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

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