Runup of Laboratory-Generated Breaking Solitary and Periodic Waves on a Uniform Slope
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 144, Issue 6
Abstract
In this article, we demonstrate that the normalized runup heights, R/H0 (R = runup height; H0 = incident wave height), for breaking solitary and periodic waves can be characterized by a single dimensionless parameter, called the surf parameter, which is defined by a theoretical wave-breaking criterion. Existing laboratory data for both breaking solitary and periodic waves were collected and are summarized in this article. Breaking waves include surging, plunging, and spilling breakers. To enhance the range of surf parameters for breaking solitary waves, a set of new laboratory experiments was carried out in a large-scale wave flume with a 1/100 slope. The maximum runup heights and the corresponding breaker types were recorded. Several wave conditions in the experiments were on the borderline of plunging and spilling breakers. When the laboratory data were plotted against the surf parameter, they collapsed into a trend, which can be described by a best-fit curve. This empirical formula can be used to provide a quick estimation of maximum runup height for both breaking solitary and periodic waves in the laboratory scale.
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Acknowledgments
This study was financially supported by the Ministry of Science and Technology, Taiwan (MOST 106-2911-I-006-301 to IWDRC of NCKU, 105-2221-E-006-121, and 105-2221-E-006-131) and the National Research Foundation, Marine Research and Development Programme, Singapore (Award MSRDP-05). The authors gratefully thank the staffs of THL for their assistance in setting up the experiments and two anonymous reviewers for their valuable comments on this article.
References
Ahrens, J. P. 1975. Wave runup on a 1 on 10 slope. Rep. No. MP12-75. Fort Belvoir, VA: US Army Coastal Engineering Research Center.
Battjes, J. A. 1974. “Surf similarity.” In Proc., 14th International Conf. on Coastal Engineering, 466–480. Reston VA: ASCE.
Boussinesq, M. J. 1871. “Théorie de l’intumescence liquide, appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire.” C. R. Acad. Sci. Paris 72: 755–759.
Bowen, A. J., D. L. Inman, and V. P. Simmons. 1968. “Wave ‘set-down’ and set-up.” J. Geophys. Res. 73 (8): 2569–2577. https://doi.org/10.1029/JB073i008p02569.
Briggs, M. J., C. E. Synolakis, G. S. Harkins, and S. T. Hughes. 1995. “Large scale three-dimensional laboratory measurements of tsunami inundation.” In Tsunami: Progress in prediction, disaster prevention and warning, edited by Y. Tsuchiya and N. Shuto, 129–149. Alphen aan de Rijn, Netherlands: Kluwer Academic.
Carrier, G. F., and H. P. Greenspan. 1958. “Water waves of finite amplitude on a sloping beach.” J. Fluid Mech. 4 (1): 97–109. https://doi.org/10.1017/S0022112058000331.
Chang, Y.-H., K.-S. Hwang, and H.-H. Hwung. 2009. “Large-scale laboratory measurements of solitary wave inundation on a 1:20 slope.” Coastal Eng. 56 (10): 1022–1034. https://doi.org/10.1016/j.coastaleng.2009.06.008.
Dean, R. G., and R. A. Dalrymple. 1991. Water wave mechanics for engineers and scientists. Vol. 2 of Advanced Series on Ocean Engineering. Singapore: World Scientific.
Fuhrman, D. R., and P. A. Madsen. 2008. “Surf similarity and solitary wave runup.” J. Waterway, Port, Coastal Eng. 134 (3): 195–198. https://doi.org/10.1061/(ASCE)0733-950X(2008)134:3(195).
Goring, D. G. 1978. “Tsunamis: The propagation of long waves onto a shelf.” Ph.D. thesis, California Institute of Technology.
Granthem, K. N. 1953. A model study of wave run-up on sloping structures. Rep. No. AD-3744. Berkeley, CA: Univ. of California, Institute of Engineering Research.
Grilli, S. T., I. A. Svendsen, and R. Subramanya. 1997. “Breaking criterion and characteristics for solitary waves on slopes.” J. Waterway, Port, Coastal Eng. 123 (3): 102–112. https://doi.org/10.1061/(ASCE)0733-950X(1997)123:3(102).
Hafsteinsson, H. J., F. M. Evers, and W. H. Hager. 2017. “Solitary wave run-up: Wave breaking and bore propagation.” J. Hydraul. Res. 55 (6): 787–798. https://doi.org/10.1080/00221686.2017.1356756.
