The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in the form of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose–Einstein condensates, while its impact on applied sciences is steadily growing. It is well-known that the classical MI dynamics can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system, consisting of the carrier wave together with a pair of unstable sidebands, is usually adopted to initiate the wave focusing process in a numerical or laboratory experiment. Breather solutions of the nonlinear Schrödinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, initialized from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi–Pasta–Ulam–Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with some distinctions.
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October 2024
Research Article|
October 02 2024
Hydrodynamic modulation instability triggered by a two-wave system
Special Collection:
Rogue waves: Theory, Methods and Applications
Yuchen He
;
Yuchen He
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University
, Hong Kong 999077, China
2
Department of Ocean Science and Engineering, Southern University of Science and Technology
, Shenzhen 518055, China
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Jinghua Wang
;
Jinghua Wang
(Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University
, Hong Kong 999077, China
3
Research Institute for Sustainable Urban Development, The Hong Kong Polytechnic University
, Hong Kong 999077, China
4
Shenzhen Research Institute, The Hong Kong Polytechnic University
, Shenzhen 518057, China
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Bertrand Kibler
;
Bertrand Kibler
(Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
5
Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR6303 CNRS-UBFC
, 21000 Dijon, France
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Amin Chabchoub
Amin Chabchoub
b)
(Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
6
Disaster Prevention Research Institute, Kyoto University
, Uji, Kyoto 611-0011, Japan
7
Marine Physics and Engineering Unit, Okinawa Institute of Science and Technology
, Onna-son, Okinawa 904-0495, Japan
8
Department of Infrastructure Engineering, The University of Melbourne
, Parkville, Victoria 3010, Australia
b)Author to whom correspondence should be addressed: amin.chabchoub@oist.jp
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b)Author to whom correspondence should be addressed: amin.chabchoub@oist.jp
a)
Electronic mail: yuchen.he@polyu.edu.hk
Chaos 34, 103108 (2024)
Article history
Received:
May 24 2024
Accepted:
September 03 2024
Citation
Yuchen He, Jinghua Wang, Bertrand Kibler, Amin Chabchoub; Hydrodynamic modulation instability triggered by a two-wave system. Chaos 1 October 2024; 34 (10): 103108. https://doi.org/10.1063/5.0220359
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