We report on next phase of our study of rotating accretion flows onto black holes. We consider hydrodynamical (HD) accretion flows with a spherically symmetric density distribution at the outer boundary but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum. We study accretion flows by means of numerical two-dimensional, axisymmetric, HD simulations for variety of the adiabatic index, $��$ and the gas temperature at infinity, $c_\infty$. Our work is an extension of work done by Proga & Begelman who consider models for only $��=5/3$. Our main result is that the flow properties such as the topology of the sonic surface and time behavior strongly depend on $��$ but little on $c_\infty$. In particular, for $1 < ��< 5/3$, the mass accretion rate shows large amplitude, slow time-variability which is a result of mixing between slow and fast rotating gas. This temporal behavior differs significantly from that in models with $��\simless 5/3$ where the accretion rate is relatively constant and from that in models with $��\simgreat 1$ where the accretion exhibits small amplitude quasi-periodic oscillations. The key parameter responsible for the differences is the sound speed of the accretion flow which in turn determines whether the flow is dominated by gas pressure, radiation pressure or rotation. Despite these differences the time-averaged mass accretion rate in units of the corresponding Bondi rate is a weak function of $��$ and $c_\infty$.

31 pages, 14 figures, accepted for publication in ApJ, for full resolution version goto http://users.camk.edu.pl/mmosc/ms.pdf