Extended inertial range phenomenology of magnetohydrodynamic turbulence

A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan Phys. Fluids 8, 1385 (1965). The role of Alfvén wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22–1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented ‘‘golden rules’’ for relating the spectral transfer time scale to the Alfvén and eddy-turnover time scales.