Abstract
Weak magnetohydrodynamic turbulence in the presence of a uniform magnetic field is dominated by three-wave interactions that mediate the collisions of shear-Alfvén wave packets propagating in opposite directions parallel to the magnetic field. The scaling of three-wave couplings is calculated by asymptotic analysis and a direct numerical evaluation of the nonlinear interaction based on the reduced magnetohydrodynamic equations. A new relation is derived between the spectral index of three-wave coupling and the spectral indices of two random-amplitude wave packets. This relation has significant implications for the anisotropic energy spectrum.
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