On the Spectrum of Magnetohydrodynamic Turbulence

We propose a phenomenological model for incompressible magnetohydrodynamicturbulence. We argue that nonlinear-wave interaction weakens as the energycascade proceeds to small scales, however, the anisotropy of fluctuations alongthe large-scale magnetic field increases, which makes turbulence strong at allscales. To explain the weakening of the interaction, we propose thatsmall-scale fluctuations of the velocity and magnetic fields becomeincreasingly dynamically aligned as their scale decreases, so that turbulenteddies become locally anisotropic in the plane perpendicular to the large-scalemagnetic field. In the limit of weak anisotropy, that is, weak large-scalemagnetic field, our model reproduces the Goldreich-Sridhar spectrum, while thelimit of strong anisotropy, that is, strong large-scale magnetic field,corresponds to the Iroshnikov-Kraichnan scaling of the spectrum. This is ingood agreement with recent numerical results.Comment: 10 pages, 1 figure; minor changes to match published versio