Numerical investigation of turbulence for surface gravity waves

In this work, we numerically study the wave turbulence of surface gravity waves. The purpose is to understand the variation of the scaling of the wave spectra with wavenumber k and energy flux P at different nonlinearity levels for different forcing/free-decay conditions. For three representative conditions (free-decay, narrow- and broadband forcing), we find that the spectral forms approach wave turbulence theory (WTT) solution S~k^-5/2 and S~P^1/3 at high nonlinearity levels. With the decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. Two hypothetical mechanisms on bound waves and finite-size effect to explain these spectral variations are investigated. Through a tri-coherence analysis, we find that the finite-size effect is responsible for the steepening of the spectra and reduced capacity of energy flux at lower nonlinearity levels in all cases. Bound waves are found to be the main reason leading to the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.