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Solitary waves perturbed by a broad sill. Part 1. Propagation across the sill

Published online by Cambridge University Press:  18 October 2019

Harrison T.-S. Ko
Affiliation:
Department of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331, USA
Harry Yeh*
Affiliation:
Department of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331, USA
*
Email address for correspondence: harry@oregonstate.edu

Abstract

Stability of a solitary wave disturbed by a submerged flat sill is investigated experimentally. For sills narrow compared with the solitary wave, the transmitted waves are found to be unaffected in waveform and amplitude. A wider sill disturbs the solitary wave resulting in the formation of a dispersive wavetrain following the transmitted wave. In some cases, the wave amplitude recovers, despite being perturbed, to the state of an unobstructed solitary-wave state at a certain distance beyond the sill. Wider sills cause wave breaking that occurs over the sill or, in some cases, after the wave passes through the sill. Details of waveform transformation leading toward the breaking and subsequent energy dissipation are discussed.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Carrier, G. F., Wu, T. T. & Yeh, H. 2003 Tsunami run-up and draw-down on a plane beach. J. Fluid Mech. 475, 7999.10.1017/S0022112002002653Google Scholar
Chang, K.-A., Hsu, T.-J. & Liu, P. L.-F. 2001 Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part I. Solitary waves. Coast. Engng 44 (1), 1336.10.1016/S0378-3839(01)00019-9Google Scholar
Chang, K.-A., Hsu, T.-J. & Liu, P. L.-F. 2005 Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part II: Cnoidal waves. Coast. Engng 52 (3), 257283.10.1016/j.coastaleng.2004.11.006Google Scholar
Chen, Y.-S. & Yeh, H. 2014 Laboratory experiments on counter-propagating collisions of solitary waves. Part 1. Wave interactions. J. Fluid Mech. 749, 577596.10.1017/jfm.2014.231Google Scholar
Christou, M., Swan, C. & Gudmestad, O. T. 2008 The interaction of surface water waves with submerged breakwaters. Coast. Engng 55 (12), 945958.10.1016/j.coastaleng.2008.02.014Google Scholar
Cooker, M. J., Peregrine, D. H., Vidal, C. & Dold, J. W. 1990 The interaction between a solitary wave and a submerged semicircular cylinder. J. Fluid Mech. 215, 122.10.1017/S002211209000252XGoogle Scholar
Dean, R. G. & Dalrymple, R. A. 1991 Water Wave Mechanics for Engineers and Scientists, vol. 2. World Scientific Publishing Co Inc.10.1142/1232Google Scholar
Diorio, J. D., Liu, X. & Duncan, J. H. 2009 An experimental investigation of incipient spilling breakers. J. Fluid Mech. 633, 271283.10.1017/S0022112009007642Google Scholar
Dold, J. W. & Peregrine, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. Numer. Meth. Fluid Dyn. II 671679.Google Scholar
Duncan, J. H. 2001 Spilling breakers. Annu. Rev. Fluid Mech. 33 (1), 519547.10.1146/annurev.fluid.33.1.519Google Scholar
Duncan, J. H., Philomin, V., Behres, M. & Kimmel, J. 1994 The formation of spilling breaking water waves. Phys. Fluids 6 (8), 25582560.10.1063/1.868146Google Scholar
Duncan, J. H., Qiao, H., Philomin, V. & Wenz, A. 1999 Gentle spilling breakers: crest profile evolution. J. Fluid Mech. 379, 191222.10.1017/S0022112098003152Google Scholar
