A probability distribution of breaking wave crest height based on a crest-acceleration threshold method

Abstract

For the designers of offshore structures, the probability of encountering a breaking wave crest at or above a specified level above the mean may be an important question. Such a probability may be stated explicity by assuming that a breaking wave has a downward crest acceleration magnitude exceeding a certain threshold α g , as in Snyder and Kennedy [ J. phys. Oceanogr. 13, 1482–1492 (1983)] and Srokosz [ J. phys. Oceanogr. 16, 382–385 (1986)]. The resulting simple expression contains the fourth moment, m 4 , as important parameter, and this is not easily measured nor included in the oceanographic data usually published because it depends critically upon the high-frequency components of the wave spectrum. By comparing oceanographic data from a buoy and photographs from the same area and time with the theory of Snyder and Kennedy for total whitecap coverage, an empirical relation between m 4 and the significant wave parameters H s and T s is suggested. This enables m 4 to be estimated for each sea-state in an H s −T s diagram, and consequently the number of breaking wave crests above any specified value is easily calculated. The results are very dependent upon the higher sea-states in the scatter diagram and are thus quite-dependent, but the method, being very simple, could be easily applied to any other H s −T s scatter diagrams.