Spectrum of weak magnetohydrodynamic turbulence

TL;DR

This paper investigates the behavior of weak magnetohydrodynamic turbulence, revealing the spontaneous formation of a residual energy condensate at small wave numbers and the asymptotic universality of energy spectra at large wave numbers.

Contribution

It introduces high-resolution simulations showing how non-balanced MHD turbulence generates a residual energy condensate and restores universal scaling at high wave numbers.

Findings

Residual energy condensate forms at small wave numbers.

Energy spectra become scale-invariant with a $k_{ot}^{-2}$ scaling at large wave numbers.

Universality of spectra is restored in the infinite Reynolds number limit.

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 $E_v-E_b$ 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 $E(k)\propto k_{\perp}^{-2}$. The generation of condensate is apparently related to the breakdown of mirror symmetry in non-balanced turbulence.