Gardarsson, S. M. & Yeh, H. 2007 Hysteresis in shallow water sloshing. J. Engng Mech. 133 (10), 10931100.10.1061/(ASCE)0733-9399(2007)133:10(1093)Google Scholar
Goring, D. G.1978, Tsunamis–the propagation of long waves onto a shelf. Rep. No. KH-R-38, California Institute of Technology.Google Scholar
Grilli, S. T., Losada, M. A. & Martin, F. 1994 Characteristics of solitary wave breaking induced by breakwaters. J. Waterways Port Coast. Ocean Engng 120 (1), 7492.10.1061/(ASCE)0733-950X(1994)120:1(74)Google Scholar
Grimshaw, R. 1971 The solitary wave in water of variable depth. Part 2. J. Fluid Mech. 46 (3), 611622.10.1017/S0022112071000739Google Scholar
Grue, J. 1992 Nonlinear water waves at a submerged obstacle or bottom topography. J. Fluid Mech. 244, 455476.10.1017/S0022112092003148Google Scholar
Hsiao, S.-C., Hsu, T.-W., Lin, T.-C. & Chang, Y.-H. 2008 On the evolution and run-up of breaking solitary waves on a mild sloping beach. Coast. Engng 55 (12), 975988.10.1016/j.coastaleng.2008.03.002Google Scholar
Huang, C.-J. & Dong, C.-M. 1999 Wave deformation and vortex generation in water waves propagating over a submerged dike. Coast. Engng 37 (2), 123148.10.1016/S0378-3839(99)00017-4Google Scholar
Huang, C.-J. & Dong, C.-M. 2001 On the interaction of a solitary wave and a submerged dike. Coast. Engng 43 (3–4), 265286.10.1016/S0378-3839(01)00017-5Google Scholar
Keulegan, G. H. 1948 Gradual damping of solitary waves. J. Res. Natl Bur. Stand. 40 (6), 487498.10.6028/jres.040.041Google Scholar
Knowles, J. & Yeh, H. 2018 On shoaling of solitary waves. J. Fluid Mech. 848, 10731097.10.1017/jfm.2018.395Google Scholar
Kobayashi, N., DeSilva, G. S. & Watson, K. D. 1989 Wave transformation and swash oscillation on gentle and steep slopes. J. Geophys. Res. 94 (C1), 951966.10.1029/JC094iC01p00951Google Scholar
Kobayashi, N., Otta, A. K. & Roy, I. 1987 Wave reflection and run-up on rough slopes. J. Waterways Port Coast. Ocean Engng 113 (3), 282298.10.1061/(ASCE)0733-950X(1987)113:3(282)Google Scholar
Li, W., Yeh, H. & Kodama, Y. 2011 On the mach reflection of a solitary wave: revisited. J. Fluid Mech. 672, 326357.10.1017/S0022112010006014Google Scholar
Li, Y. & Raichlen, F. 2003 Energy balance model for breaking solitary wave runup. J. Waterways Port Coast. Ocean Engng 129 (2), 4759.10.1061/(ASCE)0733-950X(2003)129:2(47)Google Scholar
Lin, C., Chang, S.-C., Ho, T.-C. & Chang, K.-A. 2006 Laboratory observation of solitary wave propagating over a submerged rectangular dike. J. Engng Mech. 132 (5), 545554.10.1061/(ASCE)0733-9399(2006)132:5(545)Google Scholar
Lin, M.-Y. & Huang, L.-H. 2010 Vortex shedding from a submerged rectangular obstacle attacked by a solitary wave. J. Fluid Mech. 651, 503518.10.1017/S0022112010000145Google Scholar
Lin, P. 2004 A numerical study of solitary wave interaction with rectangular obstacles. Coast. Engng 51 (1), 3551.10.1016/j.coastaleng.2003.11.005Google Scholar
Lin, P., Chang, K.-A. & Liu, P. L.-F. 1999 Runup and rundown of solitary waves on sloping beaches. J. Waterways Port Coast. Ocean Engng 125 (5), 247255.10.1061/(ASCE)0733-950X(1999)125:5(247)Google Scholar
Lin, P. & Liu, H.-W. 2005 Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape. J. Engng Mech. 131 (8), 822830.10.1061/(ASCE)0733-9399(2005)131:8(822)Google Scholar
