Diffraction of Solitary Waves by a Concentric Porous Dual-Arc Thin Wall
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 148, Issue 2
Abstract
Herein, a semianalytical model is presented for solitary wave diffraction by a surface-piercing concentric dual-arc thin wall. The two arc-shaped walls are porous and thin, and they are placed on a flat seafloor. As a key element, two imaginary closed cylindrical structures with two arc-shaped walls of different radii are introduced such that the entire computation domain can be partitioned into three subdomains, two bounded and one unbounded, based on common interfaces, within which the analytical solution is obtained using eigenfunction expression matching. Furthermore, a system of linear algebraic equations to determine the unknown coefficients is derived by satisfying the boundary and matching conditions. The numerical results obtained for the limiting cases are exactly the same as published results for a solid and porous cylindrical structure. Meanwhile, the effects of the wave incident angle, opening angle, annular spacing, and porous-effect parameter on wave loads and wave elevations are investigated. In addition, as a particular case, a concentric structure with an arc-shaped porous exterior wall is investigated as an alternative to the two-cylinder structure in practical engineering. It is discovered that the arc-shaped exterior wall can effectively reduce the wave force and wave height around the interior cylinder, compared with a single cylinder. By contrast, the wave forces and wave runup on the interior cylinder are similar to those of the interior cylinder of a concentric two-cylinder system.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was financially supported by the National Key Research and Development Program of China (grant no. 2019YFC0312400) and the Guangdong Basic and Applied Basic Research Foundation (grant no. 2020A1515110155).
References
Basmat, A. 2002. “Interaction of a solitary wave with a permeable cylindrical breakwater.” Proc. Appl. Math. Mech. 1 (1): 393–394. https://doi.org/10.1002/1617-7061(200203)1:1%3C393::AID-PAMM393%3E3.0.CO;2-W.
Cao, H. J., and D. C. Wan. 2015. “RANS-VOF solver for solitary wave run-up on a circular cylinder.” China Ocean Eng. 29 (2): 183–196. https://doi.org/10.1007/s13344-015-0014-2.
Chang, K. H., D. H. Tsaur, and L. H. Huang. 2012. “Accurate solution to diffraction around a modified V-shaped breakwater.” Coastal Eng. 68: 56–66. https://doi.org/10.1016/j.coastaleng.2012.05.002.
Cheng, J. S., G. P. Miao, and J. Q. Wang. 2007. “Analytical research on wave diffraction on arc-shaped bottom-mounted perforated breakwaters.” China Ocean Eng. 21 (3): 417–428.
Chu, Y. C., J. S. Cheng, J. Q. Wang, Z. G. Li, and K. B. Jiang. 2014. “Hydrodynamic performance of the arc-shaped bottom-mounted breakwater.” China Ocean Eng. 28 (6): 749–760. https://doi.org/10.1007/s13344-014-0058-8.
Chwang, A. T. 1983. “A porous-wavemaker theory.” J. Fluid Mech. 132: 395–406. https://doi.org/10.1017/S0022112083001676.
Chwang, A. T., and W. Li. 1983. “A piston-type porous wavemaker theory.” J. Eng. Math. 17 (4): 301–313. https://doi.org/10.1007/BF00040174.
Darwiche, M. K. M., A. N. Williams, and K. H. Wang. 1994. “Wave interaction with semiporous cylindrical breakwater.” J. Waterway, Port, Coastal, Ocean Eng. 120 (4): 382–403. https://doi.org/10.1061/(ASCE)0733-950X(1994)120:4(382).
Duan, J. H., J. S. Cheng, J. P. Wang, and J. Q. Wang. 2012. “Wave diffraction on arc-shaped floating perforated breakwaters.” China Ocean Eng. 26 (2): 305–316. https://doi.org/10.1007/s13344-012-0023-3.
Hafsia, Z., S. Nouri, S. M. Boulaaras, A. Allahem, S. Alkhalaf, and A. M. Vazquez. 2021. “Solitary wave diffraction with a single and two vertical circular cylinders.” Math. Probl. Eng. 2021 (6): 1–9. https://doi.org/10.1155/2021/6634762.
He, Y. K., W. Y. Ji, J. Ying, and B. Han. 2021. “Hydrodynamic performance of a continuous floating bridge with heave plates.” Appl. Ocean Res. 108: 102442. https://doi.org/10.1016/j.apor.2020.102442.
