Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $σc=0$ and $σc→1.$ Kolmogorov’s $53$ power law is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d⩾dc≈2.2.$ The renormalized viscosity ν^* and resistivity η^* have been calculated, and they are found to be positive for all parameter regimes. For $σc=0$ and large Alfvén ratio (ratio of kinetic and magnetic energies) $rA,$ ν^*=0.36, and η^*=0.85. As $rA$ is decreased, ν^* increases and η^* decreases, until $rA≈0.25,$ 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 $σc→1$ are also reported.