Evolution of Maximum Amplitude of Solitary Waves on Plane Beaches
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 119, Issue 3
Abstract
This paper presents a study of the transformation of solitary waves on plane beaches. A series of laboratory experiments is presented to describe the amplitude evolution of long waves; these experiments suggest that at least four different regions exist for the functional variation of the maximum amplitude, two regions before and two regions after breaking. Linear theory is used to provide an expression for the growth of solitary waves evolving first over constant depth and then over a sloping bottom, including reflection. This result is shown to be equivalent to the wave evolution expression known as Green's law, and the limitations of Green's original derivation are discussed. Other existing analytical results and certain empirical relationships are used to produce a formulation consistent with the laboratory data with the objective to model the entire process of solitary wave evolution.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions. Nat. Bureau of Standards, Washington, D.C.
2.
Basco, D. R. (1985). “A qualitative description of wave breaking.” J. Water. Harb. Coast. Engrg., 112(2), 171–188.
3.
Basco, D. R., and Yamashita, T. (1986). “Towards a simple model of the wave breaking transition region in the surf zone.” Proc. 20th Conf. Coastal Engrg., ASCE, 995–970.
4.
Basco, D. R., and Yamashita, T. (1988). “On the partition of horizontal momentum between velocity and pressure components through the transition region of breaking waves.” Proc. 21st Conf. Coastal Engrg., 682–697.
5.
Bazin, H. (1865). “Researches experimentales sur la propagation des ondes.” Mém. présentés par divers Savants á L' Acad. Sci. Inst. France, 19, 495–644 (in French).
6.
Boussinesq, M. J. (1872). “Theorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canals des vitesses sensiblement pareilles de la surface au fond.” J. Math Pures Appl., 2(17), 55–108 (in French).
7.
Camfield, F. E., and Street, R. L. (1969). “Shoaling of solitary waves on small slopes.” J. Water. Harb. Coastal Engrg., 95, 1–22.
8.
Freilich, M. H., and Guza, R. T. (1984). “Nonlinear effects on shoaling surface gravity waves.” Phil Trans. Roy. Soc. London., A 311, 1–41.
9.
Kakutani, T. (1971). “Effect of uneven bottom on gravity waves.” J. Phys. Soc. Japan, 30(1), 272–276.
10.
Keller, J. B., and Keller, H. B. (1964). “Water wave runup on a beach.” ONR Research Report No. NONR‐3828(00), Dept. of Navy, Washington, D.C.
11.
Kirby, J. T. (1991). “Intercomposition of truncated series for shallow water waves.” J. Water. Harb. Coastal Engrg., 117, 143.
12.
Liu, P.L‐F., Yoon, S. B., and Kirby, J. T. (1985). “Nonlinear refraction—diffraction of waves in shallow water.” J. Fluid Mech., 153, 184–201.
13.
Mei, C. C. (1989). The applied dynamics of ocean surface waves. World Scientific, Teaneck, N. J.
14.
Miles, J. W. (1980). “Solitary waves.” Ann Rev. Fluid Mech., 12, 11–43.
15.
Miles, J. W. (1983a). “Solitary wave evolution over a gradual slope with turbulent friction.” J. Phys. Ocean., 13(2), 551–553.
16.
Miles, J. W. (1983b). “Wave evolution over a gradual slope with turbulent friction.” J. Fluid. Mech., 132(2), 207–216.
17.
Saeki H., Hanayasou, S., Ozaki, A., and Tagaki, K. (1971). “The shading and runup height of the solitary wave.” Coastal Engrg. in Japan, 14, 25–42.
18.
Shuto, N. (1973). “Shoaling and deformation of non‐linear waves.” Coastal Engrg. in Japan, 16, 1–12.
19.
Skjelbreia, J. E. (1987). “Observation of breaking waves on beaches by use of an LDV,” Ph.D. thesis, California Institute of Technology, Pasadena, Calif.
20.
Svendsen I. A., Madsen, P. A., and Hansen, J. B. (1978). “Wave characteristics in the surf zone.” Proc. 16th Conf. Coastal Engrg., ASCE, 520–559.
21.
Synolakis, C. E. (1986). “The runup of long waves,” Ph.D. thesis, California Institute of Technology, Pasadena, Calif.
22.
Synolakis, C. E. (1987). “The runup of solitary waves.” J. Fluid Mech., 185, 525.
23.
Synolakis, C. E. (1988). “On the zeroes of ,” Qu. Appl. Math., XLVI(1), 105–107.
24.
Synolakis, C. E. (1990). “The generation of long waves in the laboratory.” J. Water Harbour Coastal Engrg., 116, 252–266.
25.
Synolakis, C. E. (1991). “Green's law and the evolution of solitary waves.” Phys. Fluids A, 3, 490–491.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jul 2, 1990
Published online: May 1, 1993
Published in print: May 1993
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.