Study of wave reflection by the Bragg breakwater with rectangular bars on the permeable seabed

Ni Yunlin; Gong Qian; Shen Mengjia

doi:10.12284/hyxb2022103

Volume 44 Issue 9

Aug. 2022

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Ni Yunlin，Gong Qian，Shen Mengjia. Study of wave reflection by the Bragg breakwater with rectangular bars on the permeable seabed[J]. Haiyang Xuebao，2022, 44(9)：124–131 doi: 10.12284/hyxb2022103

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Study of wave reflection by the Bragg breakwater with rectangular bars on the permeable seabed

doi: 10.12284/hyxb2022103

College of Marine Engineering Equipment, Zhejiang Ocean University, Zhoushan 316022, China

Received Date: 2021-10-18
Rev Recd Date: 2022-03-03

Available Online: 2022-04-15

Publish Date: 2022-08-29

Abstract

Abstract

Wave energy attenuation will occur when waves propagating over the permeable seabed, compared with the impermeable seabed. Base on the 1D modified mild slope equation for waves propagating on the permeable seabed, the finite difference model will be set up. The accuracy and applicability of the model will be verified with analytical solution for wave reflection by the rectangular Bragg breakwaters on the impermeable seabed. Furthermore, in case of a permeable seabed, the effects of the sea permeability, the bar width, the bar number and the submergence of the bars on wave reflection coefficient, as well as the difference with the case of an impermeable seabed, will be studied in details. The results show the reflection coefficient of the Bragg resonant reflection increases with the increase in the bar number, and decreases with the increase in the sea permeability and the submergence of the bars. Moreover, there exists a particular value of the bar width that maximizes the Bragg resonant reflection. Compared with the impermeable seabed, the incident wave frequency almost keep the same when Bragg resonance reflection happens, but the reflection coefficient is smaller and zero reflection or full transmission will not exit.
- permeable seabed,
- rectangular Bragg breakwater,
- Bragg resonant reflection,
- modified mild slope equation,
- finite difference method

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References(26)

