The modified nonlinear Schr6dinger (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 Schr6dinger (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.
Wave grouping is a prominent feature of ocean waves, frequently discussed in the literature. It may be partly responsible for the generation of freak waves. The simplest realization of wave groups is the bichromatic wave, achieved by mixing two monochromatic waves. In the present paper we use experiments of bichromatic waves as a benchmark to assess the capability of three different simulation models to describe wave group evolution. The three models are the linear wave equation, the cubic nonlinear Schr~dinger (NLS) equation and the modified nonlinear SchrSdinger (MNLS) equation. It is common to stress the importance of time-domain simulation, as opposed to frequency-domain simulation, of nonlinear ocean waves. However, conventional methods for measuring waves in the laboratory and the field yield time series at selected spatial locations. Space evolution is implied between the selected points. For such cases a time-domain simulator is likely not very useful, or at best quite difficult to initialize. A better approach is to interchange the role of space and time in the evolution equation to obtain a genuine space-domain simulator.