Liu, P. L.-F. & Cheng, Y. 2001 A numerical study of the evolution of a solitary wave over a shelf. Phys. Fluids 13 (6), 16601667.10.1063/1.1366666Google Scholar
Longuet-Higgins, M. S. 1994 Shear instability in spilling breakers. Proc. R. Soc. Lond. A 446 (1927), 399409.10.1098/rspa.1994.0111Google Scholar
Losada, I. J., Silva, R. & Losada, M. A. 1996 Interaction of non-breaking directional random waves with submerged breakwaters. Coast. Engng 28 (1–4), 249266.10.1016/0378-3839(96)00020-8Google Scholar
Losada, M. A., Vidal, C. & Medina, R. 1989 Experimental study of the evolution of a solitary wave at an abrupt junction. J. Geophys. Res. 94 (C10), 1455714566.10.1029/JC094iC10p14557Google Scholar
Massel, S. R. 1983 Harmonic generation by waves propagating over a submerged step. Coast. Engng 7 (4), 357380.10.1016/0378-3839(83)90004-2Google Scholar
Mei, C. C. & Black, J. L. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38 (3), 499511.10.1017/S0022112069000309Google Scholar
Mei, C. C. & Liu, L. F. 1973 The damping of surface gravity waves in a bounded liquid. J. Fluid Mech. 59 (2), 239256.10.1017/S0022112073001540Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297 (1451), 459475.Google Scholar
Pedersen, G. & Gjevik, B. 1983 Run-up of solitary waves. J. Fluid Mech. 135, 283299.10.1017/S0022112083003080Google Scholar
Ramsden, J. D. & Raichlen, F. 1990 Forces on vertical wall caused by incident bores. J. Waterway, Port, Coastal, and Ocean Engineering 116, 592613.10.1061/(ASCE)0733-950X(1990)116:5(592)Google Scholar
Rey, V., Belzons, M. & Guazzelli, E. 1992 Propagation of surface gravity waves over a rectangular submerged bar. J. Fluid Mech. 235, 453479.10.1017/S0022112092001186Google Scholar
Seabra-Santos, F. J., Renouard, D. P. & Temperville, A. M. 1987 Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J. Fluid Mech. 176, 117134.10.1017/S0022112087000594Google Scholar
Synolakis, C. E. 1987 The runup of solitary waves. J. Fluid Mech. 185, 523545.10.1017/S002211208700329XGoogle Scholar
Tanaka, M. 1993 Mach reflection of a large-amplitude solitary wave. J. Fluid Mech. 248, 637661.10.1017/S0022112093000941Google Scholar
Tang, C.-J. & Chang, J.-H. 1998 Flow separation during solitary wave passing over submerged obstacle. J. Hydraulic Engng 124 (7), 742749.10.1061/(ASCE)0733-9429(1998)124:7(742)Google Scholar
Ting, F. C. K. & Kim, Y.-K. 1994 Vortex generation in water waves propagating over a submerged obstacle. Coast. Engng 24 (1–2), 2349.10.1016/0378-3839(94)90025-6Google Scholar
Yasuda, T., Mutsuda, H. & Mizutani, N. 1997 Kinematics of overturning solitary waves and their relations to breaker types. Coast. Engng 29 (3–4), 317346.10.1016/S0378-3839(96)00032-4Google Scholar
Yeh, H. & Ghazali, A. 1987 A bore on a uniformly sloping beach. In Proc. 20th Intl Conf. on Coastal Engng, pp. 877888. ASCE.Google Scholar
Yeh, H., Ko, H., Knowles, J. & Harry, S. 2019 Solitary waves perturbed by a broad sill. Part 2. Propagation along the sill. J. Fluid Mech. (in press).Google Scholar
Young, D. M. & Testik, F. Y. 2011 Wave reflection by submerged vertical and semicircular breakwaters. Ocean Engng 38 (10), 12691276.10.1016/j.oceaneng.2011.05.003Google Scholar
Zhuang, F. & Lee, J.-J. 1997 A viscous rotational model for wave overtopping over marine structure. In Proc. 25th Intl Conf. Coastal Engng, pp. 21782191. ASCE.Google Scholar