TECHNICAL PAPERS
May 1, 2000

Joint Distribution of Wave Heights and Periods in Waters of Any Depth

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 126, Issue 3

Abstract

The short-term joint distribution of wave heights and periods gives an informative description of a sea state that is well suited for many practical applications in the coastal zone. This paper deals with modifications and extensions of recently published results, expressed in terms of the joint probability density function of wave heights and periods. The performance of the present model is shown to be improved as compared with experimental data. Waves of any bandwidth are treated in deep water as well as over a uniformly sloping bottom. The modifications of the joint distribution in deep water refer to the estimation of wave periods, the separation of swell from sea waves, and the accommodation of a breaking criterion. The modified joint distribution is then transformed as waves move in shallow water, through a wave-by-wave technique incorporating nonlinear shoaling of both Stokes third-order and cnoidal waves, depth-induced wave breaking, and wave reforming. Comparisons with experimental measurements show improved performance over past models.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Blake, I. F., and Lindsey, W. C. (1973). “Level-crossing problems for random processes.” IEEE Trans. on Information Theory, 19(3), 295–315.
2.
Cavanié, A., Arhan, M., and Ezraty, R. (1976). “A statistical relationship between individual heights and periods of storm waves.” Proc., Behaviour of Offshore Struct., Norwegian Institute of Technology, Trondheim, Norway, 354–360.
3.
Dally, W. R. (1992). “Random breaking waves: field verification of a wave-by-wave algorithm for engineering application.” Coast. Engrg., 16, 369–397.
4.
Dally, W. R., Dean, R. G., and Dalrymple, R. A. (1985). “Wave height variation across beaches for arbitrary profile.” J. Geophys. Res., 90(6), 11917–11927.
5.
Doering, J. C., and Donelan, M. A. (1993). “The joint distribution of heights and periods of shoaling waves.” J. Geophys. Res., 98(7), 12543–12555.
6.
Donelan, M. A., Hamilton, J., and Hui, W. H. (1985). “Directional spectra of wind-generated waves.” Philosophical Trans. Royal Soc., London, 315, 509–562.
7.
Goda, Y. (1975). “Irregular wave deformation in the surf zone.” Coast. Engrg. in Japan, Tokyo, 18, 13–26.
8.
Goda, Y. (1978). “The observed joint distribution of periods and heights of ocean waves.” Proc., 16th Conf. on Coast. Engrg., ASCE, New York, 227–246.
9.
Goda, Y. (1985). Random seas and design of maritime structures. University of Tokyo Press, Tokyo.
10.
Goda, Y. (1986). “Effect of wave tilting on zero-crossing wave heights and periods.” Coast. Engrg. in Japan, Tokyo, 29, 79–90.
11.
Isobe, M. (1985). “Calculation and application of first-order cnoidal wave theory.” Coast. Engrg., 9, 309–325.
12.
Kamphuis, J. W. (1994). “Wave height from deep water through breaking zone.”J. Wtrwy., Port, Coast., and Oc. Div., ASCE, 120(4), 347–367.
13.
Laitone, E. V. (1963). “Higher approximation to non-linear water waves and the limiting heights of cnoidal, solitary and Stokes waves.” Rep. TM-133, U.S. Army Corps of Engineers, Washington, D.C.
14.
Le Méhauté, B., and Webb, L. M. (1964). “Periodic gravity waves over a gentle slope at a third order of approximation.” Proc., 9th Conf. on Coast. Engrg., ASCE, New York, 23–40.
15.
Longuet-Higgins, M. S. (1983). “On the joint distribution of wave periods and amplitudes in a random wave field.” Proc., Royal Soc., London, 389, 241–258.
16.
Mase, H. (1989). “Groupiness factor and wave height distribution.”J. Wtrwy., Port, Coast., and Oc. Div., ASCE, 115(1), 105–121.
17.
Mase, H., and Iwagaki, Y. (1982). “Wave height distributions and wave grouping in surf zone.” Proc., 18th Conf. on Coast. Engrg., ASCE, New York, 58–76.
18.
Mase, H., and Kobayashi, N. (1991). “Transformation of random breaking waves and its empirical numerical model considering surf beat.” Proc., Coast. Sediments '91, ASCE, New York, 688–702.
19.
Memos, C. D. (1994a). “On the theory of the joint probability of heights and periods of sea waves.” Coast. Engrg., 22, 201–215.
20.
Memos, C. D. (1994b). “Experimental results of wave transformation across a sloping beach.” Proc., 24th Conf. on Coast. Engrg., ASCE, New York, 2350–2364.
21.
Memos, C. D., and Tzanis, K. (1994). “Numerical results of the joint probability of heights and periods of sea waves.” Coast. Engrg., 22, 217–235.
22.
Newland, D. E. (1984). An introduction to random vibrations and spectral analysis. Longman's, London.
23.
Ochi, M. K., and Tsai, C. H. (1983). “Prediction of occurrences of breaking waves in deep water.” J. Physical Oceanogr., 13, 2008– 2019.
24.
Shuto, N. (1974). “Nonlinear long waves in a channel of variable section.” Coast. Engrg. in Japan, Tokyo, 17, 1–12.
25.
Stansberg, C. T. (1994). “Effects from directionality and spectral bandwidth on nonlinear spatial modulations of deep-water surface gravity wave trains.” Proc., 24th Conf. on Coast. Engrg., ASCE, New York, 579–593.
26.
Vinje, T., and Brevig, P. (1981). “Numerical simulation of breaking waves.” Advanced Water Resour., 4, 77–82.
27.
Weggel, J. R. (1972). “Maximum breaker height.”J. Wtrwy., Harb., and Coast. Engrg. Div., ASCE, 98(4), 529–548.

Information & Authors

Information

Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 126Issue 3May 2000
Pages: 162 - 172

History

Received: Feb 24, 1998
Published online: May 1, 2000
Published in print: May 2000

Permissions

Request permissions for this article.

Authors

Affiliations

Fellow, ASCE
Assoc. Prof., Dept. of Civ. Engrg., Nat. Tech. Univ. of Athens, 15780 Zografos, Greece.
Res. Sci., Dept. of Civ. Engrg., Nat. Tech. Univ. of Athens, 15780 Zografos, Greece.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share