Random scattering and anisotropic turbulence of shear Alfvén wave packets

A theoretical model is given of anisotropic magnetohydrodynamic turbulence in the interstellar medium and the solar wind. The model is motivated by observations that show significant deviations from the Kolmogorov power law. Dimensional and heuristic arguments are given and critically assessed. On the basis of the weak turbulence approximation in which three-wave interactions dominate, analytical and numerical results are obtained for the anisotropic energy spectrum produced by the random scattering of shear Alfvén waves propagating parallel to a large-scale magnetic field. The energy spectrum is shown to be proportional to k^-2_⊥, qualitatively consistent with some observations and wave kinetic theory.