The production of turbulence by gravitational instabilities in self-gravitating differentially rotating disks

Interstellar molecular clouds can collapse under their selfgravity. As numerical calculations have shown, the process of collapse mostly leads to differentially rotating self-gravitating disks without any central condensation. Our calculation shows that these disks are mostly gravitational unstable and can build up turbulent motion by these instabilities. From the conditions of gravitational instabilities we calculate the dispersion relation and determine the most unstable wavelength. The mean turbulent velocity and the mixing length are calculated from these wavelengths. Turbulent viscosity which results from the turbulent motion determine the angular momentum transportation out of the disk and therefore the time scale of mass concentration of the whole disk. The source of turbulent energy in this case is the gravitational energy in the rotating disk.