A comparative study of joint distributions of wave height and period, as well as wave height and steepness, is presented. The analysis includes two theoretical joint distributions of wave height and wave period. These two distributions are transformed into joint distributions of wave height and wave steepness. The theoretical distributions are compared with measured data, as well as parametric models which are obtained by fitting to the data. The data used for comparison are relatively broad-banded and are obtained from measurements in deep waters on the Norwegian continental shelf. It is found that the theoretical distributions are inadequate to describe the joint distributions of the primary wave characteristics of these broad-band data, and thus it is suggested to use parametric models to describe such data. Finally, the engineering relevance of the joint distribution of wave height and wave steepness is discussed.

1.
Cavanie´, A., Arhan, M., and Ezraty, R., 1976, “A Statistical Relationship Between Individual Heights and Periods of Storm Waves,” Proceedings Conference on Behaviour of Offshore Structures, Trondheim, Norway, Vol. II, pp. 354–360.
2.
Chakrabarti
S. K.
, and
Cooley
R. P.
,
1977
, “
Statistical Distribution of Periods and Heights of Ocean Waves
,”
Journal of Geophysical Research
, Vol.
82
, pp.
1363
1368
.
3.
Goda, Y., 1978, “The Observed Joint Distribution of Periods and Heights of Sea Waves,” Proceedings 16th Conference on Coastal Engineering, Hamburg, Germany, Vol. I, pp. 227–246.
4.
Haver
S.
,
1987
, “
On the Joint Distribution of Heights and Periods of Sea Waves
,”
Ocean Engineering
, Vol.
14
, pp.
359
376
.
5.
IAHR (International Association for Hydraulic Research)
,
1989
, “
List of Sea-State Parameters
,”
Journal of Waterway, Port, Coastal, and Ocean Engineering
, ASCE, Vol.
115
, pp.
793
808
.
6.
Kjeldsen, S. P., and Myrhaug, D., 1978, “Kinematics and Dynamics of Breaking Waves,” Report No. STF60 A78100, Ships in Rough Seas, Part 4, Norwegian Hydrodynamic Laboratories, Trondheim, Norway.
7.
Kjeldsen, S. P., and Myrhaug, D., 1979, “Wave-Wave and Wave-Current Interactions in Deep Water,” Proceedings 5th International Conference on Port and Ocean Engineering Under Arctic Conditions, Trondheim, Norway, Vol. III, pp. 179–200.
8.
Lindgren
G.
, and
Rychlik
I.
,
1982
, “
Wave Characteristic Distributions for Gaussian Waves—Wave Length, Amplitude and Steepness
,”
Ocean Engineering
, Vol.
9
, pp.
411
432
.
9.
Longuet-Higgins
M. S.
,
1975
, “
On the Joint Distribution of Periods and Amplitudes of Sea Waves
,”
Journal of Geophysical Research
, Vol.
80
, pp.
2688
2694
.
10.
Longuet-Higgins
M. S.
,
1983
, “
On the Joint Distribution of Wave Periods and Amplitudes in a Random Wave Field
,”
Proceedings Royal Society of London
, Ser. A, Vol.
389
, pp.
241
258
.
11.
Myrhaug
D.
,
1994
, “
Statistics of Steep Waves in Deep Water
,”
Journal of Marine Environmental Engineering
, Vol.
1
, pp.
161
173
.
12.
Myrhaug, D., and Dahle, E. Aa., 1994, “Ship Capsize in Breaking Waves,” ed., S. K. Chakrabarti, Fluid Structure Interaction in Offshore Engineering, Computational Mechanics Publications, Southampton, England, pp. 43–84.
13.
Myrhaug
D.
, and
Kjeldsen
S. P.
,
1984
, “
Parametric Modelling of Joint Probabilitiy Density Distributions for Steepness and Asymmetry in Deep Water Waves
,”
Applied Ocean Research
, Vol.
6
, pp.
207
220
.
14.
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
.
15.
Srokosz
M. A.
, and
Challenor
P. G.
,
1987
, “
Joint Distributions of Wave Height and Period: A Critical Comparison
,”
Ocean Engineering
, Vol.
14
, pp.
295
311
.
16.
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.