Nonlinearity in Wave Crest Statistics

by David L. Kriebel, United States Naval Acad, Annapolis, United States,
Thomas H. Dawson, United States Naval Acad, Annapolis, United States,

Abstract: The statistical properties of nonlinear wave crest amplitudes are discussed for a narrow-band random sea consistent with Stokes second-order wave theory. In particular, the probability distribution for nonlinear crest amplitudes is shown to be a modified form of the Rayleigh distribution that incorporates nonlinear effects through a spectral wave steepness parameter. Predictions from this distribution are shown to be in close agreement with laboratory data and with recently published North Sea measurements for both deep water and intermediate depth conditions. This distribution is then modified to account for wave breaking in a random sea and results are again shown to be in good agreement with laboratory data.

Subject Headings: Nonlinear waves | Wave crest | Breaking waves | Probability distribution | Seas and oceans | Probability | Wave spectrum

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