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Minimal analytical model for undular tidal bore profile; Quantum and Hawking effect analogies

Research output: Contribution to journalArticle (Academic Journal)

Original languageEnglish
Article number053066
JournalNew Journal of Physics
Issue number5
DatePublished - 1 May 2018


Waves travelling up-river, driven by high tides, often consist of a smooth front followed by a series of undulations. A simple approximate theory gives the rigidly travelling profile of such 'undular hydraulic jumps', up to scaling, as the integral of the Airy function; applying self-consistency fixes the scaling. The theory combines the standard hydraulic jump with ideas borrowed from quantum physics: Hamiltonian operators and zero-energy eigenfunctions. There is an analogy between undular bores and the Hawking effect in relativity: both concern waves associated with horizons.

    Research areas

  • Airy function, caustic, Hamiltonian, horizon, nonlinearity, soft modes, wave



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