Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs

We consider the stability of warping modes in Keplerian discs. We find them to be parametrically unstable using two lines of attack, one based on thre e-mode couplings and the other on Floquet theory. We confirm the existence of the instability and investigate its non-linear development in three dime nsions, via numerical experiment. The most rapidly growing non-axisymmetric disturbances are the most nearly axisymmetric (low-m) ones. Finally, we of fer a simple, somewhat speculative model for the interaction of the paramet ric instability with the warp. We apply this model to the masing disc in NG C 4258 and show that, provided the warp is not forced too strongly, paramet ric instability can fix the amplitude of the warp.