  Context. The high-frequency quasi-periodic oscillations (HF QPOs) in neutron
star and stellar-mass black hole X-ray binaries may be the result of a
resonance between the radial and vertical epicyclic oscillations in strong
gravity. Aims. In this paper we investigate the resonant coupling between the
epicyclic modes in a torus in a strong gravitational field. Methods. We perform
numerical simulations of axisymmetric constant angular momentum tori in the
pseudo-Newtonian potential. The epicyclic motion is excited by adding a
constant radial velocity to the torus. Results. We verify that slender tori
perform epicyclic motions at the frequencies of free particles, but the
epicyclic frequencies decrease as the tori grow thicker. More importantly, and
in contrast to previous numerical studies, we do not find a coupling between
the radial and vertical epicyclic motions. The appearance of other modes than
the radial epicyclic motion in our simulations is rather due to small numerical
deviations from exact equilibrium in the initial state of our torus.
Conclusions. We find that there is no pressure coupling between the two
axisymmetric epicyclic modes as long as the torus is symmetric with respect to
the equatorial plane. However we also find that there are other modes in the
disc that may be more attractive for explaining the HF QPOs.
