Solitary Wave Interacting with a Submerged Circular Plate
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147, Issue 1
Abstract
The interaction between a solitary wave and a submerged circular plate of a finite thickness was investigated in this study. Analytical solutions based on the linear long wave theory were first derived to serve as the leading-order predictive tool for this physical process. While the analytical solutions provide an easy way to calculate the wave field, they are limited by the simplifying assumptions. To complement the analytical solutions, a 3D Navier–Stokes equation solver with the large eddy simulation turbulence model was employed. The numerical model was verified against the analytical solutions for nearly linear cases and then applied to study more nonlinear cases in which the analytical solutions were less accurate. Both the analytical solutions and the numerical results show that wave focusing occurs near the lee side of the circular plate, creating higher local wave heights than that of the incident wave. As the wave passes over the submerged plate, the plate experiences an uplifting net force, followed by a net force in the downward direction, and then an uplifting net force again. The flow and pressure fields and vortices were also examined. By presenting the analytical and numerical tools that can be used to study this problem, and discussing the overall physics of this process, it is hoped that this study paves the way for future studies on this subject.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
P. L.-F. Liu would like to acknowledge the supports received from Cornell University, National University of Singapore, and the National Research Foundation (NRF) in Singapore.
Data Availability Statement
Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions (e.g., anonymized data). List items and restrictions: (1) SPLASH3D model is used to carry out all simulation in this study. The source code of this in-house SPLASH3D model with the LES module cannot be provided. However, the predecessor of SPLASH3D, Truchas, developed at Los Alamos National Laboratory, United States, is an open-source code. The latest released version of Truchas can be downloaded from https://github.com/truchas/truchas-release. (2) Results of analytical solutions and numerical modeling were plotted using MATLAB 2015b. These data can be provided in MATLAB format if required in the review. (3) All figures in this study are plotted by using MATLAB 2015b. These codes can be provided if required in the review.
References
Bradner, C., T. Schumacher, D. Cox, and C. Higgins. 2011. “Experimental setup for a large-scale bridge superstructure model subjected to waves.” J. Waterway, Port, Coastal, Ocean Eng. 137 (1): 3–11. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000059.
Bricker, J. D., and A. Nakayama. 2014. “Contribution of trapped air, deck superelevation, and nearby structures to bridge deck failure during a tsunami.” J. Hydraul. Eng. 140 (5): 05014002. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000855.
Chang, C. W., P. L. F. Liu, C. C. Mei, and M. Maza. 2017. “Modeling transient long waves propagating through a heterogeneous coastal forest of arbitrary shape.” Coastal Eng. 122: 124–140. https://doi.org/10.1016/j.coastaleng.2017.01.010.
Cheng, Y., C. Ji, Z. Ma, G. Zhai, and G. Oleg. 2017. “Numerical and experimental investigation of nonlinear focused waves–current interaction with a submerged plate.” Ocean Eng. 135: 11–27. https://doi.org/10.1016/j.oceaneng.2017.02.038.
Chu, C. R., C. H. Chung, T. R. Wu, and C. Y. Wang. 2016. “Numerical analysis of free surface flow over a submerged rectangular bridge deck.” J. Hydraul. Eng. 142 (12): 04016060. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001177.
Francois, M. M., S. J. Cummins, E. D. Dendy, D. B. Kothe, J. M. Sicilian, and M. W. Williams. 2006. “A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework.” J. Comput. Phys. 213 (1): 141–173. https://doi.org/10.1016/j.jcp.2005.08.004.
Guo, A., Q. Fang, and H. Li. 2015. “Analytical solution of hurricane wave forces acting on submerged bridge decks.” Ocean Eng. 108: 519–528. https://doi.org/10.1016/j.oceaneng.2015.08.018.
Hayatdavoodi, M., and R. C. Ertekin. 2015. “Nonlinear wave loads on a submerged deck by the Green–Naghdi equations.” J. Offshore Mech. Arct. Eng. 137 (1): 011102. https://doi.org/10.1115/1.4028997.