References

[1]	Bragg W H, Bragg W L. The reflection of X-rays by crystals[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1913, 88(605): 428−438.
[2]	Davies A G. The reflection of wave energy by undulations on the seabed[J]. Dynamics of Atmospheres and Oceans, 1982, 6(4): 207−232. doi: 10.1016/0377-0265(82)90029-X
[3]	Mei C C, Hara T, Naciri M. Note on Bragg scattering of water waves by parallel bars on the seabed[J]. Journal of Fluid Mechanics, 1988, 186: 147−162. doi: 10.1017/S0022112088000084
[4]	Hsu T W, Chang H K, Tsai L H. Bragg reflection of waves by different shapes of artificial bars[J]. China Ocean Engineering, 2002, 16(3): 343−358.
[5]	蔡立宏. 波浪通过系列潜堤之布拉格反射研究[D]. 台南: 台湾成功大学, 2003. Cai Lihong. Study on Bragg reflection of waves passing through a series of submerged breakwaters[D]. Tainan: Cheng Kung University, 2003.
[6]	Wen C C, Tsai L H. Numerical simulation of Bragg reflection based on linear waves propagation over a series of rectangular seabed[J]. China Ocean Engineering, 2008, 22(1): 71−86.
[7]	江鸣. 波浪通过系列矩形潜堤的数值模拟[D]. 天津: 天津大学, 2012. Jiang Ming. Numerical simulation of wave propagation over a series of submerged rectangular dikes[D]. Tianjin: Tianjin University, 2012.
[8]	Liu Huanwen, Shi Yunping, Cao Dunqian. Optimization of parabolic bars for maximum Bragg resonant reflection of long waves[J]. Journal of Hydrodynamics, 2015, 27(3): 373−382. doi: 10.1016/S1001-6058(15)60495-4
[9]	Liu Huanwen, Zeng Huidan, Huang Huidong. Bragg resonant reflection of surface waves from deep water to shallow water by a finite array of trapezoidal bars[J]. Applied Ocean Research, 2020, 94: 101976. doi: 10.1016/j.apor.2019.101976
[10]	Liu Huanwen, Luo Heng, Zeng Huidan. Optimal collocation of three kinds of Bragg breakwaters for Bragg resonant reflection by long waves[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2015, 141(3): 04014039. doi: 10.1061/(ASCE)WW.1943-5460.0000278
[11]	曾慧丹. 全波谱条件下三类布拉格防波堤的最优配置[D]. 南宁: 广西民族大学, 2014. Zeng Huidan. Optimal collocation of Bragg breakwaters for Bragg resonance by water waves in the whole wave range[D]. Nanning: Guangxi University for Nationalities, 2014.
[12]	曾慧丹, 刘焕文, 唐国吉. 矩形Bragg防波堤引起线性长波共振反射的最优配置[C]//第十六届中国海洋(岸)工程学术讨论会论文集 . 北京: 海洋出版社, 2013: 663-672. Zeng Huidan, Liu Huanwen, Tang Guoji. Optimal configuration of linear long waves resonance reflection induced by rectangular Bragg breakwater[C]//Proceedings of the Sixteenth Chinese Symposium on Marine (Coastal) Engineering (Volume I). Beijing: China Ocean Press, 2013: 663−672.
[13]	Dean R G, Dalrymple R A. Water Wave Mechanics for Engineers and Scientists[M]. Singapore: World Scientific, 1984: 353.
[14]	Mendez F J, Losada I J. A perturbation method to solve dispersion equations for water waves over dissipative media[J]. Coastal Engineering, 2004, 51(1): 81−89. doi: 10.1016/j.coastaleng.2003.12.007
[15]	Ni Yunlin, Teng Bin. Bragg resonant reflection of water waves by a Bragg breakwater with porous rectangular bars on a sloping permeable seabed[J]. Ocean Engineering, 2021, 235: 109333. doi: 10.1016/j.oceaneng.2021.109333
[16]	Ni Yunlin, Teng Bin. Bragg resonant reflection of water waves by a Bragg breakwater with porous trapezoidal bars on a sloping permeable seabed[J]. Applied Ocean Research, 2021, 114: 102770. doi: 10.1016/j.apor.2021.102770
[17]	Zeng Huidan, Qin Bin, Zhang Jinghua. Optimal collocation of Bragg breakwaters with rectangular bars on sloping seabed for Bragg resonant reflection by long waves[J]. Ocean Engineering, 2017, 130: 156−165. doi: 10.1016/j.oceaneng.2016.11.066
[18]	Savage R P, Fairchild J C. Laboratory study of wave energy losses by bottom friction and percolation[J]. Beach Erosion Board, 1953, 31: 1−25.
[19]	Mizutani N, Mostafa A M. Dynamic interaction of nonlinear waves and a seawall over sand seabed[J]. International Journal of Offshore and Polar Engineering, 1998, 8(1): 30−38.
[20]	周李杰. 烟台港抛石防波堤波浪动力响应的数值分析[D]. 武汉: 武汉理工大学, 2018. Zhou Lijie. Numerical analysis of wave-induced dynamics of a rubble mould breakwater at Yantai Port[D]. Wuhan: Wuhan University of Technology, 2018.
[21]	任玉宾, 王胤, 杨庆. 颗粒级配与形状对钙质砂渗透性的影响[J]. 岩土力学, 2018, 39(2): 491−497. Ren Yubin, Wang Yin, Yang Qing. Effects of particle size distribution and shape on permeability of calcareous sand[J]. Rock and Soil Mechanics, 2018, 39(2): 491−497.
[22]	倪云林, 章哲文, 唐志波, 等. 波浪在沙质海床上传播波长变化[J]. 水利水运工程学报, 2017(3): 51−55. Ni Yunlin, Zhang Zhewen, Tang Zhibo, et al. Changes in wavelength of wave propagation over a sandy seabed[J]. Hydro-Science and Engineering, 2017(3): 51−55.
[23]	王忠涛, 栾茂田, 郑东生. 多孔介质海床对波浪传播影响理论分析[J]. 大连理工大学学报, 2009, 49(6): 891−896. doi: 10.7511/dllgxb200906020 Wang Zhongtao, Luan Maotian, Zheng Dongsheng. Dynamic analysis for effects of porous seabed on wave propagation[J]. Journal of Dalian University of Technology, 2009, 49(6): 891−896. doi: 10.7511/dllgxb200906020
[24]	Guazzelli E, Rey V, Belzons M. Higher-order Bragg reflection of gravity surface waves by periodic beds[J]. Journal of Fluid Mechanics, 1992, 245: 301−317. doi: 10.1017/S0022112092000478
[25]	Liu Huanwen, Yang Jing, Lin Pengzhi. An analytic solution to the modified mild-slope equation for wave propagation over one-dimensional piecewise smooth topographies[J]. Wave Motion, 2012, 49(3): 445−460. doi: 10.1016/j.wavemoti.2012.01.002
[26]	Liu Huanwen, Li Xiaofeng, Lin Pengzhi. Analytical study of Bragg resonance by singly periodic sinusoidal ripples based on the modified mild-slope equation[J]. Coastal Engineering, 2019, 150: 121−134. doi: 10.1016/j.coastaleng.2019.04.015