Spatial evolution of water surface waves: Numerical simulation and experiment of bichromatic waves

The modified nonlinear Schrödinger (MNLS) equation for spatial evolution of weakly nonlinear water surface waves is shown to yield good comparisons with experimental measurements of bichromatic waves in a long tank. While linear theory does not predict neither the phase velocity nor the evolution of the envelope well, the cubic nonlinear Schrödinger (NLS) equation improves the prediction of the phase velocity but not the modulation of the envelope. The MNLS equation predicts both the evolution of individual wave crests and the modulation of the envelope over longer fetch, and thus permits accurate forecasting of individual ocean wave crests over a fetch of several tens of wavelengths.