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 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.