Solitary Waves Incident on a Submerged Horizontal Plate
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140, Issue 3
Abstract
Wave scattering of a solitary wave traveling over a submerged horizontal plate was studied. Experiments for normal incidence were conducted in a wave flume, with a horizontal plate suspended at two different depths in the middle of the flume. Gauge pressures above and underneath the plate, surface elevations on and near the plate, and flow velocities at three representative fields of view were measured. The flow underneath the plate was found to behave almost like a plug flow, driven by the time-dependent, spatially uniform pressure gradient between the two openings. Complex vortices formed near the two edges of the plate as the plate acted like a flow divider. A numerical model based on two-dimensional Navier-Stokes equations was used to confirm the main features captured by the experimental measurements. Analytical solutions based on the linear long wave theory, which admits a soliton-like impulse wave solution, were also derived. The linear theory was applicable for obliquely incident impulse waves. When the analytical solutions were applied to the wave conditions used in the experiments, it was found that the theory described pressure and surface elevation satisfactorily when the nonlinearity was insignificant. Based on the pressure distribution above and beneath the plate, the total vertical force and moment exerted on the plate were calculated. As the wave passed over the plate, the plate first experienced a lift, followed by a force in the downward direction, and then a lift again. As a result, a nonzero time-varying moment existed. The analytical solution was also utilized to examine the effects of relative plate width on the transmitted and reflected waves. The effects of the angle of incidence are also discussed briefly.
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Acknowledgments
The research reported here has been supported by National Science Foundation grants to Cornell University.
References
Aoyama, T. (1988). “Study on offshore wave control by a submerged plate.” M.E. thesis, Univ. of Tokyo, Tokyo.
Carrier, G. F., and Noiseux, C. F. (1983). “The reflection of obliquely incident tsunamis.” J. Fluid Mech., 133, 147–160.
Carter, R. W. (2005). “Wave energy converters and a submerged horizontal plate.” M.S. thesis, Univ. of Hawaii at Manoa, Honolulu.
Chang, K.-A., Hsu, T.-J., and Liu, P. L.-F. (2001). “Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part I. Solitary waves.” Coast. Eng., 44(1), 13–36.
Evans, D. V., and Peter, M. A. (2011). “Asymptotic reflection of linear water waves by submerged horizontal porous plates.” J. Eng. Math., 69(2–3), 135–154.
Goring, D. G. (1978). “Tsunamis – The propagation of long waves onto a shelf.” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Graw, K.-U. (1993a). “Shore protection and electricity by submerged plate wave energy converter.” Proc., European Wave Energy Symp., National Engineering Laboratory Executive Agency, East Kilbride, Scotland, 379–384.
Graw, K.-U. (1993b). “The submerged plate wave energy converter–A new type of wave energy device.” Proc., Int. Symp. on Ocean Energy Development for Overcoming Energy and Environmental Crisis (ODEC), Int. Association for Hydraulic Research, Madrid, Spain, 1–4.
Graw, K.-U. (1996). “About the development of wave energy breakwaters.” Lacer No. 1, Leipzig Annual Civil Engineering Rep., Leipzig Univ., Leipzig, Germany.
Grimshaw, R. (1971). “The solitary wave in water of variable depth, Part 2.” J. Fluid Mech., 46(3), 611–622.
Ho, T.-C., Lin, C., and Hwang, K.-S. (2012). “Characteristics of shear layer and primary vortex induced by solitary waves propagating over rectangular structures with different Aspect Ratios.” J. Eng. Mech., 1084–1100.
Hsu, T.-J., Sakakiyama, T., and Liu, P. L.-F. (2002). “A numerical model for wave motions and turbulence flows in front of a composite breakwater.” Coast. Eng., 46(1), 25–50.
King, D. R., and LeBlond, P. H. (1982). “The lateral wave at a depth discontinuity in the ocean and its relevance to tsunami propagation.” J. Fluid Mech., 117, 269–282.
Kirby, J. T., and Dalrymple, R. A. (1983). “Propagation of obliquely incident water waves over a trench.” J. Fluid Mech., 133, 47–63.
Koraim, A. S. (2013). “Hydrodynamic efficiency of suspended horizontal rows of half pipes used as a new type breakwater.” Ocean Eng., 64, 1–22.
Lara, J. L., Losada, I. J., Maza, M., and Guanche, R. (2011). “Breaking solitary wave evolution over a porous underwater step.” Coast. Eng., 58(9), 837–850.
Lin, C., Chang, S.-C., Ho, T.-C., and Chang, K.-A. (2006). “Laboratory observation of solitary wave propagating over a submerged rectangular dike.” J. Eng. Mech., 545–554.
