A two-dimensional Weibull distribution is presented which is obtained by transforming a two-dimensional Rayleigh distribution. The emphasis herein is on its application to describe the statistics of successive wave periods, and the results are illustrated by discussing the rolling of smaller vessels in beam seas in a simplified manner. Reference is also made to the related subjects on the joint correlation of successive high waves and on the joint statistics of wave steepness parameters for two successive waves, where the wave steepness parameters considered are the crest front steepness and the total wave steepness.

1.
Abramowitz, M., and Stegun, I. A., 1972, Handbook of Mathematical Functions, Dover, New York, NY.
2.
Blagoveshensky, S. N., 1962, Theory of Ship Motions, Dover, New York, NY.
3.
Bretschneider, C. L., 1959, “Wave Variability and Spectra for Windgenerated Waves,” U.S. Army Corps of Engineers, B.E.B. Tech. Mem. 118.
4.
Dahle
E. Aa.
,
Myrhaug
D.
, and
Dahl
S. J.
,
1988
, “
Probability of Capsizing in Steep and High Waves from the Side in Open Sea and Coastal Waters
,”
Ocean Engineering
, Vol.
15
, pp.
139
151
.
5.
Johnson, N. L., and Kotz, S., 1972, Distributions in Statistics: Continuous Multivariable Distributions, John Wiley & Sons, Inc., New York, NY.
6.
Kimura, A., 1980, “Statistical Properties of Random Wave Groups,” Proceedings, 17th International Conference on Coastal Engineering, Sydney, Australia, pp. 2955–2972.
7.
Kjeldsen, S. P., and Myrhaug, D., 1979, “Formation of Wave Groups and Distributions of Parameters for Wave Asymmetry,” Report No. STF60 A79044, Ships in Rough Seas, Part 4, Norwegian Hydrodynamic Laboratories, Trondheim, Norway.
8.
Kjeldsen, S. P., and Myrhaug, D., 1980, “Wave-Wave Interactions, Current Wave Interactions and Resulting Extreme Waves and Breaking Waves,” Proceedings, 17th International Conference on Coastal Engineering, Sydney, Australia, pp. 2277–2303.
9.
Krogstad
H. E.
,
1985
, “
Height and Period Distributions of Extreme Waves
,”
Applied Ocean Research
, Vol.
7
, pp. .
158
165
.
10.
Longuet-Higgins, M. S., 1986, “Wave Group Statistics,” Oceanic Whitecaps, eds., E. C. Manohan and G. Mac Niocaill, D. Reidel Publishing Company, Dordrecht, pp. 15–35.
11.
Medina
J. R.
, and
Hudspeth
R. T.
,
1990
, “
A Review of the Analysis of Ocean Wave Groups
,”
Coastal Engineering
, Vol.
14
, pp.
515
542
.
12.
Middleton, D., 1960, Statistical Communication Theory, McGraw-Hill, New York, NY.
13.
Myrhang, D., and Dahle, E. Aa., 1994, “Ship Capsize in Breaking Waves,” Fluid Structure Interaction in Offshore Engineering, ed., S. K. Chakrabarti, Computational Mechanics Publications, Southampton, England, pp. 43–84.
14.
Myrhaug
D.
, and
Kjeldsen
S. P.
,
1984
, “
Parametric Modelling of Joint Probability Density Distributions for Steepness and Asymmetry in Deep Water Waves
,”
Applied Ocean Research
, Vol.
6
, pp.
207
220
.
15.
Myrhaug
D.
, and
Kjeldsen
S. P.
,
1987
, “
Prediction of Occurrences of Steep and High Waves in Deep Water
,”
Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE
, Vol.
113
, pp.
122
138
.
16.
Myrhugh
D.
, and
Rue
H.
,
1993
a, “
Note on a Joint Distribution of Successive Wave Periods.
,”
Journal of Ship Research
, Vol.
37
, pp.
209
213
.
17.
Myrhaug
D.
, and
Rue
H.
,
1993
b, “
Joint Distribution of Successive Wave Steepness Parameters
,”
ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING
, Vol.
115
, pp.
191
195
.
18.
Tulin
M. P.
, and
Li
J. J.
,
1992
, “
On the Breaking of Energetic Waves
,”
International Journal of Offshore and Polar Engineering
, Vol.
2
, pp.
46
53
.
This content is only available via PDF.
You do not currently have access to this content.