The statistical distribution of zero-crossing wave heights in Gaussian mixed sea states is examined by analyzing numerically simulated data. Nine different kinds of bimodal scalar spectra are used to study the effects of the relative energy ratio and the peak frequency separation between the low and high frequency wave fields on the wave height distribution. Observed results are compared with predictions of probabilistic models adopted in practice. Comparisons of the empirical data with relevant probabilistic models reveals that the Rayleigh model systematically overestimates the number of observed wave heights larger than the mean wave height, except for one of the cases analyzed. None of the models used to predict the observed exceedance probabilities is able to characterize adequately all cases of bimodal sea states examined here.

1.
Titov, L. F., 1969, Wind-Driven Waves, Israel Program for Scientific Translations, Jerusalem.
2.
Thompson, E. F., 1980, “Energy Spectra in Shallow U.S. Coastal Waters,” Tech. Paper 80-2, U.S. Army, Corps of Engineers, Coastal Engineering Research Centre.
3.
Cummings, W. E., Bales, S. L., and Gentile, D. M., 1981, “Hindcasting Waves for Engineering Applications,” Proc. Int. Symp. on Hydrodynamics in Ocean Eng., Trondheim, Vol. 1, pp. 70–89.
4.
Guedes Soares
,
C.
,
1984
, “
Representation of Double-Peaked Sea Wave Spectra
,”
Ocean Eng.
,
11
,
185
207
.
5.
Aranuvachapun
,
S.
,
1987
, “
Parameters of the Jonswap Spectral Model for Surface Gravity Waves-II Predictability from Real Data
,”
Ocean Eng.
,
14
, pp.
101
115
.
6.
Guedes Soares
,
C.
,
1991
, “
On the Occurrence of Double Peaked Wave Spectra
,”
Ocean Eng.
,
18
,
167
171
.
7.
Guedes Soares
,
C.
, and
Nolasco
,
M. C.
,
1992
, “
Spectral Modeling of Sea States with Multiple Wave Systems
,”
ASME J. Offshore Mech. Arct. Eng.
,
114
,
278
284
.
8.
Ochi, M., and Hubble, E., 1976, “On Six-Parameter Wave Spectra,” Proc. of 15th Int. Conf. Coastal Eng., pp 301–328.
9.
Tuah
,
M.
, and
Huspedth
,
R. T.
,
1982
, “
Comparisons of Numerical Random Sea Simulations
,”
J. Wtrway., Port, Coast., and Oc. Eng.
,
108
,
569
584
.
10.
Longuet-Higgins
,
M. S.
,
1952
, “
On the Statistical Distribution of the Heights of Sea Waves
,”
J. Mar. Res.
,
11
,
245
266
.
11.
Forristall
,
G. Z.
,
1978
, “
On the Statistical Distribution of Wave Heights in a Storm
,”
J. Geophys. Res.
,
83
,
2553
2558
.
12.
Longuet-Higgins
,
M. S.
,
1980
, “
On the Distribution of Heights of Sea Waves: Some Effects of Nonlinearity and Finite Bandwidth
,”
J. Geophys. Res.
,
85
(
C3
),
1519
1523
.
13.
Naess
,
A.
,
1985
, “
On the Statistical Distribution of Crest to Trough Wave Heights
,”
Ocean Eng.
,
12
,
221
234
.
14.
Vinje
,
T.
,
1989
, “
The Statistical Distribution of Wave Heights in a Random Seaway
,”
Appl. Ocean. Res.
,
119
,
143
152
.
15.
Tayfun
,
A.
,
1981
, “
Distribution of Crest-to-Trough Wave Heights
,”
J. Wtrway., Port, Coast., and Oc. Eng.
,
107
,
149
158
.
16.
Tayfun
,
A.
,
1983
, “
Effects of Spectrum Band width on the distribution of wave heights and Periods
,”
Ocean Eng.
,
10
,
107
118
.
17.
Tayfun
,
A.
,
1990
, “
Distribution of Large Wave Heights
,”
J. Wtrway., Port, Coast., and Oc. Eng.
,
116
,
686
707
.
18.
Lindgren
,
G.
, and
Rychlick
,
I.
,
1982
, “
Wave Characteristic Distributions for Gaussian Waves, Wave-Length, Amplitude and Steepness
,”
Ocean Eng.
,
9
, pp.
411
432
.
19.
Rodriguez
,
G. R.
, and
Guedes Soares
,
C.
,
1999
, “
The Bivariate Distribution of Wave Heights and Periods in Mixed Sea States
,”
ASME J. Offshore Mech. Arct. Eng.
,
121
(
2
), pp.
102
108
.
20.
Rodriguez, G. R., 1992, “Spectral and Statistical Characteristics of wind waves off Canary Islands,” Proc. of Int. Conf. Civil Engineering in the Oceans V, R. Hudspeth (Ed.), ASCE, New York, 622–636.
21.
Goda, Y., 1974, “Estimation of wave statistics from spectral information,” Proc. Int. Symp. Ocean Wave Measurement and Analysis, ASCE, New Orleans, 320–337.
22.
Goda
,
Y.
,
1970
, “
Numerical experiments on wave statistics with spectral simulation
,”
Rep. Port and Harbour Res. Inst., Japan
9
(
3
),
3
57
.
23.
Forristall
,
G. Z.
,
1984
, “
The distribution of measured and simulated wave heights as a function of spectral shape
,”
J. Geophys. Res., [Oceans]
,
89
,
10547
10552
.
24.
Rodriguez
,
G. R.
, and
Guedes Soares
,
C.
,
2001
, “
Correlation between successive wave heights and periods in mixed sea states
,”
Ocean Eng.
,
28
, pp.
1009
1030
.
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