Bridges, Thomas J. and Ratliff, Daniel (2022) Reappraisal of Whitham’s 1967 theory for wave–meanflow interaction in shallow water. Wave Motion, 115. p. 103050. ISSN 0165-2125
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Abstract
The modulation equations for Stokes waves in shallow water coupled to wave-generated meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited. Firstly, it is shown that they can be recast into two coupled classical shallow water equations, with modified gravity having the sign of the Whitham index: sign(ω0′′ω2). Secondly, it is shown that the amplitude of the meanflow and amplitude of the wave are, in general, independent. Thirdly, the implications of the coalescing characteristics, whose unfolding is associated with the Benjamin–Feir instability, are studied.
| Item Type: | Article |
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| Uncontrolled Keywords: | Benjamin–Feir instability, Coalescing characteristics, Stokes waves, Wave–mean flow interaction, Whitham modulation theory |
| Subjects: | F300 Physics G100 Mathematics |
| Department: | Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering |
| Depositing User: | Rachel Branson |
| Date Deposited: | 05 Oct 2022 13:23 |
| Last Modified: | 27 Aug 2023 03:30 |
| URI: | https://nrl.northumbria.ac.uk/id/eprint/50290 |
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