2024/10/22 by Daniel J. Ratliff, Ratliff, Daniel J., Olga Trichtchenko +3
Earth and Planetary Sciences · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.2410.17416
openalex publication_date 2024/10/22 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney-Roskes equation.