Abstract
This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM (boundary element method) solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, C R and C T , respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower C R and C T . The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting C R and C T . The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen, H. B., Tsai, C. P., and Jeng, C. C., 2007. Wave transformation between submerged breakwater and seawall. Journal of Coastal Research, SI 50: 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.
Cho, Y. S., Lee, J. I., and Kim, Y. T., 2004. Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem. Ocean Engineering, 31 (10): 1325–1335.
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.
Koley, S., Behera, H., and Sahoo, T., 2014. Oblique wave trapping by porous structures near a wall. Journal of Engineering Mechanics, 141 (3): 04014122.
Koraim, A. S., Heikal, E. M., and Zaid, A. A., 2014. Hydrodynamic characteristics of porous seawall protected by submerged breakwater. Applied Ocean Research, 46: 1–14.
Lan, Y. J., Hsu, T. W., Lai, J. W., Chang, C. C., and Ting, C. H., 2011. Bragg scattering of waves propagating over a series of poro-elastic submerged breakwaters. Wave Motion, 48 (1): 1–12.
Lee, J. F., Tu, L. F., and Liu, C. C., 2014. Nonlinear wave evolution above rectangular submerged structures. Journal of Marine Science and Technology, 22 (5): 531–541.
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.
Liu, Y., Li, H. J., and Zhu, L., 2016. Bragg reflection of water waves by multiple submerged semi-circular breakwaters. Applied Ocean Research, 56: 67–78.
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.
Muni-Reddy, M. G., and Neelamani, S., 2006. Wave interaction with caisson defenced by an offshore low-crested breakwater. Journal of Coastal Research, SI 39: 1767–1770.
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.
Sollitt, C. K., and Cross, R. H., 1972. Wave transmission through permeable breakwaters. Coastal Engineering Proceedings, 1 (13): 1827–1846.
Tsai, C. P., Yu, C. H., Chen, H. B., and Chen, H. Y., 2012. Wave height transformation and set-up between a submerged permeable breakwater and a seawall. China Ocean Engineering, 26: 167–176.
Twu, S. W., and Liu, C. C., 2004. Interaction of non-breaking regular waves with a periodic array of artificial porous bars. Coastal Engineering, 51 (3): 223–236.
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.
Yueh, C. Y., and Chuang, S. H., 2009. The reflection of normal incident waves by absorbing-type breakwaters. China Ocean Engineering, 23 (4): 729–740.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 51490675, 51322903 and 51279224.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, Y., Liu, Y., Li, H. et al. Oblique wave motion over multiple submerged porous bars near a vertical wall. J. Ocean Univ. China 16, 568–574 (2017). https://doi.org/10.1007/s11802-017-3333-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11802-017-3333-5