On the Spectrum of Magnetohydrodynamic Turbulence

We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that smallscale fluctuations of the velocity and magnetic fields become increasingly dynamically aligned as their scale decreases, so that turbulent “eddies” become locally anisotropic in the plane perpendicular to the large-scale magnetic field. In the limit of weak anisotropy, that is, weak large-scale magnetic field, our model reproduces the Goldreich-Sridhar spectrum, while the limit of strong anisotropy, that is, strong large-scale magnetic field, corresponds to the Iroshnikov-Kraichnan scaling of the spectrum. This is in good agreement with recent numerical results. Subject headings: MHD–turbulence