On the Spectrum of Magnetohydrodynamic Turbulence

• Published in: The Astrophysical journal Vol. 626; no. 1; pp. L37 - L40
• Main Author: Boldyrev, Stanislav
• Format: Journal Article
• Language: English
• Published: Chicago, IL IOP Publishing 10-06-2005; University of Chicago Press
• Subjects: MHD; turbulence; MHD turbulence
• ISSN: 1538-4357; 0004-637X; 1538-4357
• DOI: 10.1086/431649

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 small-scale 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.