Nonlinear Effects on Wave Groups in Random Seas

Abstract

Laboratory simulations of extreme random seas reveal that high wave crests occur more frequently than predicted by the Rayleigh distribution. In this paper, a theory is presented to account for nonlinearities in the sea state to second order resulting in a non-Rayleigh distribution of wave crest and trough amplitudes based on the narrow-band assumption. The resulting probability density functions are then used to predict average wave group characteristics through a modification of linear wave envelope theory which accounts, for example, for a significant decrease in the time intervals between successive runs of high crests compared to linear theory. The nonlinear theory is then verified based on a laboratory data set on deep water wave group statistics for severe seas described by Bretschneider and JONSWAP spectra.

Dynamical and statistical explanations of observed occurrence rates of rogue waves

“…He found that, as expected, crest heights increase over those given by linear theory, slightly less if the directional spread of the waves is allowed for than if not. Forristall (2000) found that the Kriebel and Dawson (1993) Formula (9) compares well with data and simulations in water that is deep enough to not significantly influence the waves, but gives too great an enhancement of crest heights in shallow water. This agreement of simulations with Eq.…”

“…More importantly, the analysis of Forristall (2000) was for exceedance probabilities no smaller than 10 −4 , and we see from Figure 1 that for smaller exceedance probabilities the Kriebel and Dawson (1993) formula departs significantly from the straight line of (13). It seems worthwhile to check from further simulations whether a plot of ln(−lnP ) versus ln(η/H s ) is well approximated 175 by a straight line or whether it curves down for small values of P .…”

“…1 that for smaller exceedance probabilities the Kriebel and Dawson (1993) formula departs significantly from the straight line of Eq. (13).…”

Shallow water effects on high order statistics and probability distributions of wave run-ups along FPSO broadside

“…As a well-known theoretical model, the Rayleigh distribution is usually utilized for estimating the probability distribution of the wave crests based on the assumptions of a narrow-band frequency spectrum and a Gaussian distribution of the wave surface elevations. For a description of the non-linear wave run-up distribution, Kriebel and Dawson [9] proposed a simplified theoretical model based on assumptions that the first and second-order wave run-ups are phase locked and that their maxima occur at the same time. The application of this model to the wave run-up on vertical cylinders shows that the prediction results are accurate enough when comparable to more complete second-order numerical simulations.…”

Probability Analysis of Wave Run-Ups and Air Gap Response of a Deepwater Semisubmersible Platform Using LH-Moments Estimation Method

“…To interpret wave run-up data with a random nature from irregular wave experiments, extreme statistics and the exceedance probability distribution need be evaluated quantitatively to determine the expected minimum air gap for design considerations. To describe nonlinear wave run-up distributions, Kriebel and Dawson (1991) proposed a two-parameter Rayleigh-Stokes model incorporating the classical Rayleigh distribution with an amplification factor based on assumptions that the first-and second-order wave run-ups are phase-locked and that the maxima occur simultaneously. Al-Humoud et al (2002) examined the model for ocean surface waves and reported that the accuracy of the qualitative prediction was questionable.…”