2022/03/08 by Thomas J. Bridges, Bridges, Thomas J., Daniel J. Ratliff +1
Earth and Planetary Sciences · Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes
paper · doi:10.48550/arxiv.2203.04033
openalex publication_date 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The modulation equations for Stokes waves in shallow water coupled to wave generated mean flow, derived in Whitham (1967), based on an averaged Lagrangian are revisited. 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 mean flow 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.