本研究提供一有效之數值計算模式，來解析海底緩變區域內大型結構物，受入射波浪與均勻水流交互作用下結構物周邊受波流交互作用後之波高分佈及波壓變化情形。首先將解析領域依地形變化分為等深地形之外領域與緩變地形之內領域，其中外領域以緩變區與等深區之交界處為邊界，一直延伸至無窮遠處，考慮在無流之情況下則控制方程式為齊次之Helmholtz方程式；內領域包含大型結構物，控制方程式為含流效應之緩坡方程式，可重新整理為非齊次之Helmholtz方程式，應用Green第二定理改寫為積分方程式，再應用邊界元素法之新技巧—雙互換邊界元素法（Dual Reciprocity Boundary Element Method）將含未知數之非齊次項移項至等號左邊，即可經由矩陣求解得到圓柱周邊之速度勢。
在建立數值模式後，首先在無水流作用之情形下，將數值解與解析解作一比較，再加入水流效應，並與前人研究如蕭等(1998)之實驗結果比較均相當吻合，驗證數值模式之適用性；另亦計算不同之週期、水流速度、波流交會角度之情況下，作用於大型圓柱周邊之波壓分佈趨勢，以探討受水流影響下作用於大型圓柱周邊波壓之變化情形，其計算結果在定性上相當合理。
由以上結果顯示，本研究所提供一新的數值計算模式，可以有效地解析實際海洋工程上有關大型結構物周邊波浪折—繞射與水流共同效應之問題。

The purpose of this study is to analyze numerically the change of wave height and wave pressure caused by wave and uniform current interactions around a large cylinder on slowly varying water depth. In order to provide an effective numerical model, we employ the mild-slope equation with current effects as a basis, and apply dual-reciprocity boundary element method ( DRBEM ) to analyze the combined effects of wave refraction-diffraction and currents.
First ,we rearrange the mild-slope equation with current effects to a nonhomogeneous Helmholtz equation. Then, we transform it to an integral equation using Green’s theorem. Comparisons are made with the analytical solutions and numerical result with no current present. Good agreements are obtained. Using this numerical model, we calculate the change of wave pressure around a large cylinder located on slowly varying water depth with current effects. The numerical result show qualitative agreements.
From the results of this study, it shows that the numerical model propose here is efficient to solve practical ocean engineering problems which include the effects of wave refraction-diffraction and currents.

內 容 頁次
中文摘要 ------------------------------------------- Ⅰ
英文摘要 ------------------------------------------- Ⅱ
目錄 ----------------------------------------------- Ⅲ
圖目錄 --------------------------------------------- Ⅴ
符號表 --------------------------------------------- Ⅷ
第一章 導論 ---------------------------------------- 1
1-1 研究目的 --------------------------------------- 1
1-2 文獻回顧 --------------------------------------- 2
1-3 研究方法與內容 --------------------------------- 6
第二章 理論基礎 ----------------------------------- 9
2-1 領域劃分及控制方程式 --------------------------- 9
2-1-1 半無限領域 -------------------------------- 13
2-1-2 有限領域 ---------------------------------- 13
2-1-3 領域邊界面之邊界條件 ---------------------- 14
2-2 水流速度勢 ------------------------------------- 15
2-3 波浪速度勢 ------------------------------------- 17
2-4 波高與波壓 ------------------------------------- 19
第三章 數值方法 ------------------------------------ 22
3-1 邊界元素法 ------------------------------------- 22
3-2 雙互換邊界元素法之應用 ------------------------- 24
3-3 波壓之計算 ------------------------------------- 28
第四章 計算結果與討論 ------------------------------ 30
4-1 數值計算例 ------------------------------------- 30
4-2 數值模式驗證 ----------------------------------- 31
4-2-1 數值計算值與解析解之比對 ------------------ 31
4-2-2 數值計算值與實驗結果之比對 ---------------- 31
4-3 結果與討論 ------------------------------------- 35
第五章 結論 ---------------------------------------- 67
參考文獻 ------------------------------------------- 69
謝 誌 ------------------------------------------- 74
作者簡歷 ------------------------------------------- 75

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