Abstract
This study gives an analytical solution for wave interaction with a partially reflecting vertical wall protected by a submerged porous bar based on linear potential theory. The whole study domain is divided into multiple sub-regions in relation to the structures. The velocity potential in each sub-region is written as a series solution by the separation of variables. A partially reflecting boundary condition is used to describe the partial reflection of a vertical wall. Unknown expansion coefficients in the series solutions are determined by matching velocity potentials among different sub-regions. The analytical solution is verified by an independently developed multi-domain boundary element method (BEM) solution and experimental data. The wave run-up and wave force on the partially reflecting vertical wall are estimated and examined, which can be effectively reduced by the submerged porous bar. The horizontal space between the vertical wall and the submerged porous bar is a key factor, which affects the sheltering function of the porous bar. The wave resonance between the porous bar and the vertical wall may disappear when the vertical wall has a low reflection coefficient. The present analytical solution may be used to determine the optimum parameters of structures at a preliminary engineering design stage.
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References
Chen, H. B., Tsai, C. P., and Jeng, C. C., 2007. Wave transformation between submerged breakwater and seawall. Journal of Coastal Research, 23 (1): 1069–1074.
Cheng, Y. Z., Jiang, C. B., and Wang, Y. Y., 2009. A coupled numerical model of wave interaction with porous medium. Ocean Engineering, 36 (12): 952–959.
Das, S., and Bora, S. N., 2014. Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom. Applied Ocean Research, 47: 373–385.
Elchahal, G., Younes, R., and Lafon, P., 2008. The effects of reflection coefficient of the harbour sidewall on the performance of floating breakwaters. Ocean Engineering, 35 (11): 1102–1112.
Goda, Y., 2010. Random Seas and Design of Maritime Structures. World Scientific Publishing Company, 732pp.
Huang, Z., Li, Y., and Liu, Y., 2011. Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review. Ocean Engineering, 38 (10): 1031–1053.
Isaacson, M., and Qu, S., 1990. Waves in a harbour with partially reflecting boundaries. Coastal Engineering, 14 (3): 193–214.
Jeng, D. S., Schacht, C., and Lemckert, C., 2005. Experimental study on ocean waves propagating over a submerged breakwater in front of a vertical seawall. Ocean Engineering, 32 (17): 2231–2240.
Jiang, C. B., Cheng, Y. Z., Chang, L. H., and Xia, B., 2012. The numerical study of wave-induced pore water pressure response in highly permeable seabed. Acta Oceanologica Sinica, 31 (6): 46–55.
Koley, S., Behera, H., and Sahoo, T., 2014. Oblique wave trapping by porous structures near a wall. Journal of Engineering Mechanics, DOI: 10.1061/(ASCE)EM.1943-7889.0000843.
Lee, J. I., and Shin, S. W., 2014. Experimental study on the wave reflection of partially perforated wall caisson with single and double chambers. Ocean Engineering, 91: 1–10.
Li, Z., and Huang, X., 1996. Wave Interaction with submerged porous structures. Proceedings of the 17th Ocean Engineering Conference, Taiwan, 273–280 (in Chinese with English abstract).
Liu, Y., Li, H. J., and Li, Y. C., 2012. A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness. Ocean Engineering, 42: 83–92.
Losada, I. J., Silva, R., and Losada, M. A., 1996. 3-D nonbreaking regular wave interaction with submerged breakwaters. Coastal Engineering, 28 (1): 229–248.
Mendez, F. J., and Losada, I. J., 2004. A perturbation method to solve dispersion equations for water waves over dissipative media. Coastal Engineering, 51: 81–89.
Pérez-Romero, D. M., Ortega-Sánchez, M., Moñino, A., and Losada, M. A., 2009. Characteristic friction coefficient and scale effects in oscillatory porous flow. Coastal Engineering, 56 (9): 931–939.
Reddy, M. G., and Neelamani, S., 2005. Hydrodynamic studies on vertical seawall defenced by low-crested breakwater. Ocean Engineering, 32 (5): 747–764.
Sollitt, C. K., and Cross, R. H., 1972. Wave transmission through permeable breakwaters. Proceedings of the 13th Coastal Engineering Conference, Vancouver, 1827–1846.
Wu, Y. T., Yeh, C. L., and Hsiao, S. C., 2014. Three-dimensional numerical simulation on the interaction of solitary waves and porous breakwaters. Coastal Engineering, 85: 12–29.
Yu, X., and Chwang, A. T., 1994. Wave motion through porous structures. Journal of Engineering Mechanics, 120 (5): 989–1008.
Zheng, Y. H., Shen, Y. M., and Tang, J., 2007. Radiation and diffraction of linear water waves by an infinitely long submerged rectangular structure parallel to a vertical wall. Ocean Engineering, 34 (1): 69–82.
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Zhao, Y., Liu, Y. & Li, H. Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar. J. Ocean Univ. China 15, 619–626 (2016). https://doi.org/10.1007/s11802-016-2837-8
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DOI: https://doi.org/10.1007/s11802-016-2837-8