Renormalized reduced magnetohydrodynamics

Abstract

A renormalized reduced magnetohydrodynamics turbulence theory based upon the direct-interaction approximation is presented. Importantly, the statistical equations derived conserve energy. The equations also properly contain the effects of magnetic shear. For stationary and homogeneous turbulence in a uniform mean magnetic field, the direct-interaction approximation naturally separates into two parts: a coherent part that can be interpreted in terms of a frequency- and wavenumber-dependent turbulent resistivity and viscosity, and an incoherent nonlinear mode coupling source term. In a two-dimensional isotropic spectrum that is narrow in wavelength (the spread in wavenumber of the energy containing modes is small compared to the mean wavenumber), the plasma response at nearby wavelengths is characterized by a turbulent resistivity that depends only on the kinetic energy of the fluctuations, while the turbulent viscosity is negligible in comparison. At much shorter wavelengths the turbulent resistivity and viscosity are identical and both depend on the total energy in the fluctuations including the magnetic energy.