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Two-dimensional accretion flows near black holes have been investigated bytime-dependent hydrodynamical calculations. We assume that the flow isaxisymmetric and that radiative losses of internal energy are negligible, sothat the disc is geometrically thick and hot. Accretion occurs due to theoverflow of the effective potential barrier near the black hole, similar to thecase of the Roche lobe overflowing star in a binary system. We make nopre-assumptions on the properties of the flow, instead our models evolveself-consistently from an initially non-accreting state. The viscosity is dueto the the small-scale turbulence and it is described by the $\alpha$-viscosityprescription. We confirm earlier suggestions that viscous accretion flows areconvectively unstable. We found that the instability produces transient eddiesof various length-scales. The eddies contribute to the strength of theviscosity in the flow by redistributing the angular momentum. They alsointroduce low amplitude oscillatory variations which have a typical frequencyabout $100\; \msun/M$ Hz for a system of mass $M$. This may be relevant to thehigh frequency ($\sim 4-10$ Hz) quasi-periodic oscillations observed in theGalactic black hole candidate X-ray sources.

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