Lin, P. (1998). “Numerical modeling of breaking waves.” Ph.D. thesis, Cornell Univ., Ithaca, NY.
Lin, P., and Liu, P. L.-F. (1998). “A numerical study of breaking waves in the surf zone.” J. Fluid Mech., 359, 239–264.
Liu, C., Huang, Z., and Keat Tan, S. (2009). “Nonlinear scattering of non-breaking waves by a submerged horizontal plate: Experiments and simulations.” Ocean Eng., 36(17–18), 1332–1345.
Liu, P. L.-F. (1984). “Diffraction of solitary waves.” J. Waterway, Port, Coastal, Ocean Eng., 201–214.
Liu, P. L.-F., and Cheng, Y. (2001). “A numerical study of the evolution of a solitary wave over a shelf.” Phys. Fluids, 13, 1660–1667.
Liu, P. L.-F., Lin, P., Chang, K.-A., and Sakakiyama, T. (1999). “Numerical modelling of wave interaction with porous structures.” J. Waterway, Port, Coastal, Ocean Eng., 322–330.
Liu, Y., and Li, Y.-C. (2011). “An alternative analytical solution for water-wave motion over a submerged horizontal porous plate.” J. Eng. Math., 69(4), 385–400.
Losada, I. J., Lara, J. L., Guanche, R., and Gonzalez-Ondina, J. M. (2008). “Numerical analysis of wave overtopping of rubble mound breakwaters.” Coast. Eng., 55(1), 47–62.
Losada, M. A., Vidal, C., and Medina, R. (1989). “Experimental study of the evolution of a solitary wave at an abrupt junction.” J. Geophys. Res., 94(C10), 14557–14566.
Mahmood-Ul-Hassan, Meylan, M. H., and Peter, M. A. (2009). “Water-wave scattering by submerged elastic plates.” Q. J. Mech. Appl. Math., 62(3), 321–344.
Miles, J. W. (1976). “Damping of weakly nonlinear shallow-water waves.” J. Fluid Mech., 76(2), 251–257.
Miles, J. W. (1982). “On surface-wave diffraction by a trench.” J. Fluid Mech., 115, 315–325.
Patarapanich, M. (1984a). “Forces and moment on a horizontal plate due to wave scattering.” Coast. Eng., 8(3), 279–301.
Patarapanich, M. (1984b). “Maximum and zero reflection from submerged plate.” J. Waterway, Port, Coastal, Ocean Eng., 171–181.
Patarapanich, M., and Cheong, H.-F. (1989). “Reflection and transmission characteristics of regular and random waves from a submerged horizontal plate.” Coast. Eng., 13(2), 161–182.
Poupardin, A., Perret, G., Pinon, G., Bourneton, N., Rivoalen, E., and Brossard, J. (2012). “Vortex kinematic around a submerged plate under water waves. Part I: Experimental analysis.” Eur. J. Mech. B Fluids, 34, 47–55.
Siew, P. F., and Hurley, D. G. (1977). “Long surface waves incident on a submerged horizontal plate.” J. Fluid Mech., 83(1), 141–151.
Williams, T. D., Meylan, M. H., and Peter, M. A. (2012). “The Wiener-Hopf and residue calculus solutions for a submerged semi-infinite elastic plate.” J. Eng. Math., 75(1), 81–106.
Wu, J., Wan, Z., and Fang, Y. (1998). “Wave reflection by a vertical wall with a horizontal submerged porous plate.” Ocean Eng., 25(9), 767–779.
Wu, Y.-T., Hsiao, S.-C., Huang, Z.-C., and Hwang, K.-S. (2012). “Propagation of solitary waves over a bottom-mounted barrier.” Coast. Eng., 62, 31–47.
Yu, X. (1990). “Study on wave transformation over submerged plate.” Ph.D. thesis, Univ. of Tokyo, Tokyo.
Yu, X. (2002). “Functional performance of a submerged and essentially horizontal plate for offshore wave control: A review.” Coast. Eng. J., 44(2), 127–147.
Yu, X., and Chwang, A. T. (1993). “Analysis of wave scattering by submerged circular disk.” J. Eng. Mech., 1804–1817.
Yu, X., and Dong, Z. (2001). “Direct computation of wave motion around submerged plates.” Proc., 29th Cong. Int. Assoc. Hydr. Res., Madrid, Spain, 14–21.
Zhang, S., and Williams, A. N. (1996). “Wave scattering by submerged elliptical disk.” J. Waterway, Port, Coastal, Ocean Eng., 38–45.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140 • Issue 3 • May 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 12, 2013
Accepted: Sep 6, 2013
Published online: Sep 9, 2013
Published in print: May 1, 2014
Discussion open until: Jul 24, 2014
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