Isaacson, M. D. S. Q. 1983. “Solitary wave diffraction around large cylinder.” J. Waterway, Port, Coastal, Ocean Eng. 109 (1): 121–127. https://doi.org/10.1061/(ASCE)0733-950X(1983)109:1(121).
Ji, C. Y., Y. Cheng, K. Yang, and G. Oleg. 2017. “Numerical and experimental investigation of hydrodynamic performance of a cylindrical dual pontoon-net floating breakwater.” Coastal Eng. 129 (3): 1–16. https://doi.org/10.1016/j.coastaleng.2017.08.013.
Li, Y. C., L. Sun, and B. Teng. 2003. “Wave action on double-cylinder structure with perforated outer wall.” In Vol. 36819 of Proc., Int. Conf. on Offshore Mechanics and Arctic Engineering, 149–156. New York: ASME.
Linton, C. M., and D. V. Evans. 1990. “The interaction of waves with arrays of vertical circular cylinders.” J. Fluid Mech. 215 (1): 549–569. https://doi.org/10.1017/S0022112090002750.
Liu, H. X., L. Zhang, H. L. Chen, W. C. Zhang, and M. Liu. 2018a. “Wave diffraction by vertical cylinder with multiple concentric perforated walls.” Ocean Eng. 166 (1): 242–252. https://doi.org/10.1016/j.oceaneng.2018.08.025.
Liu, J., and G. Lin. 2013a. “Numerical modelling of wave interaction with a concentric cylindrical system with an arc-shaped porous outer cylinder.” Eur. J. Mech. B. Fluids 37: 59–71. https://doi.org/10.1016/j.euromechflu.2012.07.005.
Liu, J., and G. Lin. 2013b. “Scaled boundary FEM solution of short-crested wave interaction with a concentric structure with double-layer arc-shaped perforated cylinders.” Comput. Fluids 79 (486): 82–104. https://doi.org/10.1016/j.compfluid.2013.03.013.
Liu, J., G. Lin, and J. B. Li. 2012. “Short-crested waves interaction with a concentric cylindrical structure with double-layered perforated walls.” Ocean Eng. 40 (4): 76–90. https://doi.org/10.1016/j.oceaneng.2011.12.011.
Liu, J. B., A. X. Guo, N. A. K. Nandasena, B. W. Melville, and H. Li. 2018b. “Theoretical and experimental investigation on wave interaction with a concentric porous cylinder form of breakwater.” Ocean Eng. 160 (2–3): 156–167. https://doi.org/10.1016/j.oceaneng.2018.04.050.
Liu, Y., Y. C. Li, and B. Teng. 2007. “Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate.” Ocean Eng. 34 (17–18): 2364–2373. https://doi.org/10.1016/j.oceaneng.2007.05.002.
Lynett, P. J., P. L. F. Liu, I. J. Losada, and C. Vidal. 2000. “Solitary wave interaction with porous breakwaters.” J. Waterway, Port, Coastal, Ocean Eng. 126 (6): 314–322. https://doi.org/10.1061/(ASCE)0733-950X(2000)126:6(314).
Sankarbabu, K., S. A. Sannasiraj, and V. Sundar. 2008. “Interaction of solitary waves with a group of dual porous circular cylinders.” In Vol. 48180 of Proc., Int. Conf. on Offshore Mechanics and Arctic Engineering, 307–313. New York: ASME.
Sarkar, A., and S. N. Bora. 2020. “Hydrodynamic forces and moments due to interaction of linear water waves with truncated partial-porous cylinders in finite depth.” J. Fluids Struct. 94 (11): 102898. https://doi.org/10.1016/j.jfluidstructs.2020.102898.
Sharma, M., R. B. Kaligatla, and T. Sahoo. 2020. “Wave interaction with a submerged floating tunnel in the presence of a bottom mounted submerged porous breakwater.” Appl. Ocean Res. 96 (2): 102069. https://doi.org/10.1016/j.apor.2020.102069.
Song, H., and L. B. Tao. 2007. “Short-crested wave interaction with a concentric porous cylindrical structure.” Appl. Ocean Res. 29 (4): 199–209. https://doi.org/10.1016/j.apor.2008.01.001.
