5. Discussion and conclusions
Acoustic waves in a differentially rotating gaseous disk can play an important role for understanding the turbulent viscosity in accretion disks. The amplitude of small-scale (in r and in z) waves grows most rapidly. Such instabilities do not destroy the initial flow at a nonlinear stage, but can effectively make the disk matter turbulent, and in turn, the turbulent viscosity generates unstable sound modes. A self-consistent regime with turbulent viscosity arises. Beside the dissipation mechanism analysed above, the development of global resonant Papaloizou-Pringle modes (Papaloizou & Pringle 1987; Savonije & Heemskerk 1990), the resonant amplification of acoustic oscillations in the regime of double-flow accretion (Mustsevoj & Khoperskov 1991) and in the case of disk accretion onto a magnetized compact object (Hoperskov et al. 1993) may be important for understanding the turbulent viscosity. It is remarkable that in all cases the characteristic time scale does not exceed the dynamical time scale (), and that all values are of the same order.
We have demonstrated the possibility of unstable high-frequency acoustic waves in a differentially rotating gaseous disk. They exist in the system for a limited period, and the presence of a positive growth rate does not mean that the perturbations reach the nonlinear stage. The perturbations leave the disk with a speed and the characteristic life-time in the disk is disk rotation periods. In view of the derived estimation for we have obtained the growth rate of wave amplitude (). Nonaxisymmetric perturbations may stay in the system for a longer time and reach a non-linear stage.
The main conclusions of this study are:
© European Southern Observatory (ESO) 1999
Online publication: April 12, 1999