We obtain global solutions for radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined by mixinglength theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solutions correspond to large viscosity parameter α 0.1-they are purely advection-dominated with no convection; they have been extensively studied in the literature. Type II solutions are for moderate α 0.01, and have a three-zone structure. The inner zone is advection-dominated, the middle zone is convection-dominated and ranges from a few tens to a few thousands of gravitational radii, and the outer zone is convectively stable and outwardly matches a Keplerian disc. The net energy flux throughout the flow is inward, as in type I solutions. Type III solutions, which are for small α 0.001, consist of two zones as Abramowicz et al. suggested previously: an inner advection-dominated zone and an outer convection-dominated zone, separated at a radius of a few tens of gravitational radii. This type of solution has an outward net energy flux. In both type II and type III solutions, the radial density profile is between the 1/2 law of the self-similar convection-dominated accretion flow model and the 3/2 law of the self-similar advection-dominated accretion flow model, and the efficiency of energy release is found to be extremely low. Our results are in good agreement with those of recent numerical simulations.

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAFs) around black holes, using a method similar to that of Chakrabarti. We choose the sonic radius of the

This paper presents global solutions of adiabatic accretion flows with isothermal shocks in Kerr black hole geometry. It is known that in the previously studied cases, where the flow including the shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of a-x type. However, the solution topology in the present case shows remarkable new characteristics: for the same flow parameters there can be two stable shock solutions satisfying physical boundary conditions, and the solution can be of three types, namely a-x, x-a and a-a type. In addition, shocks in the present case occur for a parameter region different from that for Rankine-Hugoniot shocks. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also significant that the effects of frame-dragging of a rapid Kerr black hole on the shock formation are discovered. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flows, namely those of Shakura & Sunyaev and Narayan & Yi, and some comments are made about the fact that numerous authors who have studied transonic global solutions of accretion flows have found no shocks.

This paper presents a fully relativistic study on the standing shock formation in thin, stationary, axisymmetric, adiabatic fluid flows in Kerr geometry. Wend out the energyangular momentum parameter space for which the flow may develop shocks. The multiplicity of the formal shock location is removed by employing the boundary conditions and stability analysis: the stable shock location is practically unique. The effects of the frame-dragging of a rapid rotating black hole on the shock properties are pointed out. Finally, we discuss the validity of the assumptions made about the flow and conclude that shocks are likely to be common in astrophysical flows.

This paper presents global solutions of adiabatic accretion flows with isothermal shocks in the potential of a non-rotating black hole. It is known that in the previously studied cases, where flow including shock is either entirely adiabatic or entirely isothermal, there can be no more than one stable shock solution, and the solution can only be of the a-x type; however, the solution topology in the present case shows new remarkable characteristics: for the same flow parameters there can be two stable shock solutions satisfying the physical boundary conditions, and the solution can be of three types, namely a-x, x-a, and a-a type. In addition, shocks in the present case occur for a parameter region that is different from that for RankineHugoniot shocks to occur. These results greatly increase the possibilities of shock formation in astrophysical flows. It is also noted that in the present case the efficiency of energy release at the shock can be as high as a few percent. Finally, a brief comparison is made between shocked inviscid flows and two types of shock-free viscous flow, namely that of Shakura and Sunyaev (1973, AAA 09.066.049) and that of Narayan and Yi (1994, AAA 61.064.083).