RENORMALIZATION-GROUP ANALYSIS OF REDUCED MAGNETOHYDRODYNAMICS WITH APPLICATION TO SUBGRID MODELING

The technique for obtaining a subgrid model for Navier-Stokes turbulence introduced by Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986); Phys. Rev. Lett. 57, 1772 (1986)], based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMHD) equations. A RNG treatment of the Alfven turbulence (perpendicular scale k-perpendicular-to -1 << k parallel-to -1 parallel scale) supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k --> 0, dependent on the amplitude of turbulence. When the RNG analysis is augmented by the Kolmogorov argument for energy cascade the effective viscosity and resistivity become independent of the molecular quantitities. This leads to a "universal" subgrid model, which all models approach at the largest scales. A self-contained system of equations is derived for the range of scales, 0 < k < K, where K = pi/DELTA, is the maximum wave number for a grid size DELTA. In this system the resistive and viscous dissipation is represented by differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities being computed.