Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

Abstract

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

Variable energy flux in turbulence

“…Recently, Verma et al [142] simulated MHD turbulence and analyzed the variations of the above energy fluxes. They employed random forcing to the large-scale velocity modes in the wavenumber band (2,3).…”

“…Their numerically-computed energy fluxes for the steady state are illustrated in figure 18. As shown in the figure, all the energy fluxes vary with k due to cross transfers between the u and ζ [142]. For these reasons, the above fluxes are called variable energy fluxes.…”

“…Numerical verification of the exact relations, equations ( 145)- (148). From Verma et al Reproduced from [142]. CC BY 4.0.…”

Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind

“…Many authors 8,9,12 observe that the kinetic energy spectrum (E u (k)) is steeper than the magnetic energy spectrum (E b (k)). This relative steepening of E u (k) with relative to E b (k) is attributed to the energy transfers from the kinetic energy to the magnetic energy 29,30 . Note that these energy transfers are critical for the magnetic field generation or dynamo.…”

Generalized cross-helicity in non-ideal magnetohydrodynamics

“…The energy fluxes of MHD turbulence provide a measure for the transfers of energy among the velocity and magnetic fields (Verma 2019; Verma et al. 2021).…”