Residual energy in weakly compressible turbulence with a mean guide field

Context . Energy distribution is a fundamental property of magnetohydrodynamic (MHD) turbulence. In strongly magnetized turbulence, energy imbalances can arise, which can be quantified by the so-called residual energy: E r = ( E kin − E mag ). Here, 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; whereas in highly compressible turbulence simulations, we have E r > 0. Differences arise in the cascade of E r between the two regimes. Aims . 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 . Methods . We ran a suite of direct numerical simulations with the PENCIL code. All simulations were maintained through forcing in a quasi-static regime with sonic Mach numbers close to 0.1 for a number of different crossing times. We solely changed the Alfvén Mach number or, equivalently, the plasma beta ( β ) of the simulations. We drove turbulence by either injecting velocity or magnetic fluctuations at large scales and we studied the power spectra of kinetic, magnetic, density, and E r . Results . Magnetically driven simulations show dominant Alfvénic fluctuations and a ∝ k −3/2 scaling in all spectra. In the inertial range E r ≈ 0. Turbulence is balanced with zero net cross-helicity, but exhibit strong locally imbalanced fluctuations that are qualitatively consistent with the dynamic alignment theory. Kinetically driven simulations give rise to a ∝ k −1 scaling, consistent with weakly interacting modes that preserve a high level of coherence throughout the inertial range. For the kinetically driven simulations, we report an excess in kinetic energy with respect to magnetic at all scales of the inertial range. The cascade of the residual energy ( E r ∝ k α ) depends on β and scales as: for β = 4.0, −2 ≲ α ≲ −5/3, for β = 1.0, −5/3 ≲ α ≲ −3/2, and for β = 0.3, α ≈ −1. Conclusions . 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.