Forced three-wave interactions of capillary-gravity surface waves

Annette Cazaubiel, Florence Haudin, Eric Falcon and Michaël Berhnau

Université Paris Diderot, Université de Paris, MSC, UMR 7057 CNRS, F-75 013 Paris, France

Reference: Physical Review Fluids 4, 074803 (2019)   Editor's Suggestion


Abstract:  Three-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work, Haudin et al. [Phys. Rev E 93, 043110 (2016)], we have characterized experimentally the generation by this mechanism of a daughter wave, whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersion relation. By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with non negligible dissipation.

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