Resonant Condition in Second Harmonic Generation of Water Surface Waves

Works on nonlinear effects in water surface waves are complementary stimulated by interest in understanding the spectral composition of oceanic waves and feasibility of local detection of physical parameters. On the other side, water surface waves are composite waves contributed both by surface tension and gravity, such that study of nonlinear phenomena are theoretically severe and different approaches are available, that variously attempt to consider transverse or dilational stresses, mode resonant interactions, solitons etc. In the present work, a phenomenological approach is done, that simply moves from the detection of amplitude and phase of the harmonic components present along the propagation direction of the waves, to highlight the local nonlinear interaction between the fundamental and second harmonic propagating modes. The effect is here put into evidence by detecting harmonic production at different frequencies around the so-called resonant condition, where fundamental and second harmonic share the very same velocity, maintaining a matched phase condition along the propagation direction.