Residual energy in weakly compressible turbulence with a mean guide field

Abstract

The energy distribution is a fundamental property of magnetohydrodynamic (MHD) turbulence. In strongly magnetized turbulence energy imbalances arise and are quantified by the residual energy: $E_r~=~(E_{kin}~ - ~E_{mag})$; $E_{kin}$ and $E_{mag}$ stand for the volume-averaged kinetic and magnetic energy, respectively. We explore the properties of $E_r$ in weakly compressible MHD turbulence in the presence of an initially strong (guide) magnetic field, investigating how the driving mechanism and the magnetic field strength affect the cascade of $E_r$. We run a suite of direct numerical simulations with the PENCIL code. The sonic Mach number is approximately equal to 0.1 in all simulations, whereas the plasma beta varies. We drive turbulence by either injecting velocity or magnetic fluctuations at large scales and study the power spectra of kinetic, magnetic, density, and $E_r$. Magnetically driven simulations show locally imbalanced Alfvénic fluctuations and a $\propto k^{-3/2}$ cascade, consistent with the dynamic alignment theory. In the inertial range, $E_r \approx$ 0. Kinetically driven simulations give rise to a $\propto k^{-1}$ scaling, consistent with weakly interacting modes that preserve a high level of coherence throughout the inertial range. Residual energy is positive at all scales of the inertial range. The spectral slope of the $E_r$ cascade steepens systematically with increasing magnetization, varying from approximately -1 at $β= 0.3$ to between -2.0 and -5/3 at $β= 4.0$. The energy partition in weakly compressible turbulence is strongly influenced by the forcing mechanism, even when the global sonic and Alfvénic Mach numbers are comparable across simulations.