Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: Experimental validation

Combined experimental and numerical study of spatial evolution of unidirectional random water-waves is performed. Numerous realizations of wave fields all having identical initial narrow-banded Gaussian power spectrum but random phases for each harmonic were generated by a wavemaker in a 300 m long wave tank. The measured in the vicinity of the wavemaker temporal variation of the surface elevation was used to determine the initial conditions in the numerical simulations. The cubic Schrödinger equation CSE and the modified nonlinear Schrödinger MNLS set of equations due to Dysthe were used as the theoretical models. The detailed comparison of the evolution of the wave field along the tank in individual realizations, measured by wave gauges at different distances from the wavemaker and computed using the two theoretical models, was performed. Numerous statistical wave parameters were calculated based on the whole ensemble of realizations. Comparison of the spatial variation of the computed statistical characteristics of the random wave field with laboratory measurements indicates that contrary to the deterministic case, ensemble averaged statistical parameters derived from the CSE simulations compare reasonably well with the experiments and with the results derived from the MNLS model simulations. In particular, simulations based on both models indicate that the statistical characteristics of the random wave field depend on the local width of frequency spectrum and deviate from the Gaussian statistics: the probability of extremely large the so-called freak waves is highest when the local spectral width attains maximum. In view of the satisfactory agreement of the numerical results with the laboratory experiments, the computational domain was extended to distances exceeding twice the actual length of the tank and long-scale at distances approaching 200 dominant wavelengths variation of the statistical parameters is studied. © 2010 American Institute of Physics. doi:10.1063/1.3290240