Revisiting statistical properties of surf parameter with characteristic wave parameters for single random waves including spectral bandwidth effects

Abstract

Results from a comparative study of the joint distribution of surf parameter and wave period are provided. First, two transformed joint distributions of wave height and wave period are compared. One of the distributions is a parametric model originating from a best fit to relatively broad-band field data covering a wide range of wave conditions, whilst the other distribution is theoretically based. It appears that the theoretically based distribution does not represent the features of the parametric model especially well, suggesting that parametric models should be used to describe relatively broad-banded data. Then, the theoretically based joint distribution of wave height and wave period is transformed to the joint distributions of surf parameter with wave height and wave period and it is demonstrated how these distributions are affected by the spectral bandwidth. Finally, the theoretically based distribution of wave height and wave period is also transformed to the joint distribution of wave runup time and wave period due to its relation to the stability of rubble-mound breakwaters. Comparisons are made with a limited set of data representing results from small-scale laboratory experiments related to stability of rubble-mound breakwaters. The agreement between measurements and predictions of the distribution of the surf parameter is fair, whilst the agreement is poorer for the probability of resonance.