  We provide constraints on possible configurations and interactions of two
coplanar tori orbiting a central Kerr black hole (BH), in dependence on its
dimensionless spin. The two-tori configurations can be directly linked to the
current models featuring the obscuration of galactic BH X-ray emission. The
emergence of each torus instability phases is discussed and tori collision has
been also investigated. The first simple evaluation of the center-of-mass
energy proves that collision-energy-efficiency increases with the dimensionless
BH spin. We explore the phenomenological aspects of the corotating and
counterrotating tori by analyzing properties of the orbiting toroidal
configurations related to the fluid enthalpy flux, the mass-flux, the
mass-accretion-rates, and the cusp luminosity in the two cases of corotating
and counterrotating fluids in dependence on the SMBH spin. The analysis
resulted ultimately in a comparative investigation of the properties of
corotating versus counterrotating tori, demonstrating that two accretion tori
can orbit around the central Kerr attractor only under very specific
conditions. Our results also demonstrate that the dynamics of the unstable
phases of these double tori systems is significant for the high energy
phenomena which could be observable in the X-ray emission and extremely
energetic phenomena in active galactic nuclei and quasar.
