Some breather type solutions of the NLS equation have been suggested by Henderson et al (to appear in Wave Motion) as models for a class of 'freak' wave events seen in 2D-simulations on surface gravity waves. In this paper we first take a closer look on these simple solutions and compare them with some of the simulation data (Henderson et al to appear in Wave Motion). Our findings tend to strengthen the idea of Henderson et al. Especially the Ma breather and the so called Peregrine solution may provide useful and simple analytical models for 'freak' wave events.

We discuss two independent, large scale experiments performed in two wave basins of different dimensions in which the statistics of the surface wave elevation are addressed. Both facilities are equipped with a wave maker capable of generating waves with prescribed frequency and directional properties. The experimental results show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves. Sea states characterized by long-crested and steep waves are more likely to be populated by freak waves with respect to those characterized by a large directional spreading.

Simulations have been performed with a fairly narrow band numerical gravity wave model (higher-order nls type) and a computational domain of dimensions $128\times 128$ typical wavelengths. The simulations are initiated with $\thicksim6\times10^{4}$ fourier modes corresponding to truncated jonswap spectra and different angular distributions giving both short- and long-crested waves. A development of the spectra on the so-called benjamin–feir timescale is seen, similar to the one reported by dysthe et al. (J. Fluid Mech. vol. 478, 2003, p.1). The probability distributions of surface elevation and crest height are found to fit theoretical distributions found by tayfun (J. Geophys. Res. Vol. 85, 1980, p. 1548) very well for elevations up to four standard deviations (for realistic angular spectral distributions). moreover, in this range of the distributions, the influence of the spectral evolution seems insignificant. for the extreme parts of the distributions a significant correlation with the spectral change can be seen for very long-crested waves. For this case we find that the density of large waves increases during spectral change, in agreement with a recent experimental study by onorato et al. (J. Fluid Mech. 2004 submitted).

A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrödinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrödinger equation can also provide consistent results outside its narrow-banded domain of validity.