Solitary Wave Runup on Plane Slopes
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 127, Issue 1
Abstract
This study deals with the runup of solitary waves on a uniform plane beach connected to an open ocean of constant depth. The waves are nonbreaking during the runup process. A nonlinear solution to the classical shallow water equation, that describes the wave characteristics on the beach, is obtained analytically by using a hodograph transformation. It was found that the nonlinear theory agreed well with experimental results. The maximum runup predicted by the nonlinear theory is larger than that predicted earlier and the correction is on the order of the offshore relative wave height for a given slope. This correction for nonbreaking waves on beaches decreases as the beach slope steepens.
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References
1.
Camfield, F. E., and Street, R. L. (1969). “Shoaling of solitary waves on small slopes.”J. Wtrwy. and Harb. Div., ASCE, 1, 01(Feb.), 1–22.
2.
Carrier, G. F. ( 1966). “Gravity waves on water of variable depth.” J. Fluid Mech., Cambridge, U.K., 24, 641–659.
3.
Carrier, G. F., and Greenspan, H. P. ( 1958). “Water waves of finite amplitude on a sloping beach.” J. Fluid Mech., Cambridge, U.K., 4, 97–109.
4.
Goring, D. G. ( 1978). “Tsunami: The propagation of long waves onto a shelf.” Rep. No. KH-R-12-38, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, Calif.
5.
Grilli, S. T., Svendsen, I. A., and Subramanya, R. (1997). “Breaking criterion and characteristics for solitary waves on slopes.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 123(3), 102–112.
6.
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, Office of the Chief of Engineers, U.S. Army Corps of Engineers.
7.
Heitner, K. L., and Housner, G. W. (1970). “Numerical model for tsunami runup.”J. Wtrwy., Harb. and Coast. Engrg. Div., ASCE, 3, 03(Aug.), 701–719.
8.
Keller, J. B., and Keller, H. B. ( 1964). “Water wave run-up on a beach.” ONR Res. Rep. Contract No. NONR-3828(00), Department of the Navy, Washington, D.C.
9.
Mei, C. C. ( 1983). The applied dynamics of ocean surface wave, Wiley, New York.
10.
Pedersen, G., and Gjevik, B. ( 1983). “Run-up of solitary waves.” J. Fluid Mech., Cambridge, U.K., 135, 283–290.
11.
Spielvogel, L. Q. ( 1976). “Single wave run-up on sloping beaches.” J. Fluid Mech., Cambridge, U.K., 74, 685–694.
12.
Synolakis, C. E. ( 1986). “The run-up of long waves.” PhD thesis, California Institute of Technology, Pasadena, Calif.
13.
Synolakis, C. E. ( 1987). “The run-up of solitary waves.” J. Fluid Mech., Cambridge, U.K., 185, 523–545.
14.
Tadepalli, S., and Synolakis, C. E. ( 1994). “The run-up of N-waves on sloping beaches.” Proc., Royal Soc., London, A445, 99–112.
15.
Tuck, E. O., and Hwang, L.-S. ( 1972). “Long wave generation on a sloping beach.” J. Fluid Mech., Cambridge, U.K., 51, 449–461.
16.
Zelt, J. A. ( 1986). “Tsunami: The response of harbours with sloping boundaries to long wave excitation.” Rep. No. KH-R-47, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, Calif.
17.
Zelt, J. A. ( 1991a). “The run-up of nonbreaking and breaking solitary waves.” Coast. Engrg., 15(3), 205–246.
18.
Zelt, J. A. (1991b). “Overland flow from solitary waves.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 117(3), 247–263.
19.
Zelt, J. A., and Raichlen, F. ( 1990). “A Lagrangian model for water-induced harbor oscillations.” J. Fluid Mech., Cambridge, U.K., 213, 203–225.
20.
Zhang, J. E. ( 1996). “Run-up of ocean waves on beaches.” PhD thesis, California Institute of Technology, Pasadena, Calif.
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Received: Apr 6, 1999
Published online: Feb 1, 2001
Published in print: Feb 2001
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