Transformation of Random Breaking Waves and Its Empirical Numerical Modeling Considering Surf Beat

The free surface characteristics of random waves in the shoaling and surf zones on a beach of uniform slope were examined experimentally. The effect of incident wave grouping was found for larger waves outside the surf zone; however, this effect disappeared as the fraction of breaking waves increased. The wave height distributions were not necessarily described by the Rayleigh distribution in shallow water. The assumption that the distribution of breaking wave heights is proportional to that of non-breaking wave heights was not valid in the region where the fraction of breaking waves was small. A numerical model which accounts for the effects of incident wave grouping and surf beat empirically was shown to be capable of predicting the experimental results such as the cross-shore transformations of the representative wave heights, wave height distributions and fraction of breaking waves. The mean lengths of runs and total runs, skewness, kurtosis, nondimensional crest height were observed to increase and then decrease from deep water to shallow water. The nondimensional crest width decreased and then increased in an opposite manner. For the case of deep water wave steepness smaller than 0.03, the location of the maxima and minima was where the significant wave height was maximum, and for the case of deep water wave steepness larger than about 0.04, this location was approximately at h/H 0 =1.2 for 1:30 slope. There were essentially no effects of incident wave grouping on nonlinearity and asymmetry of wave profiles in the shoaling and surf zones. The skewness and asymmetry of the wave profiles may be important in predicting the net cross-shore sediment transport in the shoaling and surf zones.