Discussion of “Distributions of Wave Steepness and Surf Parameter” by M. Aziz Tayfun

Abstract

The author presents a study on the development of approximate theoretical forms of the distributions of wave steepness and surf parameter. The approach is based on assuming the random wave process to be long crested and narrow banded. The results are compared with data from measurements at sea representing two severe storms. Both parameters are lognormal distributed. The resulting statistics for the surf parameter are applied to breakers at normal incidence on sloping beaches. As stated by the author, the joint statistics of wave steepness with wave heights or crest heights, or the wave steepness with wave heights or crest heights above a specified threshold may be more appropriate in formulating risks of capsizing of vessels, overtopping, and slamming forces on seawalls, etc. However, the wave steepness is of interest by itself, particularly in relation with many of the surf-zone processes. This discussion points out that other data sets may result in other distributions. This is exemplified by using the data referred to by the author—the data used by Myrhaug and Kjeldsen 1984, 1987 , Myrhaug and Rue 1993 , and Myrhaug and Kvalsvold 1995 . These papers discuss various aspects of wave steepness statistics using data from a large population of waves obtained by waverider buoys at three different deep water locations on the Norwegian continental shelf. Fig. 1 here shows the cdf of the normalized wave steepness s=S /Srms in Weibull scale, where Srms is as defined in Eq. 20 of the original paper. The pluses represent the Myrhaug and Kjeldsen 1984 data. The full line represents the combined lognormal and Weibull distribution obtained as a best fit by eye to the data; the pdf of the lognormal distribution is given by Eq. 17 of the original paper with , = −0.257,0.523 for s 1.2; the pdf of the Weibull distribution is given by Eq. 14 with , = 1.40,0.84 for s 1.2. It appears that this model gives a good representation of the data. Myrhaug and Rue 1993 used the Weibull model to study the statistics of two successive wave steepness parameters with the focus on steep waves S 0.10 . Myrhaug and Kjeldsen 1984 , Myrhaug and Kvalsvold 1995 , and Myrhaug 1994 discussed the joint distribution of wave height and wave steepness by taking f h ,s = f s h f h where f s h is given by the lognormal distribution in Myrhaug and Kjeldsen 1984, Eq. 4 , with x=s, Eq. 18 , and Eq. 19 , and f h is given by the Weibull distribution in Myrhaug and Kjeldsen