Spectrum of weak magnetohydrodynamic turbulence
Abstract
Turbulence of magnetohydrodynamic waves in nature and in the laboratory is generally cross-helical or non-balanced, in that the energies of Afv\'en waves moving in opposite directions along the guide magnetic field are unequal. Based on high-resolution numerical simulations it is proposed that such turbulence spontaneously generates a condensate of the residual energy Ev-Eb at small field-parallel wave numbers. As a result, the energy spectra of counter-propagating Alfv\'en waves are not scale-invariant. In the limit of infinite Reynolds number, the universality is asymptotically restored at large wave numbers, and both spectra attain the scaling E(k) k-2. The generation of condensate is apparently related to the breakdown of mirror symmetry in non-balanced turbulence.