Run-Up Distributions of Waves Breaking on Slopes

Run-up of irregular waves which break on a slope is calculated by assuming that on the average the run-up of each wave with a given height and period equals the run-up of a periodic wave train of the same height and period. General expressions are derived for the distributions of the run-up and the wave steepness as functionals of an arbitrary joint distribution of the wave height and the square of the period. Explicit results are obtained for the case when these variates are jointly Rayleigh distributed with arbitrary degree of correlation. Some of the assumptions are verified by a comparison of the analytical results with previous experimental data.