Three-wave resonance in water surface waves

Abstract

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 with respect to each other, the conditions for three-wave resonances are satisfied and a third resultant wave is produced. We 3D reconstruct surface waves using the Free-Surface Synthetic Schlieren (FS-SS) method, which removes the need for the addition of a light-diffusing agent, thereby retaining the surface tension and density properties of water. For three triads, we compute the average temporal power spectral density (PSD) using the Welch method on the surface heights. We then compare the results of taking the average spatial PSD of the wave heights to the ones graphically obtained by plotting the gravity-capillary water wave dispersion relation for each triad component in ω-k space.