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 Afvén 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 $E_v-E_b$ at small field-parallel wave numbers. As a result, the energy spectra of counter-propagating Alfvén 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 $E(k)\propto k_{\perp }^{-2}$. The generation of condensate is apparently related to the breakdown of mirror symmetry in non-balanced turbulence.

4 pages, 3 figures

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