Maximum amplitude of modulated wavetrain

For water wave predictions, it is of practical importance to know the size of the biggest wave that emerges from a given uniform wavetrain when it experiences Benjamin-Feir's modulational instability. As far as we are aware, the series of experiments performed by Su and Green 5] are the only work that has pursued this problem so far. In this work their experimental result is compared with theoretical predictions given by the nonlinear Schrödinger equation as well as with the numerical simulation of the fully nonlinear water wave equation. The result of the fully nonlinear simulation shows that the height of the biggest wave reaches more than 3.5 times the initial amplitude of the wavetrain at the maximum modulation when the initial steepness a₀k₀ of the wavetrain is 0.125.