Hall, J. V., Jr., and G. M. Watts. 1953. Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. Technical Rep. No. 33. Washington, DC: US Army Coastal Engineering Research Center.
Hammeken, A. 2017. “Wave run-up on beaches and coastal structures.” Ph.D. thesis, Univ. College London.
Hsiao, S.-C., T.-W. Hsu, T.-C. Lin, and Y.-H. Chang. 2008. “On the evolution and run-up of breaking solitary waves on a mild sloping beach.” Coastal Eng. 55 (12): 975–988. https://doi.org/10.1016/j.coastaleng.2008.03.002.
Hsu, T.-W., S.-J. Liang, B.-D. Young, and S.-H. Ou. 2012. “Nonlinear run-ups of regular waves on sloping structures.” Nat. Hazards Earth Syst. Sci. 12 (12): 3811–3820. https://doi.org/10.5194/nhess-12-3811-2012.
Huang, Z.-C., and K.-S. Hwang. 2015. “Measurements of surface thermal structure, kinematics, and turbulence of a large-scale solitary breaking wave using infrared imaging techniques.” Coastal Eng. 96: 132–147. https://doi.org/10.1016/j.coastaleng.2014.12.005.
Hwung, H.-H., Y.-S. Tai, and Y.-H. Lin. 2006. “The maximum run-up driven by nonlinear wave groups.” In Proc., 28th Ocean Engineering Conf. in Taiwan, 527–532. Kaohsiung City, Taiwan: National Sun Yat-Sen Univ.
Iribarren, C. R., and Norales, C. 1949. “Protection des ports.” In Vol. 4 of Proc., XVIIth International Navigation Congress, Section II, Communication, 31–80. Brussels, Belgium: PIANC.
Jensen, A., G. K. Pedersen, and D. J. Wood. 2003. “An experimental study of wave run-up at a steep beach.” J. Fluid Mech. 486: 161–188. https://doi.org/10.1017/S0022112003004543.
Kajiura, K. 1984. Runup of solitary wave on a slope—Investigation of the effects of wave breaking and bottom friction. [In Japanese.] Rep. of the Tsuanmi Hazards Mitigation Laboratory. Sendai, Japan: Tohoku Univ.
Kobayashi, N., and E. A. Karjadi. 1994. “Surf‐similarity parameter for breaking solitary‐wave runup.” J. Waterway, Port, Coastal Eng. 120 (6): 645–650. https://doi.org/10.1061/(ASCE)0733-950X(1994)120:6(645).
Li, Y., and F. Raichlen. 2001. “Solitary wave runup on plane slopes.” J. Waterway, Port, Coastal Eng. 127 (1): 33–44. https://doi.org/10.1061/(ASCE)0733-950X(2001)127:1(33).
Li, Y., and F. Raichlen. 2002. “Non-breaking and breaking solitary wave run-up.” J. Fluid Mech. 456: 295–318. https://doi.org/10.1017/S0022112001007625.
Li, Y., and F. Raichlen. 2003. “Energy balance model for breaking solitary wave runup.” J. Waterway, Port, Coastal Eng. 129 (2): 47–59. https://doi.org/10.1061/(ASCE)0733-950X(2003)129:2(47).
Lin, C., P.-H. Yeh, M.-J. Kao, M.-H. Yu, S.-C. Hsieh, S.-C. Chang, T.-R. Wu, and C.-P. Tsai. 2015. “Velocity fields in near-bottom and boundary layer flows in prebreaking zone of a solitary wave propagating over a 1:10 slope.” J. Waterway, Port, Coastal Eng. 141 (3): 04014038. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000269.
Liu, P. L.-F., C. E. Synolakis, and H. H. Yeh. 1991. “Report on the international workshop on long-wave run-up.” J. Fluid Mech. 229: 675–688. https://doi.org/10.1017/S0022112091003221.
Lo, H.-Y., Y. S. Park, and P. L.-F. Liu. 2013. “On the run-up and back-wash processes of single and double solitary waves—An experimental study.” Coastal Eng. 80: 1–14. https://doi.org/10.1016/j.coastaleng.2013.05.001.
Madsen, P. A., and H. A. Schäffer. 2010. “Analytical solutions for tsunami runup on a plane beach: Single waves, N-waves and transient waves.” J. Fluid Mech. 645: 27–57. https://doi.org/10.1017/S0022112009992485.
