Excitation of trapped oscillations in discs around black holes

High-frequency quasi-periodic oscillations detected in the light curves of black hole candidates can, according to one model, be identified with hydrodynamic oscillations of the accretion disc. We describe a non-linear coupling mechanism, suggested by Kato, through which inertial waves trapped in the inner regions of accretion discs around black holes are excited. Global warping and/or eccentricity of the disc have a fundamental role in this coupling: they combine with trapped modes, generating negative energy waves, that are damped as they approach the inner edge of the disc or their corotation resonance. As a result of this damping, inertial oscillations are amplified. We calculate the resulting eigenfunctions and their growth rates.