3-wave and 4-wave interactions in gravity wave turbulence

The Weak Turbulence Theory (WTT) provides a statistical framework for describing large ensembles of nonlinearly interacting waves, exemplified by the ocean surface composed of interacting surface gravity waves. This study details a laboratory experiment aimed at probing the statistical properties of turbulent gravity waves, where an isotropic state of interacting gravity waves was established in a 13 m diameter Coriolis circular wave tank using wedge wavemakers at a frequency of 1 Hz. Employing stereoscopic techniques, the surface elevation measurements were captured in both spatial and temporal resolutions. The results demonstrated that the laboratory-derived spectra exhibited steeper characteristics compared to both theoretical predictions and field observations from the Black Sea. A significant influence of surface dissipation on the scaling of the Fourier spectrum at accessible experimental scales was identified. Through the application of statistical tools like bicoherence and tricoherence in frequency and wavevector space, we analyzed the active nonlinear couplings; while 3-wave coupling primarily involved quasi-resonant interactions, 4-wave couplings were absent in laboratory results but present in field data. Finally, we addressed the implications of temporal scale separation to clarify the differences observed in the experimental and field data.