Tao, L. B., H. Song, and S. Chakrabarti. 2009. “Wave interaction with a perforated circular breakwater of non-uniform porosity.” J. Eng. Math. 65 (3): 257–271. https://doi.org/10.1007/s10665-009-9287-x.
Teng, B., L. Han, and Y. C. Li. 2000. “Ware diffraction from a vertical cylinder with two uniform columns and porous outer wall.” China Ocean Eng. 14: 297–306.
Teng, B., Y. C. Li, and L. Sun. 2001. “Wave interaction with a partial porous double-wall cylinder.” Eng. Sci. 3 (10): 41–47.
Vijayalakshmi, K., S. Neelamani, R. Sundaravadivelu, and K. Murali. 2007. “Wave runup on a concentric twin perforated circular cylinder.” Ocean Eng. 34 (2): 327–336. https://doi.org/10.1016/j.oceaneng.2005.11.021.
Wang, K., P. F. Shi, Y. C. Chen, and X. M. Cheng. 2019. “Study on submerged upper arc-shaped plate type breakwater.” China Ocean Eng. 33 (2): 219–225. https://doi.org/10.1007/s13344-019-0021-9.
Wang, K. H., and X. Ren. 1994. “Wave interaction with a concentric porous cylinder system.” Ocean Eng. 21 (4): 343–360. https://doi.org/10.1016/0029-8018(94)90009-4.
Weng, Y. L., X. N. Xu, and H. Huang. 2016. “Interaction of cnoidal waves with an array of vertical concentric porous cylinders.” Appl. Ocean Res. 58: 21–36. https://doi.org/10.1016/j.apor.2016.01.011.
Williams, A. N., and W. Li. 1998. “Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank.” Ocean Eng. 25 (2–3): 195–219. https://doi.org/10.1016/S0029-8018(97)00006-1.
Yu, X. P. 1995. “Diffraction of water waves by porous breakwaters.” J. Waterway, Port, Coastal, Ocean Eng. 121 (6): 275–282. https://doi.org/10.1061/(ASCE)0733-950X(1995)121:6(275).
Zhai, Z. F., Q. Hu, W. F. Ye, and H. Huang. 2021a. “Analytical modelling of solitary wave diffraction from a V-shaped breakwater.” Ocean Eng. 230 (3): 109014. https://doi.org/10.1016/j.oceaneng.2021.109014.
Zhai, Z. F., H. Huang, W. F. Ye, L. L. Yang, and S. Liu. 2020. “Hydrodynamic interactions between cnoidal waves and a concentric cylindrical structure with arc-shaped outer cylinder.” Ocean Eng. 209 (8): 107448. https://doi.org/10.1016/j.oceaneng.2020.107448.
Zhai, Z. F., Y. L. Shao, K. Wang, H. Huang, and H. Li. 2021b. “Semi-analytical solution of cnoidal wave diffraction around a double-layer arc-shaped vertical porous breakwater.” J. Fluids Struct. 103 (1): 103261. https://doi.org/10.1016/j.jfluidstructs.2021.103261.
Zheng, S. M., R. Porter, and D. Greaves. 2020. “Wave scattering by an array of metamaterial cylinders.” J. Fluid Mech. 903: 478. https://doi.org/10.1017/jfm.2020.660.
Zhong, Z., and K. H. Wang. 2006. “Solitary wave interaction with a concentric porous cylinder system.” Ocean Eng. 33 (7): 927–949. https://doi.org/10.1016/j.oceaneng.2005.05.013.
Zhu, D. T. 2011. “Wave run-up on a coaxial perforated circular cylinder.” China Ocean Eng. 25 (2): 201–214. https://doi.org/10.1007/s13344-011-0018-5.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 148 • Issue 2 • March 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 7, 2021
Accepted: Nov 12, 2021
Published online: Jan 12, 2022
Published in print: Mar 1, 2022
Discussion open until: Jun 12, 2022
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.
Cited by
- Jianming Miao, Dan Liu, Jie Li, Zhenfeng Zhai, Short-Crested Wave–Current Forces on a Concentric System with an ARC Exterior Porous Wall, Journal of Marine Science and Engineering, 10.3390/jmse11030573, 11, 3, (573), (2023).