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