Numerical simulation of acoustic instabilities in thin accretion disks

A second-order two-dimensional hydrodynamical code has been developed to study the stability of the Keplerian flow, using a numerical viscosity for the stabilization of shock fronts and for the damping of small-scale fluctuations in the shear flow. The linear rates are reproduced by small amplitudes of the initial fluctuations. It is found that the system does not develop supersonic fluctuations, but saturates (mainly by the dissipation in the weak shock fronts) at a Mach number of 0.5 of the fluctuations. No evidence is found for the development of turbulence. In the saturated state, the unstable modes are found to have a viscosity of alpha of about (0.3-0.9) x 10 to the -3rd.