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

Thomas J. Bridges, Daniel J. Ratliff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number103050
JournalWave Motion
Volume115
Early online date27 Aug 2022
DOIs
Publication statusPublished - 1 Nov 2022

Fingerprint

Dive into the research topics of 'Reappraisal of Whitham's 1967 theory for wave–meanflow interaction in shallow water'. Together they form a unique fingerprint.

Cite this