Numerical investigation of turbulence of surface gravity waves

In this paper, we numerically study the wave turbulence of surface gravity waves in framework Euler equations free surface. The purpose is to understand variation scaling spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under forcing/free-decay conditions. For all conditions (free decay, narrow- broadband forcing) consider, find that spectral forms approach theory (WTT) solution $S_\eta\sim k^{-5/2}$ P^{1/3}$ high levels. With decrease level, for cases become steeper, narrow-band forcing case exhibiting most rapid deviation from WTT. To interpret these variations, further investigate two hypothetical disputable mechanisms about bound finite-size effect. Through a tri-coherence analysis, effect present cases, which responsible overall steepening reduced capacity lower fraction domain generally decreases except case, exhibits transition some critical level below increase observed. This serves as main reason fastest WTT case.