A Harbor Ray Model of Wave Refraction‐Diffraction
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111, Issue 1
Abstract
A harbor ray model has been developed which describes the combined wave effects of diffraction around breakwaters and depth refraction. Ray models are computationally well suited to determining the response of large harbor areas to short period waves. This is a situation for which alternative mathematical models can use prohibitively large amounts of computing time and storage. Diffraction caused by two types of breakwater layout, commonly found at harbor entrances, is shown to be capable of being modeled by a ray method. These breakwater layouts are: (1) A small gap between two straight breakwaters; and (2) a single, straight, semi‐infinite breakwater. A new ray system is presented for the semi‐infinite breakwater problem which overcomes the difficulty of modeling the region around the geometric shadow boundary. Unlike other techniques developed to resolve this difficulty, this method retains a ray plotting solution technique and therefore keeps the computational advantages of such a technique. A comparison is made between the ray model and a finite‐element model for the two breakwater layouts on constant‐depth and sloping sea‐beds.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B., Petersen, H. M., and Skovgaard, O., “On the Numerical Modelling of Short Waves in Shallow Water,” Journal of Hydraulic Research, Vol. 16, No. 3, 1978, pp. 173–204.
2.
Berkhoff, J. C. W., “Computation of Combined Refraction and Diffraction,” Proceedings of the 13th International Conference on Coastal Engineering, Vancouver, ASCE, Vol. 1, 1973, pp. 471–490.
3.
Berkhoff, J. C. W., “Mathematical Models of Simple Harmonic Linear Water Waves. Wave Diffraction and Refraction,” Publication No. 163, Delft Hydraulics Laboratory, Holland, 1976.
4.
Bettess, P., and Bettess, J. A., “WAVE. A. Finite‐Element Program for Solving the Wave Equation,” Computer Report No. 81, Department of Civil Engineering, University College of Wales, Swansea, U.K., 1976.
5.
Bretschneider, C. L., and Reid, R. O., “Modification of Wave Height due to Bottom Friction, Percolation and Refraction,” Technical Memorandum No. 45, U.S. Army Corps of Engineers, Beach Erosion Board, Oct., 1954.
6.
Carr, J. H., and Stelzreide, M. E., “Diffraction of Water Waves by Breakwaters,” Circular No. 521, U.S. National Bureau of Standards, 1952, pp. 109–125.
7.
Gilbert, G., and Abernethy, C. L., “Refraction of Wave Spectra,” Internal Report 117, Hydraulics Research Station, Wallingford, U.K., May, 1975.
8.
Ito, Y., and Tanimoto, K., “A Method of Numerical Analysis of Wave Propagation. Application to Wave Diffraction and Refraction,” Proceedings of the 13th International Conference on Coastal Engineering, Vancouver, ASCE, Vol. 1, 1973, pp. 503–522.
9.
Jonsson, I. G., “The Refraction Equation as a Result of Wave Front Continuity,” Progress Report 43, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, Aug., 1977, pp. 31–34.
10.
Jonsson, I. G., “The General Wave Equation and the Refraction Approximation,” Progress Report 49, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, Aug., 1979, pp. 11–20.
11.
Keller, J. B., “Geometrical Theory of Diffraction,” Journal of the Optical Society of America, Vol. 52, No. 2, 1962, pp. 116–130.
12.
Kriegsmann, G. A., and Larsen, E. W., “On the Parabolic Approximation to the Reduced Wave Equation,” SIAM Journal of Applied Mathematics, Vol. 34, No. 1, Jan., 1978, pp. 200–204.
13.
Larsen, J., “A Harbour Theory for Wind‐Generated Waves based on Ray Methods,” Journal of Fluid Mechanics, Vol. 87, No. 1, 1978, pp. 143–158.
14.
Memos, C. D., “Energy Transmission by Surface Waves through an Opening,” Journal of Fluid Mechanics, Vol. 97, No. 3, 1980, pp. 557–568.
15.
Morse, P. M., and Rubenstein, P. J., “The Diffraction of Waves by Ribbons and Slits,” Physical Review, Vol. 54, 1938, pp. 895–898.
16.
Penney, W. G., and Price, A. T., “The Diffraction Theory of Sea Waves and the Shelter Afforded by Breakwaters,” Philosophical Transactions of the Royal Society, (A), Vol. 244, 1952, pp. 236–253.
17.
Porter, D., “Wave Diffraction around Breakwaters,” Internal Report 200, Hydraulics Research Station, Wallingford, U.K., Dec., 1979.
18.
Radder, A. C., “On the Parabolic Equation Method for Water‐Wave Propagation,” Journal of Fluid Mechanics, Vol. 95, No. 1, 1979, pp. 159–176.
19.
Sommerfeld, A., “Mathematische Theorie der Diffraktion,” Mathematische Annalen, Vol. 47, 1896, pp. 317–374.
20.
Southgate, H. N., “Ray Methods for Combined Refraction and Diffraction Problems,” Internal Report 214, Hydraulics Research Station, Wallingford, U.K., July, 1981.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111 • Issue 1 • January 1985
Pages: 29 - 44
Copyright
Copyright © 1985 ASCE.
History
Published online: Jan 1, 1985
Published in print: Jan 1985
Authors
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.