Instability of high-frequency acoustic waves in accretion disks with turbulent viscosity

The dynamics of linear perturbations in a differentially rotating accretion disk with a non-homogeneous vertical structure is investigated. We find that turbulent viscosity results in instability of both pinching oscillations, and bending modes. Not only the low-frequency fundamental modes, but also the high-frequency reflective harmonics appear to be unstable. The question of the limits of applicability of the thin disk model (MTD) is also investigated. Some differences in the dispersion properties of the MTD and of the three-dimensional model appear for wave numbers k <∼ (1–3)/h (h is the half-thickness of a disk). In the long-wavelength limit, the relative difference between the eigenfrequencies of the unstable acoustic mode in the 3D-model and the MTD is smaller than 5%. In the short wavelength case (kh > 1) these differences are increased.