Experiments on Surface Elevation Probability Distribution and Statistics in Surfand Swash Zones

摘要

Three irregular wave tests, with distinct breaker characteristics, were conductedon a 1:16 smooth slope to investigate the detailed cross-shore variations of the probability distributions and statistics of the free surface elevations and mid-depth horizontal velocities in the shoaling, surf and swash zones. The exponential gamma distribution, with measured mean, standard deviation, and skewness, is shown to be capable of describing the measured probability distributions in a unified manner. The probability distribution of the free surface elevation, limited by the beach face in the swash zone, becomes exponential with the skewness S = 2 and the root-mean-square wave height H(rms) = (square root of 8) times h, with h = mean water depth. These upper limits of S and H(rms)/h in the swash zone are in agreement with the data, and indicate that the swash zone is very different from the surf zone. The cross-shore variations of the mean (undertow) and standard deviation of the mid-depth horizontal velocity measured in the shoaling and surf zones can be predicted using the simple relationships derived using linear long-wave theory together with the measured values of h and H(rms).