  Two-dimensional (axially symmetric) numerical hydrodynamical calculations of
accretion flows which cannot cool through emission of radiation are presented.
The calculations begin from an equilibrium configuration consisting of a thick
torus with constant specific angular momentum. Accretion is induced by the
addition of a small anomalous azimuthal shear stress which is characterized by
a function \nu. We study the flows generated as the amplitude and form of \nu
are varied. A spherical polar grid which spans more than two orders of
magnitude in radius is used to resolve the flow over a wide range of spatial
scales. We find that convection in the inner regions produces significant
outward mass motions that carry away both the energy liberated by, and a large
fraction of the mass participating in, the accretion flow. Although the
instantaneous structure of the flow is complex and dominated by convective
eddies, long time averages of the dynamical variables show remarkable
correspondence to certain steady-state solutions. Near the equatorial plane,
the radial profiles of the time-averaged variables are power-laws with an index
that depends on the radial scaling of the shear stress. We find that regardless
of the adiabatic index of the gas, or the form or magnitude of the shear
stress, the mass inflow rate is a strongly increasing function of radius, and
is everywhere nearly exactly balanced by mass outflow. The net mass accretion
rate through the disc is only a fraction of the rate at which mass is supplied
to the inflow at large radii, and is given by the local, viscous accretion rate
associated with the flow properties near the central object.
