Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

Abstract

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $σ_c =0$ and $σ_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d \ge d_c \approx 2.2$. The renormalized viscosity $ν^*$ and resistivity $η^*$ have been calculated, and they are found to be positive for all parameter regimes. For $σ_c=0$ and large Alfvén ratio (ratio of kinetic and magnetic energies) $r_A$, $ν^*=0.36$ and $η^*=0.85$. As $r_A$ is decreased, $ν^*$ increases and $η^*$ decreases, untill $r_A \approx 0.25$ where both $ν^*$ and $η^*$ are approximately zero. For large $d$, both $ν^*$ and $η^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $σ_c \to 1$ are also reported.