  We performed axisymmetric hydrodynamical simulations of oscillating tori
orbiting a non-rotating black hole. The tori in equilibrium were constructed
with a constant distribution of angular momentum in a pseudo-Newtonian
potential (Klu{\'z}niak-Lee). Motions of the torus were triggered by adding
sub-sonic velocity fields: radial, vertical and diagonal to the tori in
equilibrium. As the perturbed tori evolved in time, we measured $L_{2}$ norm of
density and obtained the power spectrum of $L_{2}$ norm which manifested
eigenfrequencies of tori modes. The most prominent modes of oscillation excited
in the torus by a quasi-random perturbation are the breathing mode and the
radial and vertical epicyclic modes. The radial and the plus modes, as well as
the vertical and the breathing modes will have frequencies in an approximate
3:2 ratio if the torus is several Schwarzschild radii away from the innermost
stable circular orbit. Results of our simulations may be of interest in the
context of high-frequency quasi-periodic oscillations (HF QPOs) observed in
stellar-mass black hole binaries, as well as in supermassive black holes.

High Energy Astrophysical Phenomena