Numerical modeling of formation of high density solitary vortices in a circumstellar disk

The gravitational instability in the two-phase medium of a circumstellar disk is studied numerically. The formation process for high density solitary clumps is reproduced. The hybrid model of an unstable circumstellar disk includes the gas dynamics equations, the collisionless Boltzmann equation, and the equation for the self-consistent gravitational field. The code developed allows one to calculate the nonlinear modes of instability development in massive disks. It is shown that all clumps on the stage of their formation are vortices with the maximum of pressure and density at the center and with the solid-body rotation irrespective of their size and formation time.