本文探討波浪通過系列潛堤發生布拉格反射效應。理論解析方面以Miles (1981) 的理論為基礎，推導不同系列潛堤佈置的反射率；數值模式則以Zhang等人 (1999) 混合模式為基礎所發展演進型式緩坡方程式(Evolution Equation for Mild-Slope Equation，EEMSE)，模擬波浪通過系列潛堤的布拉格反射。此外，本文進行一系列水工模型試驗，利用試驗結果驗證理論及數值模式計算值。
數值計算結果顯示，在不同波浪入射作用下，各種系列潛堤佈置之反射率變化及布拉格反射趨勢與試驗結果相當一致。以Miles (1981) 的理論為基礎解析值，雖能表現布拉格反射現象及反射率變化趨勢，但因忽略底床變動所造成波速及群波波速變化的影響，在相對堤高較大情況，與試驗結果產生較大誤差，且無法表現反射率尖峰值向低頻平移的現象。
本文針對波浪通過系列潛堤之影響參數進行有系統的探討，包括潛堤高度、潛堤寬度、潛堤長度、潛堤個數、潛堤間距、潛堤間距比、底床坡度、入射水深、入射角度以及波浪週期等。等間距系列潛堤佈置之情況，數值計算與試驗分析結果均發現布拉格反射現象發生在波長為2倍堤距附近，與前人之研究結果一致。本文發展不等潛堤間距的複合式系列潛堤，能增加布拉格反射帶寬，改進等間距系列潛堤波浪頻率受限缺點。布拉格反射強度隨潛堤堤高、堤長、堤數、堤距、底床坡度等增加及入射角愈小而遞增；反射率帶寬及發生反射率尖峰值平移量，則隨潛堤高度、底床坡度的增加及堤數與堤距的減少與碎波發生而增大。以試驗值迴歸之經驗公式，提供代表布拉格反射的參數與各影響因子間的量化關係。

Hydraulic experiments, theory, and numerical model are carried out to study the Bragg reflection for monochromatic waves over a series of submerged breakwaters. Based on Miles’ (1981) theory, the wave reflection coefficient induced by the Bragg scattering for wave propagation over various shapes of multiply composite series submerged breakwaters is first derived. An Evolution Equation for Mild-Slope Equation (EEMSE) is developed on the basis of Hybrid Model (HM) addressed by Zhang et al. (1999) in which the higher-order terms neglected in the mild-slope equation are retained for steep undulate beds. Numerical computation and theoretical results are fairly good compared with experimental results.
By adding the forcing factors, such as bottom slope, bottom curvature, rapidly varying component as well as energy dissipation due to wave breaking into the mild-slope equation, the present is able to solve shoaling, refraction, diffraction, reflection, breaking and energy dissipation phenomena for waves passing over bottom undulation. Miles’ (1981) theoretical solution can demonstrate the tendency of the Bragg reflection and reflection coefficient. But, due to neglecting the influence of wave celerity and group velocity producing by bottom undulation, the discrepancy between theoretical and experimental results becomes larger. It is found that Miles’ theory is unable to predict the shift phenomenon of peak reflection coefficient for larger relative height of breakwaters.
Systematic studies for wave propagating over series submerged breakwaters are conducted. Both numerical calculation and laboratory test results indicate that waves propagate over different combinations of series breakwaters, the Bragg reflection occurs in vicinity of two time of breakwater spacing equal to wave length. The bandwidth of reflection coefficient for the Bragg reflection is increased by unequal spacing of multiply series submerged breakwaters. The density of the Bragg reflection increases with the increase of height, length, number, spacing and bottom slope of submerged breakwaters as well as the decrease of incident angle. The bandwidth and the shift value of the reflection coefficient depend on the height of breakwater and bottom slope. Key features of Bragg reflection influenced by forcing parameters are analyzed with the experimental data, including the peak reflection coefficient of primary harmonic, its corresponding relative breakwater spacing and the bandwidth of in primary harmonic reflection. A regression equation is proposed based on experimental data. Based on the results of the analysis empirical equations are established.

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