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Ocean Engineering

The Second Order Statistics of High Waves in Wind Sea and Swell

[+] Author and Article Information
Peter Tromans

 Ocean Wave Engineering, Bezuidenhoutseweg 496, 2594 BG The Hague, The Netherlandspt7185@hotmail.com Engineering Systems, Avenue Molière, 5/5, 1300 Wavre, Belgiumpt7185@hotmail.com Shell International Exploration and Production, 2280 AB Rijswijk, The Netherlandspt7185@hotmail.com

Luc Vanderschuren

 Ocean Wave Engineering, Bezuidenhoutseweg 496, 2594 BG The Hague, The Netherlandsluc.vanderschuren@skynet.be Engineering Systems, Avenue Molière, 5/5, 1300 Wavre, Belgiumluc.vanderschuren@skynet.be Shell International Exploration and Production, 2280 AB Rijswijk, The Netherlandsluc.vanderschuren@skynet.be

Kevin Ewans

 Ocean Wave Engineering, Bezuidenhoutseweg 496, 2594 BG The Hague, The Netherlandskevin.ewans@shell.com Engineering Systems, Avenue Molière, 5/5, 1300 Wavre, Belgiumkevin.ewans@shell.com Shell International Exploration and Production, 2280 AB Rijswijk, The Netherlandskevin.ewans@shell.com

J. Offshore Mech. Arct. Eng 133(3), 031104 (Mar 30, 2011) (7 pages) doi:10.1115/1.2979799 History: Received July 17, 2007; Revised June 06, 2008; Published March 30, 2011; Online March 30, 2011

The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The nonlinearity of steep waves is modeled to the second order using Sharma and Dean kinematics, and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, nonlinearity makes extreme crests higher than the corresponding linear ones. The nonlinear effects on the wave height are relatively small.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Exceedance probability of the normalized crest elevation (upper) and the normalized exceedance probability of the normalized crest (lower) for the SRS unidirectional, Forristall unidirectional, SRS directionally spread, and Forristall directional spread seas

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Figure 2

Exceedance probability of the normalized height (upper) and the normalized exceedance probability of the normalized height (lower) for the SRS unidirectional, Forristall, and SRS directionally spread

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Figure 3

Fetch-limited JONSWAP spectra

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Figure 4

Crest to Hs ratios with a 0.001 exceedance probability as a function of fetch

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Figure 5

Wave steepness (continuous line) and spectral halfwidth—spectral width at the half peak height (dashed line)—as a function of fetch

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Figure 6

Height to Hs ratios with a 0.001 exceedance probability as a function of fetch

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Figure 7

Contours of the ratio of crest height to significant wave height for an exceedance probability of 0.001, against the lognormal standard deviation and peak period

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Figure 8

Contours of the ratio of crest height to significant wave height for an exceedance probability of 0.001, against the lognormal standard deviation and peak period, for a water depth of 10 m

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Figure 9

Contours of the ratio of crest height to significant wave height for an exceedance probability of 0.001, against the relative wind sea and swell direction difference and the difference between the swell and wind sea peak periods. Water depth is 2000 m.

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Figure 10

Contours of the ratio of height to significant wave height for an exceedance probability of 0.001, against the relative wind sea and swell direction difference and the difference between the swell and wind sea peak periods. Water depth is 2000 m.

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Figure 11

Contours of the ratio of crest height to significant wave height for an exceedance probability of 0.001, against the relative wind sea and swell direction difference and the difference between the swell and wind sea peak periods. Water depth is 30 m.

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Figure 12

Contours of the ratio of height to significant wave height for an exceedance probability of 0.001, against the relative wind sea and swell direction difference and the difference between the swell and wind sea peak periods. Water depth is 30 m.

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Figure 13

Variance density spectrum of the Draupner recording, together with the estimated swell and wind-sea components

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Figure 14

Crest exceedance probabilities of the Draupner Jan. 1, 1995, 1520 recording, together with second order SRS and Forristall estimates and linear (Rayleigh) estimates

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Figure 15

Wave height exceedance probabilities of the Draupner Jan. 1, 1995, 1520 recording, together with second order SRS and Forristall estimates and linear (Rayleigh) estimates

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