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.

Issue Section:
Ocean Engineering
Keywords:
ocean waves, response surface methodology, statistical analysis
Topics:
Probability, Seas, Waves, Wind, Statistics
1.
Forristall
,
G. Z.
, 2000, “
Wave Crest Distributions: Observations and Second Order Theory
,”
J. Phys. Oceanogr.
1520-0485,
30
, pp.
1931
–
1943
.
Crossref
Search ADS
 
2.
Gibson
,
R. S.
,
Swan
,
C.
, and
Tromans
,
P. S.
, 2007, “
Fully Nonlinear Statistics of Wave Crest Elevation Calculated Using a Spectral Response Surface Method: Application to Unidirectional Sea States
,”
J. Phys. Oceanogr.
1520-0485,
37
, pp.
3
–
15
.
Crossref
Search ADS
 
3.
Gibson
,
R.
, and
Swan
,
C.
, 2007, “
The Evolution of Large Ocean Waves: The Role of Local and Rapid Spectral Changes
,”
Proc. R. Soc. London, Ser. A
0950-1207,
463
, pp
21
–
48
.
Crossref
Search ADS
 
4.
Donelan
,
M. A.
, and
Magnusson
,
A. K.
, 2005, “
The Role of Meteorological Focusing in Generating Rogue Wave Conditions
,”
Proceedings of the Aha Huliko’a Hawaiian Winter Workshop
,
University of Hawaii
, Manoa.
5.
Bitner-Gregersen
,
E.
, and
Hagen
,
O.
, 2003, “
Effects of Two-Peak Spectra on Wave Crest Statistics
,”
Proceedings of the OMAE 2003
,
Cancun, Mexico
, June 8–13.
6.
Tromans
,
P.
, and
Vanderschuren
,
L.
, 2004, “
A Spectral Response Surface Method for Calculating Crest Elevation Statistics
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
126
, pp.
51
–
53
.
Crossref
Search ADS
 
7.
Baxevani
,
A.
,
Hagberg
,
O.
, and
Rychlik
,
I.
, 2005, “
Note on the Distribution of Extreme Wave Crests
,”
Proceedings of the OMAE
,
Halkidiki, Greece
, Jun. 12–17.
8.
Fedele
,
F.
, and
Tayfun
,
M. A.
, 2006, “
On the Statistics and Expected Shapes of Large Wave Crests
,
Proceedings of the OMAE 2006
, Hamburg, Germany, June 4-9.
9.
Forristall
,
G. Z.
, 1978, “
On the Statistical Distributions of Wave Heights in a Storm
,”
J. Geophys. Res.
0148-0227,
83
(
C5
), pp.
2353
–
2358
.
Crossref
Search ADS
 
10.
Sharma
,
J. N.
, and
Dean
,
R. G.
, 1979, “
Second-Order Directional Seas and Associated Wave Forces
,”
Proceedings of the Offshore Technology Conference
, Houston, April 30-May 3, Paper No. 3645, pp.
2505
–
2514
.
11.
Naess
,
A.
, 1985, “
On the Distribution of Crest to Trough Wave Heights
,”
Ocean Eng.
0029-8018,
12
(
3
), pp.
221
–
234
.
Crossref
Search ADS
 
12.
Boccoti
,
P.
, 2000,
Wave Mechanics for Ocean Engineering
,
Elsevier
,
Amsterdam
.
13.
Ewans
,
K. C.
, 2001, “
Directional Spreading in Ocean Swell
,”
Proceedings of the Fourth International Symposium Waves 2001
,
ASCE
, San Francisco, CA, Reston, VA, Sept. 2–6.
14.
Ewans
,
K. C.
, 1998, “
Observations of the Directional Spectrum of Fetch-Limited Waves
,”
J. Phys. Oceanogr.
1520-0485,
28
(
3
), pp.
495
–
512
.
Crossref
Search ADS
 
15.
Hasselmann
,
K.
,
Barnett
,
T. P.
,
Bouws
,
E.
,
Carlson
,
H.
,
Cartwright
,
D. E.
,
Enke
,
K.
,
Ewing
,
J. A.
,
Gienapp
,
H.
,
Hasselmann
,
D. E.
,
Kruseman
,
P.
,
Meerburg
,
A.
,
Müller
,
P.
,
Olbers
,
D. J.
,
Richter
,
K.
,
Sell
,
W.
, and
Walden
,
H.
, 1973, “
Measurements of Wind-Wave Growth and Swell Decay During the Joint North Sea Wave Project (JONSWAP)
,”
Dtsch. Hydrogr. Z.
0012-0308,
8
(
12
).
16.
Carter
,
D. J. T.
, 1982, “
Prediction of Wave Height and Period for a Constant Wind Velocity Using the JONSWAP Results
,”
Ocean Eng.
0029-8018,
9
(
1
), pp.
17
–
33
.
Crossref
Search ADS
 
17.
Haver
,
S.
, and
Andersen
,
O. J.
, 2000, “
Freak Waves: Rare Realizations of a Typical Population or Typical Realizations of a Rare Population?
,”
Proceedings of the ISOPE’2000
,
Seattle, WA
, June.
18.
Lehner
,
S.
,
Gunther
,
H.
, and
Rosenthal
,
W.
, 2005, “
Extreme Wave Observations From Radar Data Sets
,”
Proceedings of Waves’2005
,
Madrid
, July 3-7.
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 by American Society of Mechanical Engineers
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