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Resonant interactions of nonlinear water waves in a finite basin
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Kartashova, Elena, Nazarenko, Sergey and Rudenko, Oleksii (2008) Resonant interactions of nonlinear water waves in a finite basin. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Volume 78 (Number 1, Part 2). Article No. 016304 . doi:10.1103/PhysRevE.78.016304 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.78.016304
Abstract
We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) Angle resonances which cannot directly cascade energy but which can redistribute it among the initially excited modes and (2) scale resonances which are much more rare but which are the only ones that can transfer energy between different scales. We find such resonant quartets and their clusters numerically on the set of 1000 x 1000 modes, classify and quantify them and discuss consequences of the obtained cluster structure for the wave-field evolution. Finite box effects and associated resonant interaction among discrete wave modes appear to be important in most numerical and laboratory experiments on the deep water gravity waves, and our work is aimed at aiding the interpretation of the experimental and numerical data.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Water waves, Nonlinear waves, Waves -- Mechanics, Turbulence | ||||
| Journal or Publication Title: | Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1539-3755 | ||||
| Official Date: | July 2008 | ||||
| Dates: |
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| Volume: | Volume 78 | ||||
| Number: | Number 1, Part 2 | ||||
| Number of Pages: | 9 | ||||
| Page Range: | Article No. 016304 | ||||
| DOI: | 10.1103/PhysRevE.78.016304 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Fonds zur Förderung der Wissenschaftlichen Forschung (Austria) (FWF), Sixth Framework Programme (European Commission) (FP6), National Science Foundation (U.S.) (NSF) | ||||
| Grant number: | P20164-N18 (FWF), 026133 (FP6), PHY05-51164 (NSF) |
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