  In this Paper, we present theoretical arguments that the observationally
established index saturation effect vs mass accretion rate is a signature of
the bulk (converging) flow onto the black hole. We demonstrate that the index
saturation value depends on the plasma temperature of converging flow. We
self-consistently calculate the Compton cloud (CC) plasma temperature as a
function of mass accretion rate using the energy balance between energy
dissipation and Compton cooling. We explain the observable phenomenon, index-
mdot correlations using a Monte-Carlo simulation of radiative processes in the
innermost part (CC) of a BH source and we account for the Comptonization
processes in the presence of thermal and bulk motions, as basic types of plasma
motion. We show that, when mdot increases, BH sources evolve to high and very
soft states (HSS and VSS, respectively), in which the strong blackbody-like and
steep power-law components are formed in the resulting X-ray spectrum. The
simultaneous detections of these two components strongly depends on sensitivity
of high energy instruments, given that the relative contribution of the hard
power-law tail in the resulting VSS spectrum can be very low, which is why, to
date {\it RXTE} observations of the VSS X-ray spectrum has been characterized
by the presence of the strong BB-like component only. We also predict specific
patterns for high-energy efold (cutoff) energy (E_{fold}) evolution with mdot
for thermal and dynamical (bulk) Comptonization cases. For the former case,
E_{fold} monotonically decreases with mdot, in the latter case, the
E_{fold}-decrease is followed by its increase at high values of mdot. The
observational evolution of E_{fold} vs mdot can be one more test for the
presence of a converging flow effect in the formation of the resulting spectra
in the close vicinity of BHs.
