Non-Gaussian statistics from a laboratory experiment with a 36-hour random wave simulation are presented. Unidirectional deep-water waves with a narrow-banded spectrum are run. Records from wave probes distributed over a large area of propagation are included. Results for the statistical skewness show good agreement with second-order theory all over the wave field. However, the kurtosis as well as the extreme crest and wave heights show significant increase beyond second-order theory after 10–15 wavelengths of propagation. Analysis of wave groups leading to the extreme events indicate that nonlinear group formation may explain the highest waves.
There is growing evidence that extreme individual peak-to-peak wave heights in random records may under certain conditions become higher (or more frequent) than predicted by the Rayleigh distribution based on the linear wave assumption. This is supported by various fullscale observations showing extreme wave heights higher than twice the significant value, such as in Kjeldsen (1990), Sand et. al. (1990), Skourup et. al. (1996) and Yasuda et. al. (1998). It has also been confirmed by results from laboratory measurements, Stansberg (1993), (1998a). Nonlinear theoretical and numerical models indicating the presence and nature of such effects have also been presented, Wang et. al. (1993), Yasuda & Mori (1994), Clauss (1999). Possible physical mechanisms are also discussed in Taylor & Haagsma (1994), Johannessen & Swan (1999) and in Stansberg (1998a). In contrast to non-Rayleigh extreme crest heights, which are more frequent and to some extent described by second-order models, non-Rayleigh wave heights must be described by higher-order models. A proper statistical prediction is, however, not straightforward. The extremes are rare events, and conclusions based on a few large wave height observations only are in most cases statistically uncertain.
