ORCID
- Raphael Stuhlmeier: 0000-0002-6568-1543
Abstract
In this manuscript we investigate the Benjamin–Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave interactions in deep water without restrictions on spectral bandwidth. Spatial evolution, with measurements at discrete locations, is pertinent for laboratory hydrodynamic experiments, such as in wave flumes, which rely on time-series measurements at fixed gauges installed along the facility. This setting is likewise appropriate for experiments in electromagnetic and plasma waves. Through a reformulation of the problem for a degenerate quartet, we bring to bear techniques of phase-plane analysis which elucidate the full dynamics without recourse to linear stability analysis. In particular we find hitherto unexplored breather solutions and discuss the optimal transfer of energy from carrier to sidebands. We show that the maximal energy transfer consistently occurs for smaller side-band separation than the fastest linear growth rate. Finally, we discuss the observability of such discrete solutions in light of numerical simulations.
DOI
10.1016/j.wavemoti.2024.103381
Publication Date
2024-01-01
Publication Title
Wave Motion
Volume
130
ISSN
0165-2125
Keywords
Benjamin–Feir instability, Breathers, Modulational instability, Resonant wave interactions, Spatial wave evolution, Wave-wave interaction
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Stuhlmeier, R., Heffernan, C., & Chabchoub, A. (2024) 'Nonlinear spatial evolution of degenerate quartets of water waves', Wave Motion, 130. Available at: https://doi.org/10.1016/j.wavemoti.2024.103381
