Residual energy in weakly compressible turbulence with a mean guide field

TL;DR

This study investigates the behavior of residual energy in weakly compressible MHD turbulence with a strong guide field, revealing how different driving mechanisms and plasma beta influence the energy cascade and spectral slopes.

Contribution

It provides new insights into the spectral properties and cascade behaviors of residual energy in weakly compressible MHD turbulence under various plasma conditions and driving mechanisms.

Findings

Residual energy spectral slope varies with plasma beta.

Magnetically-driven turbulence shows a $k^{-3/2}$ cascade.

Kinetically-driven turbulence exhibits a $k^{-1}$ cascade.

Abstract

The energy distribution is a fundamental property of magnetohydrodynamic (MHD) turbulence. In strongly magnetized turbulence energy imbalances can arise, quantified by the so-called residual energy: $E_r~=~(E_{kin}~ - ~E_{mag})$; $E_{kin}$ and $E_{mag}$ stand for the volume-averaged kinetic and magnetic energy, respectively. Numerical simulations of incompressible turbulence yield $E_r < 0$, which is consistent with Solar wind observations, while in highly compressible turbulence simulations $E_r > $ 0. Differences arise in the cascade of $E_r$ between the two regimes. We explore the properties of $E_r$ in weakly compressible MHD turbulence in the presence of an initially strong (guide) magnetic field. We study the influence of different driving mechanisms and field strengths on the cascade of $E_r$. We run a suite of direct numerical simulations with the PENCIL code. All simulations are maintained through forcing in a quasi-static regime with sonic Mach numbers close to 0.1. We solely change the Alfv\'en Mach number, or equivalently the plasma beta ($\beta$) of the simulations. 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 Alfv\'enic fluctuations and a $\propto k^{-3/2}$ cascade, consistent with the dynamic alignment theory. Kinetically-driven simulations give rise to a $\propto k^{-1}$ scaling, consistent with interactions between Alfv\'en waves scattered by density inhomogeneities -- a hallmark of reflection-driven turbulence. Residual energy is positive with a spectral slope ($\alpha$) depending on $\beta$ as: for $\beta = 4.0$, $-2 \lesssim \alpha \lesssim -5/3$, for $\beta = 1.0$, $-5/3 \lesssim \alpha \lesssim -3/2$, and for $\beta = 0.3$, $\alpha \approx -1$.