Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

TL;DR

This study uses direct numerical simulations to analyze the energy cascade rate in isothermal compressible MHD turbulence, highlighting the dominant role of compressible flux and the effects of magnetic guide fields and Mach numbers.

Contribution

It provides a detailed analysis of the energy cascade in compressible MHD turbulence using a recently derived exact law, including the impact of magnetic guide fields and the importance of appropriate statistical decomposition methods.

Findings

Compressible flux is the main contributor to the energy cascade rate.

Source and hybrid terms become significant at small scales with strong guide fields.

Isotropic decomposition can produce spurious results compared to axisymmetric analysis.

Abstract

Three-dimensional direct numerical simulations are used to study the energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. Our analysis is guided by a two-point exact law derived recently for this problem in which flux, source, hybrid, and mixed terms are present. The relative importance of each term is studied for different initial subsonic Mach numbers $M_S$ and different magnetic guide fields ${\bf B}_0$. The dominant contribution to the energy cascade rate comes from the compressible flux, which depends weakly on the magnetic guide field ${\bf B}_0$, unlike the other terms whose modulus increase significantly with $M_S$ and ${\bf B}_0$. In particular, for strong ${\bf B}_0$ the source and hybrid terms are dominant at small scales with almost the same amplitude but with a different sign. A statistical analysis made with an isotropic decomposition based on the SO(3) rotation group is shown to generate spurious results in presence of ${\bf B}_0$, when compared with an axisymmetric decomposition better suited to the geometry of the problem. Our numerical results are compared with previous analyses made with in-situ measurements in the solar wind and the terrestrial magnetosheath.