title: Experimental study of three-wave interactions among capillary-gravity surface waves.
abstract: In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France.
authors.forename: Florence
authors.initials: F
authors.lastname: Haudin
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France.|Ecole Normale Supérieure, Département de Physique, 75005 Paris, France.
authors.forename: Annette
authors.initials: A
authors.lastname: Cazaubiel
authors.affiliation: Scripps Institution of Oceanography, University of California San Diego, San Diego, California 92093, USA.
authors.forename: Luc
authors.initials: L
authors.lastname: Deike
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France.
authors.forename: Timothée
authors.initials: T
authors.lastname: Jamin
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France.
authors.forename: Eric
authors.initials: E
authors.lastname: Falcon
authors.affiliation: Université Paris Diderot, Sorbonne Paris Cité, MSC, CNRS (UMR 7057), 75013 Paris, France.
authors.forename: Michael
authors.initials: M
authors.lastname: Berhanu