Forced three-wave interactions of capillary-gravity surface waves

Three-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work [Haudin et al. Phys. Rev E 93, 041110 (2016)], we 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 bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation. 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 nonnegligible dissipation.