The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp o f large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resona nt wave propagation found in inviscid Keplerian discs does not occur. The e quations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the w arp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. T his method generalizes the linear theory of Papaloizou & Pringle to allow f or an arbitrary rotation law, and extends it into the non-linear domain, wh ere it connects with a generalized version of the theory of Pringle. The as trophysical implications of this analysis are discussed briefly.