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Observations of distorted discs have highlighted the ubiquity of warps in avariety of astrophysical contexts. This has been complemented by theoreticalefforts to understand the dynamics of warp evolution. Despite significantefforts to understand the dynamics of warped discs, previous work fails toaddress arguably the most prevalent regime -- nonlinear warps in Kepleriandiscs for which there is a resonance between the orbital, epicyclic andvertical oscillation frequencies. In this work, we implement a novel nonlinearring model, developed recently by Fairbairn and Ogilvie, as a framework forunderstanding such resonant warp dynamics. Here we uncover two distinctnonlinear regimes as the warp amplitude is increased. Initially we find asmooth modulation theory which describes warp evolution in terms of theaveraged Lagrangian of the oscillatory vertical motions of the disc. This hintstowards the possibility of connecting previous warp theory under a generalisedsecular framework. Upon the warp amplitude exceeding a critical value, whichscales as the square root of the aspect-ratio of our ring, the disc enters intoa bouncing regime with extreme vertical compressions twice per orbit. Wedevelop an impulsive theory which predicts special retrograde and progradeprecessing warped solutions, which are identified numerically using our fullequation set. Such solutions emphasise the essential activation of nonlinearvertical oscillations within the disc and may have important implications forenergy and warp dissipation. Future work should search for this behaviour indetailed numerical studies of the internal flow structure of warped discs.

Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics