Diffraction of Water Waves by Porous Breakwaters
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 121, Issue 6
Abstract
Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an underestimate of the functional performance of a porous breakwater.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bender, C. M., and Orszag, S. A. (1978). Advanced mathematical methods for scientists and engineers . McGraw-Hill, New York, N.Y.
2.
Berkhoff, J. C. W. (1972). “Computation of combined refraction and diffraction.”Proc., 13th Conf. on Coastal Engrg., ASCE, New York, N.Y., 471–490.
3.
Buchal, R. N., and Keller, J. B. (1960). “Boundary layer problem in diffraction theory.”Commun. Pure and Appl. Math., Vol. 13, 85–144.
4.
CERC. (1984). Shore protection manual . U.S. Army Corps of Engrs., Washington, D.C.
5.
Chen, H. S., and Mei, C. C. (1971). “Scattering and radiation of gravity waves by an elliptical cylinder.”Tech. Rep., No. 140, Parsons Lab., Massachusetts Inst. of Technol. (M.I.T.), Cambridge, Mass.
6.
Chwang, A. T. (1983). “A porous wave-maker theory.”J. Fluid Mech., Vol. 132, 395–406.
7.
Chwang, A. T., and Dong, Z. (1984). “Wave trapping due to a porous plate.”Proc., 15th Symp. on Naval Hydrodynamics, NOR, 32–42.
8.
Dalrymple, R. A., Losada, M. A., and Martin, P. A. (1991). “Reflection and transmission from porous structures under oblique wave attack.”J. Fluid Mech., Vol. 224, 625–644.
9.
Dalrymple, R. A., and Martin, P. A.(1990). “Wave diffraction through offshore breakwaters.”J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 116(6), 721–741.
10.
Goda, Y., Takayama, T., and Suzuki, Y. (1978). “Diffraction diagrams for directional random waves.”Proc., 16th Conf. on Coast. Engrg., ASCE, 628–650.
11.
Havelock, T. H. (1940). “The pressure of water waves upon a fixed obstacle.”Proc., Royal Soc., London, England, 175(A), 409–421.
12.
Horikawa, K. (1978). Coastal engineering; an introduction to ocean engineering . Univ. of Tokyo Press, Japan.
13.
Hotta, S. (1980). “Wave height distribution around permeable breakwaters.”Proc., 17th Conf. on Coast. Engrg., ASCE, 221–240.
14.
Houston, J. R. (1978). “Interaction of tsunamis with the Hawaiian islands calculated by a finite element numerical model.”J. Phys. Oceanography, Vol. 8, 93–102.
15.
Izumiya, T., Furumata, H., and Mizukami, J. (1990). “Study on the linear resistance coefficient of a porous structure and the resulting local reflection.”Proc., Coast. Engrg., JSCE, Tokyo, Japan, Vol. 37, 544–548.
16.
Kondo, H., and Toma, S. (1972). “Reflection and transmission for a porous structure.”Proc., 13th Conf. on Coast. Engrg., ASCE, 1847–1866.
17.
Lee, J. J. (1971). “Wave induced oscillation in harbors of arbitrary geometry.”J. Fluid Mech., Vol. 45, 375–394.
18.
Lick, W.(1978). “Diffraction of waves by a wedge.”J. Wtrwy., Port, Coast. and Oc. Engrg. Div., ASCE, 104(2), 119–133.
19.
Lin, P. L. F., and Mei, C. C.(1976). “Wave motion on a beach in the presence of a breakwater. 1: Waves.”J. Geophy. Res., 81(18), 3079–3084.
20.
Madsen, O. S.(1974). “Wave transmission through porous structures.”J. Wtrwy., Harb. and Coast. Engrg. Div., ASCE, 102(1), 169–188.
21.
Omer, G. C., and Hall, H. H.(1949). “The scattering of a tsunami by a cylindrical island.”J. Seismological Soc. Am., 39(4), 257–260.
22.
Penney, W. G., and Price, A. T. (1952). “The diffraction theory of sea waves and the shelter afforded by breakwaters.”Phil. Trans., Royal Soc., London, England, 244(A), 236–253.
23.
Sakakiyama, T., Abe, N., and Kajima, R. (1990). “Analysis of nonlinear wave motion around a porous structures.”Proc., Coast. Engrg., JSCE, Tokyo, Japan, Vol. 37, 554–558 (in Japanese).
24.
Sarpkaya, T., and Isaacson, M. (1981). Mechanics of wave force on offshore structures . Van Nostrand Reinhold, New York, N.Y.
25.
Sobey, R. J., and Johnson, T. L.(1986). “Diffraction patterns near narrow breakwater gaps.”J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 112(4), 512–528.
26.
Sollitt, C. K., and Cross, R. H. (1972). “Wave transmission through porous breakwaters.”Proc., 13th Conf. on Coast. Engrg., ASCE, 1827–1846.
27.
Watanabe, A., and Maruyama, K. (1986). “Numerical modeling of nearshore wave field under combined refraction, diffraction and breaking.”Coast. Engrg. in Japan, Tokyo, Japan, Vol. 29, 19–39.
28.
Wiegel, R. L. (1964). Oceanographic engineering . Prentice-Hall Inc., Englewood Cliffs, N.J.
29.
Williams, A. N.(1985). “Wave forces on an elliptic cylinder.”J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 111(2), 433–449.
30.
Yu, X., Isobe, M., and Watanabe, A.(1992). “Finite element solution of wave field around structures in nearshore zone.”Coast. Engrg. in Japan, Tokyo, Japan, 35(1), 21–33.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Nov 1, 1995
Published in print: Nov 1995
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.