以水槽實驗研究波浪經過直立式薄型結構物與布拉格 散射之關係

Abstract

陣列式海洋結構物與單一結構物在波浪反射行為上存在本質差異，前者會在相鄰結構間引發波浪之干涉作用。透過調整結構物間距，可放大或削弱反射波之強度，此由週期性結構所導致之干涉現象即為布拉格散射（Bragg scattering）。當結構間距B 約為入射波波長L 的一半，即B/L ≈ (2n)/4, n = 1, 2, . . . 時，反射波會產生共振性增強，稱為布拉格共振；當B/L ≈ (2n + 1)/4, n = 0, 1, . . . 時則出現破壞性干涉，導致反射波強度顯著下降。雖然傳統布拉格共振與干涉條件的經典理論已能對上述行為提供合理解釋與預測，然而在現有的研究中，多數情況下反射波的極值往往並未剛好出現在上述預測的B/L 下，且相關實驗數據多半零散、品質不一。為釐清上述問題，本研究選用最簡化之結構形式「直立式薄型結構物」作為研究對象，其厚度極薄，可視為數學模型中之零厚度邊界。本文首先基於線性勢流理論，推導週期波通過單層與雙層結構物陣列的理論解析解；為驗證線性理論結果，進一步於二維水槽中進行實驗觀測。實驗中使用超音波感測器搭配Goda 兩點法求得反射係數Cr 與透射係數Ct；同時使用粒子影像測速法（PIV）觀測流場分佈與渦度變化。結果顯示，Cr 的極值位置皆較傳統布拉格散射預測略偏低頻，此現象不僅出現在線性理論推導中，亦於實驗中反覆觀察，顯示此偏移現象具有一定普遍性。此外，在相對潛沒深度d/h 較淺或較接近淺水波條件時，實驗中觀察到強烈局部渦旋，導致實測流場結果與線性理論預測產生明顯偏差；但在d/h 較深情況下，線性勢流理論模型能合理捕捉流場行為與反射特性。整體而言，本研究從理論與實驗雙重角度探討潛沒式結構物的布拉格干涉行為與共振特性，並觀察共振位置偏移與渦流影響。

Multiple marine structures exhibit fundamentally different wave reflection behaviors compared to single structures, the former induces wave interference between adjacent elements. By adjusting the spacing between structures, the intensity of reflected waves can be either amplified or reduced. This interference phenomenon, caused by periodic structures, is known as Bragg scattering. When the structural spacing B is approximately half the incident wavelength L, i.e., B/L ≈ 2n/4, n = 1, 2, . . . , a resonant enhancement of reflection, termed Bragg resonance, occurs. Conversely, when B/L ≈ (2n + 1)/4, n = 0, 1, . . . , destructive interference arises, leading to significantly reduced reflection. Although classical Bragg theory provides reasonable explanations and predictions for such behavior, existing studies have shown that the peak and trough positions of the reflection coefficient often do not align exactly with the predicted B/L ratios. Furthermore, relevant experimental data are frequently scattered and inconsistent in quality. To clarify these issues, this study investigates the simplified case of vertical thin plate, idealized as zero-thickness boundaries in the mathematical model. Theoretical solutions based on linear potential flow theory are first derived for periodic waves interacting with single-barrier and double-barrier arrays. To validate these solutions, experiments are conducted in a 2D wave flume. In the experiments, ultrasonic wave gauges are employed in combination with the Goda method to calculate the reflection coefficient Cr and transmission coefficient Ct. Simultaneously, Particle Image Velocimetry (PIV) technique is used to observe flow field distributions and vorticity evolution. Results indicate that the peak positions of Cr are consistently shifted toward lower frequencies compared to classical Bragg predictions. This deviation is observed not only in theoretical predictions but also repeatedly confirmed in experiments, suggesting its generality. Moreover, under shallow relative submergence depths (d/h) or shallower water wave conditions, strong local vortices are observed, resulting in noticeable discrepancies between measured and theoretical flow fields. However, for deeper submergence conditions, the linear potential model adequately captures both flow field behavior and wave reflection characteristics. Overall, this study investigates the Bragg interference and resonance behavior of submerged vertical thin structures from both theoretical and experimental perspectives, highlighting the frequency shift of resonant conditions and the influence of vortex structures.