Density Statistics of Compressible MHD Turbulence
  Density is the turbulence statistics that is most readily available from observations. Different regimes of turbulence correspond to different density spectra. For instance, the viscosity-damped regime of MHD turbulence relevant, for instance, to partially ionized gas, can be characterized by shallow and very anisotropic spectrum of density. This spectrum can result in substantial variations of the column densities. Addressing MHD turbulence in the regime when viscosity is not important over the inertial range, we demonstrate with numerical simulations that it is possible to reproduce both the observed Kolmogorov spectrum of density fluctuations observed in ionized gas by measuring scintillations and more shallow spectra that are obtained through the emission measurements. We show that in supersonic turbulence the high density peaks dominate shallow isotropic spectrum, while the small-scale underlying turbulence that fills most of the volume has the Kolmogorov spectrum and demonstrates scale-dependent anisotropy. The limitations of the spectrum in studying turbulence induce searches of alternative statistics. We demonstrate that a measure called "bispectrum" may be a promising tool. Unlike spectrum, the bispectrum preserves the information about wave phases. 
A. Lazarian, G. Kowal, A. Beresnyak