固定于水面的多个半圆形结构物的水波Bragg反射
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摘要
基于线性波浪理论,应用边界元法(BEM)研究固定于静水面的多个半圆形结构物的水波Bragg反射现象.计算固定于海底的多个半圆形结构物的反射系数,并将计算结果与文献中的理论解进行比较,以验证BEM的正确性.计算并对比水面单个半圆形结构和多个半圆形结构的反射系数,以证明基于Bragg反射原理的多个结构物衰减波浪的有效性.进而分析多个半圆形结构物的个数、半径、间距等参数对Bragg反射特性的影响,研究结果可为基于Bragg反射原理的防波堤设计提供参考依据.
Bragg reflection of water waves by multiple semicircular structures fixed on the water surface is investigated by using the boundary element method(BEM). It is based on the linear wave theory. In order to verify the correctness of BEM, the reflection coefficient of multiple semicircular structures fixed on the seabed is calculated. And the numerical results are compared with the theoretical results in literature. The effectiveness of the multiple semicircular structures fixed on the water surface in attenuating waves based on the principle of Bragg reflection is also proved. The effects of the number, the radius and the spacing of semicircular structures on the characteristics of Bragg reflection are investigated. The results of this study can provide a certain reference for the design of breakwater based on the principle of Bragg reflection.
Bragg reflection of water waves by multiple semicircular structures fixed on the water surface is investigated by using the boundary element method(BEM). It is based on the linear wave theory. In order to verify the correctness of BEM, the reflection coefficient of multiple semicircular structures fixed on the seabed is calculated. And the numerical results are compared with the theoretical results in literature. The effectiveness of the multiple semicircular structures fixed on the water surface in attenuating waves based on the principle of Bragg reflection is also proved. The effects of the number, the radius and the spacing of semicircular structures on the characteristics of Bragg reflection are investigated. The results of this study can provide a certain reference for the design of breakwater based on the principle of Bragg reflection.
引文
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[12] DING W W,ZOU Z J,WU J P.Bragg reflection of water waves by multiple composite flexible membranes[J].International Journal of Offshore and Polar Engineering,2018,28(2):135-142.
[13] DING W W,ZOU Z J,WU J P.Characteristics of Bragg reflection of water waves by multiple vertical flexible membranes[C]//Proceedings of the ASME 37th International Conference on Ocean,Offshore and Arctic Engineering.Madrid,Spain:ASME,2018:V07AT06A036.
[14] OUYANG H T,CHEN K H,TSAI C M.Investigation on Bragg reflection of surface water waves induced by a train of fixed floating pontoon breakwaters[J].International Journal of Naval Architecture and Ocean Engineering,2015,7(6):951-963.
[15] BAILARD J A,DEVRIES J W,KIRBY J T.Considerations in using Bragg reflection for storm erosion protection[J].Journal of Waterway,Port,Coastal,and Ocean Engineering,1992,118(1):62-74.
[16] LIU P L-F,ABBASPOUR M.An integral equation method for the diffraction of oblique waves by an infinite cylinder[J].International Journal for Numerical Methods in Engineering,1982,18(10):1497-1504.
[17] LIU Y,LI H J,ZHU L.Bragg reflection of water waves by multiple submerged semi-circular breakwaters[J].Applied Ocean Research,2016,56:67-78.
[2] BRAGG W H,BRAGG W L.The reflection of X-rays by crystals[J].Proceedings of the Royal Society of London,1913,88(605):428-438.
[3] HEATHERSHAW A D.Seabed-wave resonance and sand bar growth[J].Nature,1982,296(5855):343-345.
[4] 刘焕文.沙坝及人工沙坝引起海洋表面波Bragg共振反射的研究进展[J].应用数学和力学,2016,37(5):459-471.LIU Huanwen.Advances in research on Bragg resonance of ocean surface waves by sandbars and artificial sandbars[J].Applied Mathematics and Mechanics,2016,37(5):459-471.
[5] CHOU T.Band structure of surface flexural-gravity waves along periodic interfaces[J].Journal of Fluid Mechanics,1998,369:333-350.
[6] BENNETTS L G,SQUIRE V A.Wave scattering by multiple rows of circular ice floes[J].Journal of Fluid Mechanics,2009,639:213-238.
[7] GARNAUD X,MEI C C.Bragg scattering and wave-power extraction by an array of small buoys[J].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2010,466(2113):79-106.
[8] LINTON C M.Water waves over arrays of horizontal cylinders:Band gaps and Bragg resonance[J].Journal of Fluid Mechanics,2011,670:504-526.
[9] KARMAKAR D,BHATTACHARJEE J,GUEDES SOARES C.Scattering of gravity waves by multiple surface-piercing floating membrane[J].Applied Ocean Research,2013,39:40-52.
[10] 许玲,吴静萍,丁伟伟,等.基于Bragg共振原理水面多重竖直板消浪性能实验研究[J].水动力学研究与进展,2016,31(4):449-453.XU Ling,WU Jingping,DING Weiwei,et al.Experimental study on the attenuating waves performance of multiple vertical plates based on Bragg resonance[J].Chinese Journal of Hydrodynamics,2016,31(4):449-453.
[11] WU J P,PAN J,DING W W,et al.Experimental studies on the transmission coefficients of multiple plates[C]//Proceedings of the Twenty-sixth International Ocean and Polar Engineering Conference.Rhodes,Greece:International Society of Offshore and Polar Engineers,2016:1395-1399.
[12] DING W W,ZOU Z J,WU J P.Bragg reflection of water waves by multiple composite flexible membranes[J].International Journal of Offshore and Polar Engineering,2018,28(2):135-142.
[13] DING W W,ZOU Z J,WU J P.Characteristics of Bragg reflection of water waves by multiple vertical flexible membranes[C]//Proceedings of the ASME 37th International Conference on Ocean,Offshore and Arctic Engineering.Madrid,Spain:ASME,2018:V07AT06A036.
[14] OUYANG H T,CHEN K H,TSAI C M.Investigation on Bragg reflection of surface water waves induced by a train of fixed floating pontoon breakwaters[J].International Journal of Naval Architecture and Ocean Engineering,2015,7(6):951-963.
[15] BAILARD J A,DEVRIES J W,KIRBY J T.Considerations in using Bragg reflection for storm erosion protection[J].Journal of Waterway,Port,Coastal,and Ocean Engineering,1992,118(1):62-74.
[16] LIU P L-F,ABBASPOUR M.An integral equation method for the diffraction of oblique waves by an infinite cylinder[J].International Journal for Numerical Methods in Engineering,1982,18(10):1497-1504.
[17] LIU Y,LI H J,ZHU L.Bragg reflection of water waves by multiple submerged semi-circular breakwaters[J].Applied Ocean Research,2016,56:67-78.