Velocity Field of Compressible MHD Turbulence: Wavelet Decomposition and Mode Scalings

TL;DR

This paper introduces a wavelet-based method to decompose compressible MHD turbulence into modes, enabling detailed analysis of their spectra, statistics, and intermittency, with implications for astrophysical processes.

Contribution

It extends the Fourier-based decomposition to wavelet analysis, allowing local magnetic field variations to improve mode separation and turbulence characterization.

Findings

Intermittency varies among different turbulence components.

Local magnetic field analysis reveals different intermittency statistics.

Fast mode intermittency is highly sensitive to Mach number changes.

Abstract

We study compressible MHD turbulence, which holds key to many astrophysical processes, including star formation and cosmic ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid we use wavelet decomposition of the turbulent velocity field into Alfven, slow and fast modes, which presents an extension of the Cho & Lazarian (2003) decomposition approach based on Fourier transforms. The wavelets allow to follow the variations of the local direction of magnetic field and therefore improve the quality of the decomposition compared to the Fourier transforms which are done in the mean field reference frame. For each resulting component we calculate spectra and two-point statistics such as longitudinal and transverse structure functions, as well as, higher order intermittency statistics. In addition, we perform the Helmholtz-Hodge decomposition of the velocity field into the incompressible and compressible parts and analyze these components. We find that the turbulence intermittency is different for different components and we show that the intermittency statistics depend on whether the phenomenon was studied in the global reference frame related to the mean magnetic field or it was studied in the frame defined by the local magnetic field. The dependencies of the measures we obtained are different for different components of velocity, for instance, we show that while the Alfven mode intermittency changes marginally with the Mach number the intermittency of the fast mode is substantially affected by the change.