On the spectrum of MHD turbulence

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  • 2 March 2005
Abstract
We propose a phenomenological model for the energy spectrum of incompressible MHD turbulence. We argue that the nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the external magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that fluctuations of velocity and magnetic fields become dynamically aligned, so that turbulent "eddies" become locally anisotropic in the plane perpendicular to the large-scale magnetic field. The alignment is scale-dependent, i.e., it is stronger for smaller scales. In the limit of weak anisotropy (i.e., weak large-scale magnetic field) our model reproduces the Goldreich-Sridhar spectrum, while the limit of strong anisotropy (i.e., strong large-scale magnetic field) corresponds to the Iroshnikov-Kraichnan scaling of the spectrum. This is in good agreement with recent numerical results.

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