# 臺灣博碩士論文加值系統

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 本文求解三維、時變的Navier-Stokes方程及完整的自由液面邊界條件，模擬波浪通過半無限長防波堤時之波形演變及流場特性。在數值方法上，本文將有限解析法擴展到三維用來離散Navier-Stokes方程，同時將處理自由液面的Marker and Cell (MAC)方法推廣到三維。在數值計算域中給定一直推式造波版作為造波之用。由於三維計算域之網格數量龐大，本文之結果主要是聯結多台個人電腦構成叢集電腦(PC-cluster)進行計算所得。為了驗證本數值模式之準確性，本文首先模擬波浪通過半無限長防波堤所產生之波場，數值計算結果與理論結果相當吻合。此外，本文也模擬波浪通過二維梯形潛堤及孤立波通過半無限長防波堤時結構物附近波形變化，數值結果與實驗結果比較亦非常吻合。在驗證過本數值模式的準確性後，本文模擬不同波浪，包括︰孤立波、橢圓函數波及規則波通過半無限長防波堤所衍生的波場、流場、邊界層流及流體質點軌跡。數值計算結果顯示孤立波通過防波堤時，於堤頭附近有渦流產生，渦流所在位置具有向上方向之速度分量，應為堤頭沖刷之主要原因。
 In this study, the unsteady 3D Navier-Stokes equations and the fully nonlinear free surface boundary conditions were solved numerically to simulate both the wave and flow fields induced by waves propagating through a semi-infinite breakwater. The finite-analytic method was used to discretize the partial different equation, and the mark-and-cell (MAC) method was extended to treat the 3D free surfaces. A piston-type wave generator was incorporated in the computational domain to generate the incident waves. As the 3D numerical computation requires a huge memory and a long computational time, the computational was carried out on a PC-cluster established by connecting ten personal computers. The accuracy of the numerical model was verified by checking the relative volume error in the computational domain with respect to the size of grid cell and time step. The numerical wave fields induced by linear waves propagating through a semi-infinite breakwater were shown to be in good agreement with the theoretical solutions. Before investigating the interaction of waves and a semi-infinite breakwater, the 3D wave tank simulated the propagation of water waves over a submerged 2D breakwater and the diffraction of a solitary wave by a semi-infinite breakwater. Comparing numerical results with the experimental data proves that this wave tank can correctly simulate the interaction of waves and offshore structures. Our numerical results show that as a solitary wave propagates over a semi-infinite breakwater, vortices and vertical velocity components are induced at the region near the head of the breakwater. These may be the primary reasons for causing the scouring near the breakwater head.
 中文摘要 IAbstract II誌謝 III目錄 IV表目錄 VI圖目錄 VII符號說明 IX第一章 緒論 11.1 研究動機 11.2 前人研究 31.3 本文架構 5第二章 理論分析 62.1 控制方程式 62.2 無因次化處理 72.3 邊界條件和初始條件 8第三章 數值方法 12第四章 結果與討論 174.1 數值模式之驗證 174.2 現場波浪條件及數值模擬轉換 294.3 孤立波與半無限長防波堤互制作用 30 4.3.1 波高水深比0.3 30 4.3.2 波高水深比0.1 404.4 橢圓函數波 (Cn波)與半無限長防波堤的互制作用 624.5 線性規則波與半無限長防波堤的互制作用 92第五章 結論與建議 955.1 結論 955.2 建議 97參考文獻 98
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 1 波浪通過潛堤之渦流行為 2 波浪與潛沒平板之交互作用 3 波浪通過沙漣底床邊界流之特性 4 波狀曲面上震盪層流邊界層特性之研究

 1 26. 王豪偉、黃清哲2006孤立波通過三維潛堤所衍生之波場與流場，海洋工程學刊，第六卷，第二期，第1-22頁（2006）。 2 27. 黃惠欽、董志明、黃清哲 2005 數值波浪水槽中Cn波之產生及其傳遞特性之研究，海洋工程學刊，第五卷，第一期，第13-30頁（2005）。 3 30. 劉景毅 (2003) 直立防波堤前海流導致底床沖刷之數值模擬，海洋工程學刊, 第3卷，第一期，第15-33頁。

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