Statistics of Wave Crests in Storms
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130, Issue 4
Abstract
The least-upper-bound (lub) theory recently proposed by Tayfun and Al-Humoud as a model for the statistical distribution of nonlinear wave crests is explored further. The theoretical distribution of the lub to the largest crest in N waves is also considered, deriving expressions for the associated mode, mean, and standard deviation. These provide a rational basis for describing the nature and occurrence of freak waves and outliers in observational data. The lub distribution and related statistics are then checked with additional measurements gathered during the peaks of two severe storms in the North Sea. The data comprise two hourly records and coincide with the extremes of more extensive measurements discussed by Forristall. Analyses of both records yield crest height distributions and statistics that compare with the lub model predictions quite well, thus confirming the validity of the lub theory convincingly. The theoretical expressions describing the statistics of the largest crest in N waves are then used to examine the nature of two exceptionally large waves recorded within the two hourly measurements. Although these waves display characteristics in apparent conformity with freak-wave occurrences, they are shown to be simple outliers that can be predicted well within the context of the extreme-value statistics derived here.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 130 • Issue 4 • July 2004
Pages: 155 - 161
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Mar 5, 2003
Accepted: Dec 2, 2003
Published online: Jun 15, 2004
Published in print: Jul 2004
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