Study of wave reflection by the Bragg breakwater with rectangular bars on the permeable seabed
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摘要: 与海床不可渗透的情况相比,波浪在可渗透海床上传播时会发生波能衰减。本文将基于可渗透海床上一维修正型缓坡方程,建立方程求解的有限差分模型。将通过与不可渗透海床上矩形Bragg防波堤对波浪反射系数解析解的对比,验证有限差分模型的正确性和适用性。将进一步研究海床可渗透情况下,海床的渗透性参数、坝体的相对宽度、数量、浸没度对波浪反射系数的影响及其与海床不可渗透情况下的差异。本文研究发现,Bragg共振发生时的反射系数随坝体数量的增多而增大,随海床渗透性参数和坝体浸没度的增大而减小,并且存在一个坝体相对宽度值会使Bragg共振反射达到最大。相较于海床不可渗透的情况,发生Bragg共振反射的波浪频率几乎相同,但反射系数减小,而且零反射(或全透射)现象不再存在。
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关键词:
- 渗透海床 /
- 矩形Bragg防波堤 /
- Bragg共振反射 /
- 修正型缓坡方程 /
- 有限差分法
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. -
表 1 不同多孔介质的渗透性参数T取值
Tab. 1 Values of the permeability parameter T for different porous media
表 2 海床不同渗透性参数下Bragg共振反射的特征值
Tab. 2 Eigenvalues of Bragg resonance reflection under different permeability of seabed
坝体数量(N) 渗透性参数(T)/s 入射波相对波长(2d/L) 反射系数(KR) 3 0 0.919 0.416 0.005 0.919 0.403 0.010 0.919 0.391 0.030 0.919 0.347 4 0 0.919 0.526 0.005 0.919 0.504 0.010 0.919 0.484 0.030 0.919 0.415 表 3 不同坝体浸没度情况下Bragg共振反射的特征值
Tab. 3 Characteristic values of Bragg resonance reflection under different bar submergence
渗透性参数
(T)/s坝体浸没度
(S)入射波相对波长
(2d/L)反射系数
(KR)0 0.5 0.909 0.860 0.625 1.056 0.651 0.75 1.225 0.416 0.875 1.373 0.201 0.005 0.5 0.909 0.842 0.625 1.056 0.634 0.75 1.225 0.403 0.875 1.373 0.195 -
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