Effect of Porous Breakwaters and the Harbor under Oblique Wave Impact

海岸與港灣工程之設計是否能達到最佳化之消波效果，與是否能對波場作正確之分析與模擬息息相關；而水波與多孔介質構造物之互制作用則是波場消波分析之關鍵因素。然而，以往之研究仍有未盡完善之處，如當入射水波之波向平行於多孔介質構造物時，以往之相關研究結果皆產生水波完全滲透至牆面另一側之弔詭現象。 本研究係探討斜向水波作用於剛性多孔介質薄牆之波場解析；復應用其所得結果於港池波場之數值運算，以求得更符合物理機制之港池共振與波能消散分析。 首先，本研究重新闡釋了無限水深多孔介質牆受斜向微小振幅黏性水波作用下之三維邊界值問題。接著依據Lamb (1945) 與Beavers and Joseph (1967)所演繹之類似概念，推導出適用於多孔介質薄牆受勢流斜向波作用下之部分滑移牆面邊界條件(partial-slipping boundary condition)，並求得勢流模式之線性解析解，此分析結果消除了側向波作用於多孔介質薄牆之弔詭。此外，為了解多孔介質牆面附近波場之物理機制，本研究應用邊界層近似法(boundary-layer approximation)求得侷限於薄牆表面層流模式之線性解析解，並進一步探討邊界層內之黏滯效應，使本研究之分析架構更趨完整。 其次，為應用勢流條件所推得之部分滑移邊界條件於港池共振之消波分析與港灣工程之規劃設計中，本研究進行了有限水深多孔介質薄牆及後方不透水岸壁受斜向水波作用下之勢流解析，並推導出適用於港池內佈設多孔介質消波體之波場反射係數及牆面邊界條件。接續上述之成果，本研究繼而完成了佈設於港池內側之多孔介質薄牆受斜向水波作用之港池波場數值分析。經由邊界元素法數值模式於開放矩形港池之驗證結果，並針對港池外不同角度入射波作用下，不同港池形狀與位置之波場行為進行深入探討後，可確認本研究成果應用於港池波場共振與波能消散分析之適用性。 由本文所獲致之研究成果綜合評估，應可確信本研究於斜向水波作用於多孔介質薄牆之波場分析方面，較以往之文獻具備更為正確之詮釋能力；而觀諸港池波場之數值模擬結果，本研究亦呈現更為符合實際波場之物理機制。故未來進行港池震盪與波場行為之探討時，可依據本文之研究成果，進一步探究更臻系統化與標準化之規劃方式，冀能達成港灣工程與港池消波設施之最佳化設計。Optimizing design to the harbor and coastal structures for the purpose of eliminating wave energy always depends on accurate analysis and simulation to the wave field, and the interaction between water waves and porous structures is the key factor. However, when the incoming water wave is parallel to the porous breakwater, a paradoxical phenomenon that the water wave permeates completely into the original quiescent wave field inevitably occurs in all the earlier researches. It is indeed questionable and obviously against our physical expectation. For more reasonable analysis of harbor resonance and wave energy elimination, the wave field and physical mechanism of an oblique water wave impacting on a solid porous wall is investigated in the present study, and the result is further applied in numerical analysis of harbor wave field. Firstly, the three-dimensional boundary value problem of an oblique small-amplitude water wave impacting on an infinite-depth porous wall is formulated in the present study. And according to the similar concept proposed by Lamb (1945) and Beavers and Joseph (1967), the partial-slipping boundary condition applicable for the thin porous wall impacted by oblique potential waves is thus obtained, followed by the analytical solution of the potential flow model. The obtained result eliminates the above mentioned paradox of parallel waves impacting on the thin porous wall. Moreover, in order to investigate the physical phenomenon in the neighborhood of porous wall surfaces, the boundary-layer approximation is adopted in this study to analyze the viscous boundary layer effect, which provides proper boundary conditions on the thin porous wall for laminar flow and gives more detailed flow information. Secondly, in order to apply the partial-slipping boundary condition in analysis of wave field in the harbor with porous walls inside, the analytical solution of oblique waves impacting on a thin porous wall with a vertical impermeable bank behind is thus obtained in the present study. And a simplified reflection coefficient and the boundary condition applicable for porous breakwaters inside the harbor are thus found. Furthermore, the boundary element method (BEM) is adopted to analyze the wave field of the harbor in which porous breakwaters are arranged alongside the inner walls. By applying our partial-slipping boundary condition including undetermined incident angles, the iteration method is used in the BEM model to find out the most appropriate incident angle for each boundary element. And the wave field of the harbor with porous breakwaters inside is well investigated and proven in better agreement with physical expectation than the earlier investigations. Due to the reasonable expression for oblique water waves impacting on the thin porous wall and the desirable analysis of the harbor wave field, it can be concluded that the present study is well expected to be the theoretical basis for optimization of harbor oscillation and design of coastal structures for more effective wave energy elimination.誌謝 I 中文摘要 III ABSTRACT V 目錄 VII 表目錄 X 圖目錄 XI 符號說明 XV 第一章 導論 1 1.1 研究動機與目的 1 1.2 文獻回顧 5 1.2.1 水波與多孔介質互制之研究 5 1.2.2 港池共振之研究 11 1.3 章節介紹 15 第二章 無限水深多孔介質牆之斜向波邊界值問題 17 2.1 控制方程式 17 2.2 邊界條件 19 第三章 無限水深多孔介質薄牆之斜向波勢流解析 25 3.1 多孔介質薄牆之部分滑移邊界條件 25 3.2 線性解析解 30 3.3 結果與討論 33 第四章 無限水深多孔介質薄牆之斜向波黏滯效應分析 36 4.1 多孔介質薄牆之黏性流邊界條件 36 4.2 邊界層近似法之黏性流分析 39 4.3 線性解析解 42 4.4 結果與討論 43 第五章 有限水深多孔介質薄牆及不透水岸壁之斜向波勢流解析50 5.1 有限水深多孔介質薄牆及不透水岸壁之斜向波邊界值問題 50 5.1.1 控制方程式 50 5.1.2 邊界條件 52 5.2 線性解析解 55 5.3 結果與討論 57 第六章 多孔介質薄牆佈於港池之斜向波數值分析 59 6.1 多孔介質薄牆佈於港池之斜向波邊界值問題 59 6.1.1 控制方程式 59 6.1.2 邊界條件 61 6.1.3 入射角求解 63 6.2 數值模式之驗證 64 6.3 結果與討論 66 第七章 結論與建議 71 7.1 結論 71 7.2 建議 74 參考文獻 76 作者簡歷 11