Integral Equation Model for Wave Propagation with Bottom Frictions
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 120, Issue 6
Abstract
An integral equation method is developed to calculate wave propagation and runup in a two‐dimensional wave channel. First, the problem is formulated as a potential flow with nonlinear free‐surface boundary conditions. The effects of bottom friction are included in the model via a boundary‐layer approximation. Numerical solutions are obtained for the maximum runup heights of solitary waves and cnoidal waves on a constant slope. Numerical solutions are compared with available experimental data. A very good agreement is observed. The maximum runup height of a cnoidal wave is larger than that of an equivalent sinusoidal wave. However, the runup height of cnoidal wave is smaller than that of solitary wave with the same wave height. The runup height of cnoidal waves is not a monotonic function of the incident wavelength. Numerical solutions for the maximum runup heights confirm that the bottom frictional effects are important when the slope is less than 20°.
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, Natl. Bur. Stands., Washington, D.C.
2.
Goring, D. G. (1978). “Tsunamis—the propagation of long waves onto a shelf.” Rep. No. KH‐R‐38. W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, Calif.
3.
Grilli, S. T., Skourup, J., and Svendsen, I. A. (1989). “An efficient boundary element method for nonlinear water waves.” Engrg. Anal. Boundary Elements, 6, 97–107.
4.
Hall, J. V., and Watts, J. W. (1953). “Laboratory investigation of the vertical rise of solitary waves on impermeable slopes.” Tech. Memo. 33, Beach Erosion Board, U.S. Army Corps of Engineers, Washington, D.C.
5.
Jonsson, I. G. (1966). “Wave boundary layers and friction factors.” Proc., 10th Conf. Coast. Engrg., ASCE, 127–148.
6.
Kamiya, N., and Miyazawa, H. (1990). “Sloshing in two‐dimensional container with inclined side wall‐boundary‐element approach.” Commun. Appl. Numer. Methods, 6, 207–214.
7.
Keller, J. B., and Keller, H. B. (1964). “Water wave run‐up on a beach.” ONR Res. Rep. Contract No. NONR‐3838(00), Dept. of the Navy, Washington, D.C.
8.
Kim, S.‐K., Liu, P. L.‐F., and Liggett, J. A. (1983). “Boundary integral equation solutions for solitary wave generation, propagation and runup.” Coastal Engrg., 7, 299–317.
9.
Langsholt, M. (1981). “Experimental study of wave run‐up,” Thesis, Univ. of Oslo, Oslo, Norway.
10.
Liggett, J. A., and Liu, P. L.‐F. (1983). Boundary integral equation method for porous media flow, George Allen & Unwin, London, U.K.
11.
Liu, P. L.‐F., Hsu, H.‐W., and Lean, M. H. (1992). “Applications of boundary integral equation methods for two‐dimensional nonlinear water wave problems.” Int. J. for Numer. Meth. in Fluids, 15, 1119–1141.
12.
Longuet‐Higgins, M. S., and Cokelet, E. D. (1976). “The deformation of steep surface waves on water.” Proceedings of the Royal Society of London, London, U.K., A, 350, 1–26.
13.
Medina, D. E., Liggett, J. A., Birchwood, R. A., and Torrance, K. E. (1991). “A consistent boundary element method for free surface hydrodynamic calculations.” Int. J. for Numer. Meth. in Fluids, 12, 835–857.
14.
Mei, C. C. (1989). The applied dynamics of ocean surface waves, World Scientific Publishing Co., River Edge, N.J.
15.
Mei, C. C., and Liu, P. L.‐F. (1973). “The damping of surface waves in a bounded liquid.” J. Fluid Mech., 59, 239–256.
16.
Ohyama, T. (1987). “A boundary element analysis for cnoidal wave runup.” Proceedings of the Japan Society of Civil Engineers, Tokyo, Japan, 381, 189–198, (in Japanese).
17.
Skourup, J., and Jonsson, I. G. (1992). “Computations of forces on, and particle orbits around horizontal cylinders under steep waves.” Ocean Engrg., 19, 527–553.
18.
Svendsen, I. A., and Grilli, S. T. (1989). “Nonlinear waves on steep slopes.” J. Coast. Res., 7, 185–202.
19.
Synolakis, C. E. (1987). “The runup of solitary waves.” J. Fluid Mech., 185, 523–545.
20.
Synolakis, C. E. (1990). “Generation of long waves in laboratory.” J. Wtrway, Port, Coast., and Oc. Engrg., ASCE, 116(2), 252–266.
21.
Synolakis, C. E., Deb, M. K., and Skjelbreia, J. E. (1988). “The anomalous behavior of the runup of cnoidal waves.” Phy. of Fluids A, 31, 3–5.
22.
Zelt, J. A. (1991). “The runup of nonbreaking and breaking solitary waves.” Coastal Engrg., 15, 205–246.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 120 • Issue 6 • November 1994
Pages: 594 - 608
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jun 7, 1993
Published online: Nov 1, 1994
Published in print: Nov 1994
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.