  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.
