ar X iv : a st ro - p h / 06 08 04 6 v 2 5 A ug 2 00 6 Velocity Coordinate Spectrum as a Tool to study

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 Coordinate Spectrum (VCS) technique that are based on the analytical description of the spectral line statistics. We stress that a great advantage of VCS is that it does not necessary require good spatial resolution. Moreover, both emission and absoprtion lines can be used. 1. Turbulence and Doppler shifted lines As a rule astrophysical fluids are turbulent and the turbulence is magnetized. This ubiquitous turbulence determines the transport properties of interstellar medium many properties of Solar and stellar winds, accretion disks etc. One may say that to understand heat conduction, transport and acceleration of cosmic rays, propagation of electromagnetic radiation in different astrophysical environments it is absolutely essential to understand the properties of underlying turbulence. The mysterious processes of star formation (see McKee & Tan 2002, Elmegreen 2002, Pudritz 2001) and interstellar chemistry (see Falgarone 1999 and references therein), shattering and coagulation of dust (see Lazarian & Yan 2003 and references therein) are also intimately related to properties of magnetized compressible turbulence (see reviews by Elmegreen & Scalo 2004). From the point of view of fluid mechanics astrophysical turbulence is characterized by huge Reynolds numbers, Re, which is the inverse ratio of the eddy turnover time of a parcel of gas to the time required for viscous forces to slow it appreciably. For Re ≫ 100 we expect gas to be turbulent and this is exactly what we observe in HI (for HI Re ∼ 10 8). Statistical description is a nearly indispensable strategy when dealing with turbulence. The big advantage of statistical techniques is that they extract underlying regularities of the flow and reject incidental details. Kolmogorov description of unmagnetized incompressible turbulence is a statistical one. For instance it predicts that the difference