Hayatdavoodi, M., B. Seiffert, and R. C. Ertekin. 2014. “Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part II: Deck with girders.” Coastal Eng. 88: 210–228. https://doi.org/10.1016/j.coastaleng.2014.02.007.
Hayatdavoodi, M., B. Seiffert, and R. C. Ertekin. 2015. “Experiments and calculations of cnoidal wave loads on a flat plate in shallow-water.” J. Ocean Eng. Mar. Energy 1 (1): 77–99. https://doi.org/10.1007/s40722-014-0007-x.
Hirt, C. W., and B. D. Nichols. 1981. “Volume of fluid (VOF) method for the dynamics of free boundaries.” J. Comput. Phys. 39 (1): 201–225. https://doi.org/10.1016/0021-9991(81)90145-5.
Kojima, H., A. Yoshida, and T. Nakamura. 1994. “Linear and nonlinear wave forces exerted on a submerged horizontal plate.” Coastal Eng. Proc. 1 (24): 1312–1326. https://doi.org/10.9753/icce.v24.%p.
Lalli, F., A. Bruschi, L. Liberti, V. Pesarino, and P. Bassanini. 2012. “Analysis of linear and nonlinear features of a flat plate breakwater with the boundary element method.” J. Fluids Struct. 32: 146–158. https://doi.org/10.1016/j.jfluidstructs.2012.01.009.
Lin, H. X., D. Z. Ning, Q. P. Zou, B. Teng, and L. F. Chen. 2014. “Current effects on nonlinear wave scattering by a submerged plate.” J. Waterway, Port, Coastal, Ocean Eng. 140 (5): 04014016. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000256.
Liu, C., Z. Huang, and W. Chen. 2017. “A numerical study of a submerged horizontal heaving plate as a breakwater.” J. Coastal Res. 33 (4): 917–930. https://doi.org/10.2112/JCOASTRES-D-16-00152.1.
Liu, C., Z. Huang, and S. K. Tan. 2009. “Nonlinear scattering of non-breaking waves by a submerged horizontal plate: Experiments and simulations.” Ocean Eng. 36 (17–18): 1332–1345. https://doi.org/10.1016/j.oceaneng.2009.09.001.
Liu, P. L. F. 1984. “Diffraction of solitary waves.” J. Waterway, Port, Coastal, Ocean Eng. 110 (2): 201–214. https://doi.org/10.1061/(ASCE)0733-950X(1984)110:2(201).
Liu, P. L. F., and M. Iskandarani. 1991. “Scattering of short-wave groups by submerged horizontal plate.” J. Waterway, Port, Coastal, Ocean Eng. 117 (3): 235–246. https://doi.org/10.1061/(ASCE)0733-950X(1991)117:3(235).
Liu, P. L. F., T. R. Wu, F. Raichlen, C. E. Synolakis, and J. C. Borrero. 2005. “Runup and rundown generated by three-dimensional sliding masses.” J. Fluid Mech. 536: 107–144. https://doi.org/10.1017/S0022112005004799.
Lo, H. Y., and P. L. F. Liu. 2013. “Solitary waves incident on a submerged horizontal plate.” J. Waterway, Port, Coastal, Ocean Eng. 140 (3): 04014009.
McIver, M. 1985. “Diffraction of water waves by a moored, horizontal, flat plate.” J. Eng. Math. 19 (4): 297–319. https://doi.org/10.1007/BF00042875.
Mei, C. C., M. Stiassnie, and D. K. P. Yue. 2005. Vol. 23 of Theory and applications of ocean surface waves. Singapore: World Scientific.
Miles, J. W. 1976. “Damping of weakly nonlinear shallow-water waves.” J. Fluid Mech. 76 (2): 251–257. https://doi.org/10.1017/S002211207600061X.
Mo, W., K. Irschik, H. Oumeraci, and P. L. F. Liu. 2007. “A 3D numerical model for computing non-breaking wave forces on slender piles.” J. Eng. Math. 58 (1-4): 19–30. https://doi.org/10.1007/s10665-006-9094-6.
