Reappraisal of Whitham’s 1967 theory for wave–meanflow interaction in shallow water

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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Official URL: https://doi.org/10.1016/j.wavemoti.2022.103050

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
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: 05 Oct 2022 13:30
URI: https://nrl.northumbria.ac.uk/id/eprint/50290

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