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Nonlinear Effects on Wave Envelope and Phase

by M. Aziz Tayfun, (M.ASCE), Kuwait Univ, Safat, Kuwait,



Document Type: Proceeding Paper

Part of: Ocean Wave Measurement and Analysis

Abstract:

The representation of second-order random waves is examined in terms of the effect of second-order nonlinearities on the wave envelope and phase. Theoretical expressions describing the joint, marginal, and conditional distributions of wave envelope and phase are derived systematically, correct to first order in the rms surface slope. Some immediate implications of these results are discussed in detail. In particular, it is found that the wave envelope is Rayleigh-distributed, as in the case of linear waves, whereas the wave-phase distribution is nonuniform over the interval (0, 2?). As the rms surface slope and thereby the surface skewness increase, the phase distribution deviates from uniformity progressively, indicating an excess of values near the mean phase 2? and corresponding symmetrical deficiencies away from the mean toward 0 and 2?. Comparisons with four sets of wave data gathered in the Gulf of Mexico during a hurricane provide a favorable confirmation of these theoretical results, and thus reinforce the validity of the second-order random wave model.

Subject Headings: Random waves | Water waves | Wind waves | Wave equations | Nonlinear waves | Mathematical models | Surface waves | Gulf of Mexico

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