We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B0 qq∥. Numerically and analytically, we find energy spectra E± approx. k⊥n±, such that n+ + n- = -4, where E± are the spectra of the Elsasser variables z± = v ± b in the two-dimensional case (k∥ = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.
ASJC Scopus subject areas
- Condensed Matter Physics