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 ${\sigma }_c=0$ and ${\sigma }_c\to 1$. 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 ${\nu }^{\ast }$ and resistivity ${\eta }^{\ast }$ have been calculated, and they are found to be positive for all parameter regimes. For ${\sigma }_c=0$ and large Alfvén ratio (ratio of kinetic and magnetic energies) $r_A$, ${\nu }^{\ast }=0.36$ and ${\eta }^{\ast }=0.85$. As $r_A$ is decreased, ${\nu }^{\ast }$ increases and ${\eta }^{\ast }$ decreases, untill $r_A\approx 0.25$ where both ${\nu }^{\ast }$ and ${\eta }^{\ast }$ are approximately zero. For large $d$, both ${\nu }^{\ast }$ and ${\eta }^{\ast }$ vary as $d^{-1/2}$. The renormalized parameters for the case ${\sigma }_c\to 1$ are also reported.

19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001)

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