Mo, W., A. Jensen, and P. L. F. Liu. 2013. “Plunging solitary wave and its interaction with a slender cylinder on a sloping beach.” Ocean Eng. 74 (7): 48–60. https://doi.org/10.1016/j.oceaneng.2013.09.011.
Mo, W. H. 2010. “Numerical investigation of solitary wave interaction with group of cylinders.” Ph.D. thesis, Graduate School of Civil and Environmental Engineering, Cornell Univ.
Morison, J. R., J. W. Johnson, and S. A. Schaaf. 1950. “The force exerted by surface waves on piles.” J. Pet. Technol. 2 (05): 149–154. https://doi.org/10.2118/950149-G.
Ning, D., L. Chen, H. Lin, Q. Zou, and B. Teng. 2019. “Interaction mechanisms among waves, currents and a submerged plate.” Appl. Ocean Res. 91: 101911. https://doi.org/10.1016/j.apor.2019.101911.
Patarapanich, M. 1984. “Forces and moment on a horizontal plate due to wave scattering.” Coastal Eng. 8 (3): 279–301. https://doi.org/10.1016/0378-3839(84)90006-1.
Rey, V., and J. Touboul. 2011. “Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current.” Appl. Ocean Res. 33 (2): 88–99. https://doi.org/10.1016/j.apor.2011.02.002.
Rider, W. J., and D. B. Kothe. 1998. “Reconstructing volume tracking.” J. Comput. Phys. 141 (2): 112–152. https://doi.org/10.1006/jcph.1998.5906.
Seiffert, B., M. Hayatdavoodi, and R. C. Ertekin. 2014. “Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part I: Flat plate.” Coastal Eng. 88: 194–209. https://doi.org/10.1016/j.coastaleng.2014.01.005.
Siew, P. F., and D. G. Hurley. 1977. “Long surface waves incident on a submerged horizontal plate.” J. Fluid Mech. 83 (1): 141–151. https://doi.org/10.1017/S0022112077001098.
Smagorinsky, J. 1963. “General circulation experiments with the primitive equations. I: The basic experiment.” Mon. Weather Rev. 91 (3): 99–164. https://doi.org/10.1175/1520-0493(1963)091%3C0099:GCEWTP%26gt;2.3.CO;2.
Telluride Team. 2003. Truchas: Physics and algorithms. Technical Rep. LA-UR-03-0166. Los Alamos, NM: Los Alamos National Laboratory.
Wroniszewski, P. A., J. C. Verschaeve, and G. K. Pedersen. 2014. “Benchmarking of Navier–Stokes codes for free surface simulations by means of a solitary wave.” Coastal Eng. 91: 1–17. https://doi.org/10.1016/j.coastaleng.2014.04.012.
Wu, T. R., C. R. Chu, C. J. Huang, C. Y. Wang, S. Y. Chien, and M. Z. Chen. 2014. “A two-way coupled simulation of moving solids in free-surface flows.” Comput. Fluids 100: 347–355. https://doi.org/10.1016/j.compfluid.2014.05.010.
Yu, X. 2002. “Functional performance of a submerged and essentially horizontal plate for offshore wave control: A review.” Coastal Eng. J. 44 (02): 127–147. https://doi.org/10.1142/S0578563402000470.
Yu, X., and A. T. Chwang. 1993. “Analysis of wave scattering by submerged circular disk.” J. Eng. Mech. 119 (9): 1804–1817. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:9(1804).
Zarruk, G. A., E. A. Cowen, T. R. Wu, and P. F. Liu. 2015. “Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure.” J. Fluids Struct. 52: 181–198. https://doi.org/10.1016/j.jfluidstructs.2014.11.001.
Zhang, S., and A. N. Williams. 1996. “Wave scattering by submerged elliptical disk.” J. Waterway, Port, Coastal, Ocean Eng. 122 (1): 38–45. https://doi.org/10.1061/(ASCE)0733-950X(1996)122:1(38).
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jul 15, 2019
Accepted: Jun 10, 2020
Published online: Sep 23, 2020
Published in print: Jan 1, 2021
Discussion open until: Feb 23, 2021
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.