Probability Density Function of the Crest to Trough Heights of Waves and on the Physics of Extreme Waves Including Results from Hurricane Camille

摘要

A sequence of 11,000 waves that passed on ODGP platform during Hurricane Camille is studied as 55 successive samples of 200 waves each to determine whether or not the Rayleigh probability density function fits the crest to trough heights defined in the conventional manner and whether or not the highest wave in the sample, which was 72.2 feet from crest to trough, was highly improbable in terms of extreme value theory. Five reasons why a sample of wave heights can depart from the theoretical Rayleigh distribution are analysed. Two are theoretical; two have to do with sampling problems; and the last is concerned with spectral estimation procedures. It was not possible to isolate each of the five reasons. The results do however show that if the last three are taken into account, the Rayleigh distribution comes close to describing the samples adequately. The highest waves that occurred were not unusual when tested against extreme value theory.