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.