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

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 fix...

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Bibliographic Details
Published inNew journal of physics Vol. 20; no. 5; p. 53066
Main Author Berry, M V
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 31.05.2018
Subjects
Airy function
caustic
Eigenvectors
Hamiltonian
High tide
horizon
Hydraulic jump
nonlinearity
Operators (mathematics)
Physics
Quantum theory
Relativity
wave
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Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/aac285