Tilted accretion discs in cataclysmic variables: tidal instabilities and superhumps

We investigate the growth of tidal instabilities in accretion discs in a binary star potential, using three dimensional numerical simulations. As expected from analytic work, the disc is prone to an eccentric instability provided that it is large enough to extend to the 3:1 resonance. The eccentric disc leads to positive superhumps in the light curve. It has been proposed that negative superhumps might arise from a tilted disc, but we find no evidence that the companion gravitational tilt instability can grow fast enough in a fluid disc to create a measurable inclination. The origin of negative superhumps in the light curves of cataclysmic variables remains a puzzle.