulence have been calculated by solving the flux equation to the first order in perturbation series. We find that the magnetic energy cascades forward. The Kolmogorov's constant for $d=3$ does not vary significantly with $r_A$ and is found to be close to the constant for fluid turbulence.