In this paper, the wave crest distribution using wave data from model tests at Marintek will be compared with a second order wave crest distribution. The higher than second order effects observed in the model tests will be discussed. Comparison to full-scale field measurements will be made. Differences between wave crests generated in a model basin compared to what we observe in the ocean will be addressed.
The surface elevation is now being more commonly described by use of second order theory. The increase in crest height from Rayleigh to second order depends on the water depth and steepness of the sea state. For a water depth of 100 m the second order amplification is 10- 20%, where the highest amplification applies for the steepest waves. George Forristall (Forristall 2000) established a second order crest distribution, based on a large number of simulations. This is now commonly being used to describe the short time second order crest distribution. In general the second order crest distribution is found to overall match the observed distribution in the ocean (Krogstad et al. 2008), (Christou and Ewans 2011),(Lian and Haver In-press). There are, though special storm events that show a crest distribution beyond second order. See (Gibson, Christou, and Feld 2014), (Lian and Haver In-press). The real sea surface process is higher order, not limited to second order, so an important question is how much higher crests than second order we could expect to observe in the extreme storm events at a q-annual probability level of about 10−4. Several experimental laboratory studies have previously been performed, and reporting higher than second order effects.(Stansberg 1999) (Stansberg 2003) (Buchner et al. 2011) (Latheef and Swan 2013). The increase beyond second order seems to be higher for long crested sea than in short crested. The sea surface will always have some directional spreading, but the expected spreading for a q-annual event of 10−4 is an open question. However it is assumed that an assumption of long crested waves will be somewhat conservative. In this paper we first study the higher than second order effects in long crested seas from 20 different wave spectra in intermediate to deep water. From each wave spectrum there has at least been performed 10 realizations. We have looked into the higher order effects with respect to the steepness, skewness and kurtosis. By comparing the long crested laboratory test with ocean measurements, we observe more higher than second order effects in the laboratory than in the ocean. An indication of the effect of including some spreading in the generated laboratory waves is presented. The effect seems to be largest for the steepest waves.
