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Observation of resonant interactions among surface gravity waves

Published online by Cambridge University Press:  20 September 2016

F. Bonnefoy ,
F. Haudin ,
G. Michel ,
B. Semin ,
T. Humbert ,
S. Aumaître ,
M. Berhanu  and
E. Falcon
F. Bonnefoy*
Affiliation:
École Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
F. Haudin
Affiliation:
Univ. Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
G. Michel
Affiliation:
École Normale Supérieure, LPS, UMR 8550 CNRS, F-75 005 Paris, France
B. Semin
Affiliation:
École Normale Supérieure, LPS, UMR 8550 CNRS, F-75 005 Paris, France
T. Humbert
Affiliation:
Univ. Paris-Scalay, CEA-Saclay, SPEC, DRF, UMR 3680 CNRS, F-91 191 Gif-sur-Yvette, France
S. Aumaître
Affiliation:
Univ. Paris-Scalay, CEA-Saclay, SPEC, DRF, UMR 3680 CNRS, F-91 191 Gif-sur-Yvette, France
M. Berhanu
Affiliation:
Univ. Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
E. Falcon
Affiliation:
Univ. Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
*
†Email address for correspondence: felicien.bonnefoy@ec-nantes.fr
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Abstract

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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 805 , 25 October 2016 , R3
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Copyright
© 2016 Cambridge University Press 

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References

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Bonnefoy et al. supplementary 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)

Download Bonnefoy et al. supplementary movie(Video)
Video 37.1 MB

Bonnefoy et al. supplementary 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)

Download Bonnefoy et al. supplementary movie(Video)
Video 114 MB
Supplementary material: PDF

Bonnefoy et al. supplementary material

Supplementary material

Download Bonnefoy et al. supplementary material(PDF)
PDF 108.3 KB