Runup and Rundown of Solitary Waves on Sloping Beaches
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 125, Issue 5
Abstract
This paper presents a combined experimental and numerical effort to study solitary wave runup and rundown on beaches. Both nonbreaking and breaking solitary waves are investigated. A two-dimensional numerical model that solves both mean flow and turbulence is employed in this study. For the nonbreaking solitary wave on a steep slope, numerical results of the present model are verified by experimental data and numerical results obtained from the boundary integral equation method model, in terms of both velocity distribution and free surface profiles. The characteristics of flow patterns during runup and rundown phases are discussed. The vertical variations of the horizontal velocity component are large at some instances, implying that the shallow water approximation may be inaccurate even for the nonbreaking wave runup and rundown. For the breaking solitary wave on a mild slope, numerical results of the present model are compared with experimental data for free surface displacements. The present model is found to be more accurate than the depth-averaged equations models. Using this numerical model, the mean velocity field and turbulence distribution under the breaking wave are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Adrian, R. J. (1986). “Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry.” Appl. Opt., 25(21), 3855–3858.
2.
Carrier, G. F., and Greenspan, H. P. (1958). “Water waves of finite amplitude on a sloping beach.” J. Fluid Mech., Cambridge, U.K., 17, 97–110.
3.
Chang, K.-A., and Liu, P. L.-F. (1998). “Velocity, acceleration and vorticity under a breaking wave.” Phys. Fluids, 10, 327–329.
4.
Goring, D. G. (1978). “Tsunamis—the propagation of long waves onto a shelf.” Rep. No. KH-R-38, California Institute of Technology, Pasadena, Calif.
5.
Greated, C. A., Skyner, D. J., and Bruce, T. (1992). “Particle image velocimetry (PIV) in the coastal engineering laboratory.” Proc., 23rd Int. Conf. Coast. Engrg., ASCE, New York, 212–225.
6.
Grilli, S., and Svendsen, I. A. ( 1990). “Computation of nonlinear wave kinematics during propagation and runup on a slope.” Water wave kinematics, A. Torum and O. T. Gudmestad, eds., NATO ASI Series E: Applied Sciences, 178, Kluwer Academic, Norwell, Mass.
7.
Ippen, A. T., and Kulin, G. (1954). “The shoaling and breaking of the solitary wave.” Proc., 5th Conf. Coast. Engrg., ASCE, New York, 27–49.
8.
Kanoglu, U., and Synolakis, C. E. (1998). “Long wave runup on piecewise linear topographies.” J. Fluid Mech., Cambridge, U.K., 374, 1–28.
9.
Kim, S. K., Liu, P. L.-F., and Liggett, J. A. (1983). “Boundary integral equation solutions for solitary wave generation, propagation and run-up.” Coast. Engrg., 7, 299–317.
10.
Kobayashi, N., Otta, A., and Roy, I. (1987). “Wave reflection and runup on rough slopes.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 113(3), 282–298.
11.
Lee, J.-J., Skjelbreia, E., and Raichlen, F. (1982). “Measurement of velocities in solitary waves.”J. Wtrwy., Port, Coast., and Oc. Div., ASCE, 108(2), 200–218.
12.
Lemos, C. M. (1992). Wave breaking. Springer, Berlin.
13.
Lin, P. ( 1998). “Numerical modeling of breaking waves,” PhD thesis, Cornell Univ., Ithaca, N.Y.
14.
Lin, P., and Liu, P. L.-F. (1998a). “A numerical study of breaking waves in the surf zone.” J. Fluid Mech., Cambridge, U.K., 359, 239–264.
15.
Lin, P., and Liu, P. L.-F. (1998b). “Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zones.” J. Geophys. Res., 103(C8), 15,677–15,694.
16.
Liu, P. L.-F., and Lin, P. (1997). “A numerical model for breaking wave: the volume of fluid method.” Res. Rep. No. CACR-97-02, Ctr. for Appl. Coast. Res. Oc. Engrg. Lab., University of Delaware, Newark, Del.
17.
Liu, P. L.-F., Synolakis, C. E., and Yeh, H. (1991). “Report on the international workshop on long-wave run-up.” J. Fluid Mech., Cambridge, U.K., 229, 675–688.
18.
Liu, P. L.-F., Yoon, S. B., Seo, S. N., and Cho, Y.-S. ( 1994). “Numerical simulation of tsunami inundation at Hilo, Hawaii.” Recent development in tsunami research. M. I. El-Sabh, ed., Kluwer Academic, Boston.
19.
Liu, P. L.-F., Cho, Y.-S., Briggs, M. J., Kanoglu, U., and Synolakis, C. (1995). “Runup of solitary waves on a circular island.” J. Fluid Mech., Cambridge, U.K., 302, 259–285.
20.
Lourenco, L., and Krothapalli, A. (1994). “On the accuracy of velocity and vorticity measurements with PIV.” Experiments in fluids, 18, 421–428.
21.
Nishimura, H., and Takewaka, S. (1990). “Experimental and numerical study on solitary wave breaking.” Proc., 22nd Int. Conf. Coast. Engrg., ASCE, New York, 1033–1045.
22.
Rodi, W. (1980). Turbulence models and their application in hydraulics—a state-of-the-art review. International Association for Hydraulic Research, Delft, The Netherlands.
23.
Shih, T.-H., Zhu, J., and Lumley, J. L. (1996). “Calculation of wall-bounded complex flows and free shear flows.” Int. J. Numer. Methods in Fluids, 23, 1133–1144.
24.
Skjelbreia, J. E. (1987). “Observations of breaking waves on sloping bottoms by use of laser doppler velocimetry.” Rep. No. KH-R-48, California Institute of Technology, Pasadena, Calif.
25.
Synolakis, C. E., and Skjelbreia, J. E. (1993). “Evolution of maximum amplitude of solitary waves on plane beaches.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 119(3), 323–342.
26.
Synolakis, C. E. ( 1986). “The runup of long waves,” PhD thesis, California Institute of Technology, Pasadena, Calif.
27.
Synolakis, C. E. (1987a). “The runup of solitary waves.” J. Fluid Mech., Cambridge, U.K., 185, 523–545.
28.
Tadepalli, S., and Synolakis, C. E. (1994). “The run-up of N-waves on sloping beaches.” Proc., Royal Soc. London, 445, 99–112.
29.
Tadepalli, S., and Synolakis, C. E. (1996). “Model for the leading waves of tsunamis.” Physical Rev. Let., 77(10), 2141–2144.
30.
Titov, V. V., and Synolakis, C. E. (1995). “Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2.”J. Wtrwy., Port, Coast., and Oc. Engrg., ASCE, 121(6), 308–316.
31.
Titov, V. V., and Synolakis, C. E. (1998). “Numerical modeling of tidal wave runup.” J. Wtrwy. Port, Coast., and Oc. Engrg., 124(4), 157–171.
32.
Zelt, J. A. (1991). “The run-up of nonbreaking and breaking solitary waves.” Coast. Engrg., 15, 205–246.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 125 • Issue 5 • September 1999
Pages: 247 - 255
History
Received: Aug 4, 1998
Published online: Sep 1, 1999
Published in print: Sep 1999
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.