Abstract
A combined analytical and experimental investigation of solitary waves interacting with a submerged impermeable breakwater is presented in this study. To the leading order of approximation, the integral forms of the analytical solutions of reflected and transmitted velocity potentials and wave elevations are derived according to the Fourier integral approach. The unknown coefficients are determined from the mixed-breakwater boundary conditions using the method of least squares. Experimental data in terms of wave elevations in the reflected and transmitted regions under various wave and breakwater conditions were recorded in a wave tank for validating the analytical solutions. Generally, the analytically predicted incident and transmitted wave profiles are found to agree reasonably well with the experimental measurements, although the analytical model in the cases with greater breakwater height overestimates the peak of the reflected waves. The variations of wave transmission–related and wave reflection–related solution coefficients versus the breakwater height are analyzed. The effect of breakwater height on the peak of reflected and transmitted waves is also examined. It is found that with an increase in the breakwater height the transmission coefficient decreases. Also, more wave energy is transmitted through the breakwater than that contributed to the reflected waves, even in the cases with high ratio of breakwater height to water depth.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abdul-Khader, M. H., and Rai, S. P. (1980). “A study of submerged breakwaters.” J. Hydraul. Res., 18(2), 113–121.
Abul-Azm, A. G. (1993). “Wave diffraction through submerged breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 587–605.
Beji, S., and Battjes, J. A. (1993). “Experimental investigation of wave propagation over a bar.” J. Waterway, Port, Coastal, Ocean Eng., 19(1–2), 151–162.
Dalrymple, R. A., and Martin, P. A. (1990). “Wave diffraction through offshore breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 727–741.
Dick, T. M., and Brebner, A. (1968). “Solid and permeable submerged breakwaters.” Proc., 11th Conf. Coast. Eng., ASCE, New York, NY, II, 1141–1158.
Goring, D. G. (1978). “Tsunamis—the propagation of long waves onto a shelf.” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Isaacson, M., de St.Q. (1983). “Solitary wave diffraction around large cylinder.” J. Waterway, Port, Coastal, Ocean Eng., 121–127.
Johnson, J. W., Fuchs, R. A., and Morison, J. R. (1951). “The damping action of submerged breakwaters.” Transaction American Geological Union, 32(5), 704–718.
Losada, I. J., Silva, R., and Losada, M. A. (1996). “Interaction of non-breaking directional random waves with submerged breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 28(1–4), 249–266.
Ming, Z., Liang, C., and Bin, T. (2007). “Numerical simulation of solitary wave scattering by a circular cylinder array.” J. Waterway, Port, Coastal, Ocean Eng. 34(3–4), 489–499.
Ohyama, K. (1991). “Numerical method of solitary forces acting on a large vertical cylinder.” Proc., 22 Coast. Eng. Conf., ASCE, Reston, VA, 840–852.
Sneddon, I. N. (1966). Mixed boundary value problems in potential theory, North Holland Publishing Co., Amsterdam, Netherlands.
Sogimoto, N., Hosokawa, K., and Kakutani, T. (1987). “Reflection and transmission of a shallow water soliton over a barrier.” J. Phys. Soc. Jpn., 56(8), 2744–2754.
Stephan, T. G., Miguel, A. L., and Francisco, M. (1994). “Characteristics of solitary wave breaking induced by breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 74–92.
Ursell, F. (1947). “The effect of a fixed vertical barrier by the infinite grating of circular water.” Proc., Cambridge Philosophical Soc., 43(3), 374–382.
Wang, K. H., Wu, T. Y., and Yates, G. T. (1992). “Three dimensional scattering of solitary waves by vertical cylinder.” J. Waterway, Port, Coastal, Ocean Eng., 551–566.
Wang, K. H., and Ren, X. (1993). “Water waves on flexible and porous breakwaters.” J. Eng. Mech., 1025–1047.
Wang, K. H., and Jiang, L. (1994). “Solitary wave interactions with an array of two vertical cylinders.” Appl. Ocean Res, 15(6), 337–350.
Wang, K. H., and Ren, X. (1998). “Interactions of cnoidal waves with cylinder arrays.” J. Waterway, Port, Coastal, Ocean Eng., 26(1), 1–20.
Wu, T. Y. (1981). “Long waves on ocean and coastal waters.” J. Eng. Mech, 107(3), 501–522.
Yates, G. T., and Wang, K. H. (1994). “Solitary wave scattering by vertical cylinder: experimental study.” Proc., 4th Int. Offshore and Polar Eng. Conf., Int. Society of Offshore and Polar Engineers, 118–124.
Yu, X., and Chwang, A. T. (1994). “Water waves above submerged porous plate.” J. Eng. Mech., 1270–1282.
Wu, Y.-T., Hsiao, S.-C., Huang, Z.-C., and Hwang, K.-S. (2012). “Propagation of solitary waves over a bottom-mounted barrier.” J. Waterway, Port, Coastal, Ocean Eng., 62, 31–47.
Zhong, Z., and Wang, K. H. (2006). “Solitary wave interaction with a concentric porous cylinder system.” J. Waterway, Port, Coastal, Ocean Eng., 33(7), 927–949.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 141 • Issue 9 • September 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Sep 29, 2014
Accepted: Jan 21, 2015
Published online: May 4, 2015
Published in print: Sep 1, 2015
Discussion open until: Oct 4, 2015
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.