# On cnoidal waves and bores

@article{Benjamin1954OnCW, title={On cnoidal waves and bores}, author={Thomas Brooke Benjamin and Michael James Lighthill}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, year={1954}, volume={224}, pages={448 - 460} }

For a train of gravity waves of finite amplitude in a frame of reference in which they are stationary, it is suggested that, in addition to the volume flow per unit span Q and the total head R, one may usefully study a third constant S, the rate of flow of horizontal momentum(corrected for pressure force, and divided by the density). The values of Q, R and S probably determine the wave-train uniquely; this is proved explicitly for long waves in a new presentation of the ‘cnoidal wave’ theory…

## 274 Citations

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- PhysicsJournal of Fluid Mechanics
- 1973

A steady nonlinear dispersive wave theory is developed in terms of three important invariants of channel flow: discharge, energy, and momentum flux. As such, the work is an extension of Benjamin &…

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