Obtaining Statistics of Turbulent Velocity from Astrophysical Spectral   Line Data
  Turbulence is a crucial component of dynamics of astrophysical fluids dynamics, including those of ISM, clusters of galaxies and circumstellar regions. Doppler shifted spectral lines provide a unique source of information on turbulent velocities. We discuss Velocity-Channel Analysis (VCA) and its offspring Velocity Coordinate Spectrum (VCS) that are based on the analytical description of the spectral line statistics. Those techniques are well suited for studies of supersonic turbulence. We stress that a great advantage of VCS is that it does not necessary require good spatial resolution. Addressing the studies of mildly supersonic and subsonic turbulence we discuss the criterion that allows to determine whether a traditional tool for such a research, namely, Velocity Centroids are dominated by density or velocity. We briefly discuss the use of higher order correlations as the means to study intermittency of turbulence. We discuss observational data available and prospects of the field. 
A. Lazarian