# Energy transfer in compressible magnetohydrodynamic turbulence

## TL;DR

This paper extends energy transfer analysis to compressible MHD turbulence, deriving new transfer functions and analyzing simulations to reveal local, forward energy cascades and regime-dependent behaviors.

## Contribution

It introduces four new transfer functions for compressible MHD turbulence and demonstrates their application through simulation analysis, expanding understanding of energy dynamics.

## Key findings

- Energy transfer is local and forward in both cascades.
- Magnetic cascade is stronger than kinetic cascade.
- Certain transfer functions show regime and method dependence.

## Abstract

Magnetic fields, compressibility and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e. how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.