Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids

TL;DR

This paper derives an exact relation for energy transfer in compressible, self-gravitating MHD turbulence, accounting for various physical effects and providing insights into energy flux behaviors in different regimes.

Contribution

It introduces a simplified, exact relation for energy transfer in compressible MHD turbulence that includes effects like rotation and magnetic fields, improving upon previous formulations.

Findings

Solid-body rotation does not affect energy flux.

Background magnetic fields have a non-trivial impact on flux.

Compressible turbulence exhibits non-zero energy flux due to alignments.

Abstract

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by S. Banerjee and S. Galtier (Phys. Rev. E,93, 033120, 2016) and S. Banerjee and S. Galtier (J. Phys. A, Math. and Theor.,50, 015501, 2017), an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be non-trivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.