Wave Crest Distributions: Observations and Second-Order Theory

Forristall, George Z.

doi:10.1175/1520-0485(2000)030<1931:wcdoas>2.0.co;2

Cited by 365 publications

(337 citation statements)

References 15 publications

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“…The observed values for these parameters are given by ¡i= 0.067, Um = 0.093, |4 = 0.071 and v = 0.38 for Experiment 3. The Forristall model (Forristall, 2000) for crest heigthts is given by where the parameters a and (3 depend upon a steepness S^ and the Ursell-type number U r defined, respectively, as…”

Section: -F (••And•mentioning

confidence: 99%

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Offshore stereo measurements of gravity waves

Benetazzo

Fedele

Gallego

et al. 2012

Coastal Engineering

112

104

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Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. To prove this, we consider an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea. In particular, we deployed WASS at the oceanographic platform Acqua Alta, off the Venice coast, Italy. Three experimental studies were performed, and the overlapping field of view of the acquired stereo images covered an area of approximately 1100 m 2 . Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics that agree well with theoretical models. From the observed wavenumber-frequency spectrum one can also predict the vertical profile of the current flow underneath the wave surface. Finally, future improvements of WASS and applications are discussed.

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Section: -F (••And•mentioning

confidence: 99%

“…Following Forristall (2000), for unidirectional (2-D) seas a=a 2 = 0.374, p=p 2 = 1-848, whereas for multidirectional (3-D) seas a= a 3 = 0.372 and (3=(3 3 = 1.874, and the associated models ( 17 ) are labeled as F2 and F3 respectively. The observed crest exceedance is given in Fig.…”

Section: -F (••And•mentioning

confidence: 99%

Offshore stereo measurements of gravity waves

Benetazzo

Fedele

Gallego

et al. 2012

Coastal Engineering

112

104

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“…Forristall (2000) reviewed studies by Tayfun (1980) and others that lead to an expected exceedance probability for the crest height η given by…”

Section: Second Order Effectsmentioning

confidence: 99%

Dynamical and statistical explanations of observed occurrence rates of rogue waves

Gemmrich

Garrett

2011

Nat. Hazards Earth Syst. Sci.

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Abstract. Extreme surface waves occur in the tail of the probability distribution. Their occurrence rate can be displayed effectively by plotting ln(−lnP ), where P is the probability of the wave or crest height exceeding a particular value, against the logarithm of that value. A Weibull distribution of the exceedance probability, as proposed in a standard model, then becomes a straight line. Earlier North Sea data from an oil platform suggest a curved plot, with a higher occurrence rate of extreme wave and crest heights than predicted by the standard model. The curvature is not accounted for by second order corrections, non-stationarity, or Benjamin-Feir instability, though all of these do lead to an increase in the exceedance probability. Simulations for deep water waves suggest that, if the waves are steep, the curvature may be explained by including up to fourth order Stokes corrections. Finally, the use of extreme value theory in fitting exceedance probabilities is shown to be inappropriate, as its application requires that not just N, but also lnN, be large, where N is the number of waves in a data block. This is unlikely to be adequately satisfied.

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“…[11] In this paper Forristall's [2000] perturbated Weibull model, for the second-order crest height distribution, is considered. He proposed a two parameters Weibull law for the probability of exceedance of the crest height, which is defined as the probability that a crest height is greater than h in a sea state with significant wave height H s :…”

Section: Second-order Distribution Of the Crest Heights In A Sea Statementioning

confidence: 99%

“…[6] The second-order crest height distribution, for the more general condition of three-dimensional waves (that is including effects of both finite bandwidth and directional spreading function) was finally given by Forristall [2000]. This distribution gives results in good agreement with both field data [Prevosto and Forristall, 2004] and other secondorder crest height models [Prevosto et al, 2000;Al-Humoud et al, 2002;Fedele and Arena, 2005].…”

Section: Introductionmentioning

confidence: 98%

Return period of nonlinear high wave crests

Arena

Pavone

2006

J. Geophys. Res.

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[1] This paper deals with the long-term statistics for extreme nonlinear crest heights. First, a new analytical solution for the return period R(h), of a sea storm in which the maximum nonlinear crest height exceeds a fixed threshold h, is obtained by applying the 'Equivalent Triangular Storm' model and a second-order crest height distribution. The probability P(h c max > hj[0, L]) that maximum nonlinear crest height in the time span L exceeds a fixed threshold is then derived from R(h) solution, assuming that the occurrence of storms with highest crest larger than h is given by a Poisson process. In the applications, both R(h) and P(h c max > hj[0, L]) are calculated for some locations. It is shown that narrowband second-order approach is slightly conservative, with respect to the more general condition of crest distribution for second-order three-dimensional waves. Finally, a comparison with Boccotti, Jasper and Krogstad models is presented.

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Wave Crest Distributions: Observations and Second-Order Theory

Cited by 365 publications

References 15 publications

Offshore stereo measurements of gravity waves

Offshore stereo measurements of gravity waves

Dynamical and statistical explanations of observed occurrence rates of rogue waves

Return period of nonlinear high wave crests

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