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Detection and visualization of water surface three-wave resonance via a synthetic Schlieren method

Three-wave resonance is one of the most fundamental energy-transfer mechanisms that can occur among weakly nonlinear surface waves. Here we show experimentally that if two source waves are propagating at an angle to each other, the conditions for three-wave resonances are satisfied and a third resultant wave is produced. We present 3D visualization of surface waves using the Free-Surface Synthetic Schlieren method, which removes the need for the addition of a light-diffusing agent, thereby retaining the surface tension and viscous properties of water. For three triad frequencies, we compute the average temporal power spectral density (PSD) of the wave heights. The direction of wave propagation is visualized by integrating the temporal PSD and by obtaining the average spatial PSD for each triad. Our results are in good agreement with the theory.