We present the numerical study of dynamical instability of a
pressure-supported relativistic torus, rotating around the black hole with a
constant specific angular momentum on a fixed space-time background, in case of
perturbation by a matter coming from the outer boundary. Two dimensional
hydrodynamical equations are solved at equatorial plane using the HRSCS to
study the effect of perturbation on the stable systems. We have found that the
perturbed torus creates an instability which causes the gas falling into the
black hole in a certain dynamical time. All the models indicate an oscillating
torus with certain frequency around their instant equilibrium. The dynamic of
the accreted torus varies with the size of initial stable torus, black hole
spin and other variables, such as Mach number, sound speed, cusp location of
the torus, etc. The mass accretion rate is slightly proportional to the
torus-to-hole mass ratio in the black hole-torus system, but it strongly
depends on the cusp location of the torus. The cusp located in the
equipotential surfaces of the effective potential moves outwards into the
torus. The dynamical change of the torus increases the mass accretion rate and
triggers the Papaloizou-Pringle instability. It is also observed that the
growth of the m=1 mode of the Papaloizou-Pringle instability occurs for a
wide range of fluid and hydrodynamical parameters and a black hole spin. We
have also computed the QPOs from the oscillating relativistic torus.Comment: 14 Pages, 14 Figures, High resolution version of Figs.1 and 7 can be
found in the original manuscript. Substantial revision has been made. The
title, abstract and whole text are revise
