Observation of resonant interactions among

surface gravity waves

 F. Bonnefoy1, F. Haudin2, G. Michel3, B. Semin3,
T. Humbert
4, S. Aumaître4, M. Berhanu2 and E. Falcon2
1 Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
2 Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS, UMR 7057, F-75 013 Paris, France
3 Ecole Normale Supérieure, LPS, UMR 8550 CNRS, F-75 205 Paris, France
4 CEA-Saclay, Sphynx, DSM, URA 2464 CNRS, F-91 191 Gif-sur-Yvette, France

Reference: Journal of Fluid Mechanics - Rapids 805, R3 (2016)

URL: http://dx.doi.org/10.1017/jfm.2016.576
DOI:  http://dx.doi.org/10.1017/jfm.2016.576
Key words: surface gravity waves, waves/free-surface flows


We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated.

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Supplemental Ma

* Text (PDF)

* Movie
Generation of a daughter wave by a resonant interaction between two oblique crossing waves in a large basin (50 m long): 0-4 s: basin at rest; 4-10 s: generation of the mother wave 1 only; 10-19 s: generation of the mother wave 3 only; 19-42 s: simultaneous generation of the two mother waves 1 and 3. In the latter, note the growth of waves in the expected direction of the daughter wave. Additional dashed lines are aligned with crests and separated by a wavelength. Arrows indicate the wave direction (Perspective view, resonance conditions, mother-wave steepnesses = 0.05)

Press Items:

Our work has been highlighted in a Focus on Fluids article by Journal of Fluid Mechanics, 24 November 2016

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