  High-frequency quasi-periodic oscillations (HFQPOs) observed in the emission
of black-hole X-ray binary systems promise insight into strongly curved
spacetime. `Discoseismic' oscillations with frequencies set by the intrinsic
properties of the central black hole, in particular `trapped inertial waves'
(r-modes), offer an attractive explanation for HFQPOs. To produce an observable
signature, however, such oscillations must be excited to sufficiently large
amplitudes. Turbulence driven by the magnetorotational instability (MRI) fails
to provide the necessary amplification, but r-modes may still be excited via
interaction with accretion disc warps or eccentricities. We present 3D global
hydrodynamic simulations of relativistic accretion discs, which demonstrate for
the first time the excitation of trapped inertial waves by an imposed
eccentricity in the flow. While the r-modes' saturated state depends on the
vertical boundary conditions used in our unstratified, cylindrical framework,
their excitation is unambiguous in all runs with eccentricity >0.005 near the
ISCO. These simulations provide a proof of concept, demonstrating the
robustness of trapped inertial wave excitation in a non-magnetized context. In
a companion paper, we explore the competition between this excitation, and
damping by magnetohydrodynamic turbulence.

High Energy Astrophysical Phenomena