An experimental study of large waves in intermediate and shallow water depths. Part I: Wave height and crest height statistics

This paper describes a series of laboratory observations undertaken in a purpose-built wave flume. The objective of the study was to simulate a range of realistic ocean spectra evolving over a number of mild bed slopes (m); the chosen sea states allowing a systematic investigation of the role of local water depth, spectral peak period, significant wave height, spectral bandwidth and bed slope. The focus of the present paper lies in the statistical distribution of both the wave height (H) and the wave crest elevation (eta(c)); the laboratory data being used to provide both an understanding of the importance of the various parameters and an assessment of the commonly adopted design distributions. The results of the study have shown that both the wave height and the crest height distributions are primarily dependent upon the effective water depth (k(p)d), where k(p) is the wave number corresponding to the spectral peak and d the water depth, and the sea state steepness (1/2H(s)k(p)), where H-s is the significant wave height. Conversely, the distributions are independent of the mild bed slope (for m1 <=/100) and the spectral bandwidth; the latter result being very different to that which arises in deep water. Following detailed comparisons, across a wide parameter range, the wave height distributions in the deeper water depths (k(p)d>1.0) are shown to be in reasonable agreement with the (Forristall, 1978) and (Glukhovskii, 1966) distributions; the latter becoming more important as the proportion of breaking waves increases. As the water depth reduces, the (Mendez et al., 2004) distribution as well as the (Bates 82 Groenendijk, 2000) composite Weibull distribution (CWD) become increasingly applicable. However, comparisons between sea states of varying steepness, but with all other parameters held constant, suggest that the empirical parameters on which the latter solution is based may not be universally applicable. Finally, in the shallowest water depths (k(p)d approximate to 0.5), none of the existing distributions provide a good description of the measured data; all leading to an over-estimate of the largest wave heights. (C) 2012 Elsevier B.V. All rights reserved.