Accretion discs around black holes: two dimensional, advection cooled flows

Two-dimensional accretion flows near black holes have been investigated by time-dependent hydrodynamical calculations. We assume that the flow is axisymmetric and that radiative losses of internal energy are negligible, so that the disc is geometrically thick and hot. Accretion occurs due to the overflow of the effective potential barrier near the black hole, similar to the case of the Roche lobe overflowing star in a binary system. We make no pre-assumptions on the properties of the flow, instead our models evolve self-consistently from an initially non-accreting state. The viscosity is due to the the small-scale turbulence and it is described by the $\alpha$-viscosity prescription. We confirm earlier suggestions that viscous accretion flows are convectively unstable. We found that the instability produces transient eddies of various length-scales. The eddies contribute to the strength of the viscosity in the flow by redistributing the angular momentum. They also introduce low amplitude oscillatory variations which have a typical frequency about $100\; \msun/M$ Hz for a system of mass $M$. This may be relevant to the high frequency ($\sim 4-10$ Hz) quasi-periodic oscillations observed in the Galactic black hole candidate X-ray sources.