Turbulent MHD transport coefficients: an attempt at self-consistency

Abstract

The authors complete some multiple-scale perturbation calculations of turbulent MHD transport coefficients. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. They address the problem of rendering such calculations self-consistent, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg (1948) for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation (1964). The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit a value of 1.72 is extracted for the Kolmogorov constant (1941).