Manoj Kumar, G., V. Sriram, and T. Schlurmann. 2017. “Propagation and breaking characteristics of solitons and N-wave in fresh water and brine.” J. Hydraul. Res. 55 (4): 557–572. https://doi.org/10.1080/00221686.2016.1275050.
Marivela-Colmenarejo, R., R. Weiss, and C. E. Synolakis. 2017. “Temporal and spatial evolution of potential energy, kinetic energy, and momentum flux in tsunami waves during breaking and inundation.” J. Waterway, Port, Coastal Eng. 143 (5): 04017018. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000402.
Neelamani, S., H. Schüttrumpf, M. Muttray, and H. Oumeraci. 1999. “Prediction of wave pressures on smooth impermeable seawalls.” Ocean Eng. 26 (8): 739–765. https://doi.org/10.1016/S0029-8018(98)00026-2.
Pedersen, G. K., E. Lindstrøm, A. F. Bertelsen, A. Jensen, D. Laskovski, and G. Sælevik. 2013. “Runup and boundary layers on sloping beaches.” Phys. Fluids 25 (1): 012102. https://doi.org/10.1063/1.4773327.
Pujara, N., P. L.-F. Liu, and H. H. Yeh. 2015a. “An experimental study of the interaction of two successive solitary waves in the swash: A strongly interacting case and a weakly interacting case.” Coastal Eng. 105: 66–74. https://doi.org/10.1016/j.coastaleng.2015.07.011.
Pujara, N., P. L.-F. Liu, and H. H. Yeh. 2015b. “The swash of solitary waves on a plane beach: Flow evolution, bed shear stress and run-up.” J. Fluid Mech. 779: 556–597. https://doi.org/10.1017/jfm.2015.435.
Roos, A., and J. A. Battjes. 1976. “Characteristics of flow in run-up of periodic waves.” In Proc., 15th Int. Conf. Coastal Engineering, 781–795. Reston, VA: ASCE.
Saeki, H., S. Hanayasu, A. Ozaki, and K. Takagi. 1971. “The shoaling and run-up height of the solitary wave.” Coastal Eng. Jpn. 14 (1): 25–42. https://doi.org/10.1080/05785634.1971.11924124.
Savage, R. P. 1958. “Wave runup on roughened and permeable slopes.” J. Waterway Harb. Div. 84 (3): 1–38.
Saville, T. 1956. “Wave run-up on shore structures.” J. Waterway Harb. Div. 82 (2): 1–14.
Smith, L., A. Jensen, and G. Pedersen. 2017. “Investigation of breaking and non-breaking solitary waves and measurements of swash zone dynamics on a 5° beach.” Coast. Eng. 120: 38–46. https://doi.org/10.1016/j.coastaleng.2016.11.004.
Sumer, B. M., P. M. Jensen, L. B. Sørensen, J. Fredsøe, P. L.-F. Liu, and S. Carstensen. 2010. “Coherent structures in wave boundary layers. Part 2. Solitary motion.” J. Fluid Mech. 646: 207–231. https://doi.org/10.1017/S0022112009992837.
Synolakis, C. E. 1987. “The runup of solitary waves.” J. Fluid Mech. 185: 523–545. https://doi.org/10.1017/S002211208700329X.
Wijetunge, J. J. 2004. “Effect of water depth and surface roughness on wave run-up.” In Proc., 29th Int. Conf. on Coastal Engineering, 4354–4366. Singapore: World Scientific.
Wijetunge, J. J. 2007. “Large-scale wave run-up and overtopping measurements over a straight rubblemound breakwater without a crown wall.” In Proc., 5th Coastal Structures Int. Conf., 1285–1296. Singapore: World Scientific.
Wu, Y.-T., K.-W. Huang, H.-H. Hwung, and R.-Y. Yang. 2017. “Experimental study on the run-up of breaking solitary waves on impermeable slopes.” In Proc., 39th Ocean Engineering Conf. in Taiwan, 95–100. Taichung, Taiwan: Hongguang Univ. of Science and Technology.
Zhou, Z., J. Sangermano, T.-J. Hsu, and F. C. K. Ting. 2014. “A numerical investigation of wave-breaking-induced turbulent coherent structure under a solitary wave.” J. Geophys. Res. Oceans 119 (10): 6952–6973. https://doi.org/10.1002/2014JC009854.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 144 • Issue 6 • November 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Mar 15, 2018
Accepted: May 18, 2018
Published online: Aug 30, 2018
Published in print: Nov 1, 2018
Discussion open until: Jan 30, 2019
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