臺灣博碩士論文加值系統

本文以數值方法求解二維非穩態的Navier-Stokes方程及完整的自由液面邊界條件，藉以探討不同入射波浪底部邊界層之特性。入射波浪係藉由一置放於數值領域中之直推式造波板所產生。自由液面水位及邊界層內流體速度及壓力的數值計算結果與解析解及實驗資料比較，結果皆相當吻合。在確立數值模式的正確性後，本文研究線性波、有限振幅波等不同入射波浪條件下邊界層內的速度、壓力及剪應力隨Ur數的極值變化，及底床剪應力、最大水平流速在邊界層內之相位差，並探討波浪底部摩擦係數和雷諾數之間的關係及不同定義的參考邊界層厚度變化。最後我們針對孤立波邊界層速度、壓力及剪應力等特性變化加以研究。

Abstract
A numerical scheme was developed to solve the unsteady, two-dimensional Navier-Stokes equations and the exact free surface boundary conditions for investigating the bottom boundary layer flows induced by water waves. A piston-type wavemaker was set up in the computational domain to produce the incident waves, which include the small-, and the finite-amplitude waves as well as the solitary waves. The numerical results for the incident wave profiles and the velocity profiles from the bottom to the free surface have been shown to be consistent with the analytical and experimental data. After having verified the accuracy of the present numerical scheme, the effect of the Ursell number on the main characteristics of the boundary layer flows were systematically studied. These include the velocity profile within the boundary layer, the bottom shear stresses, the phase difference between the bottom shear stress and the wave profile, etc. The variation of the friction factor with respect to the Reynolds number was also discussed. Finally, the main characteristics of the boundary layer flow induced by a solitary wave was discussed in terms of the velocity profile, the temporal variation of the pressure and the bottom shear stresses.

目錄
中文摘要 Ⅰ
英文摘要 Ⅱ
謝誌 Ⅲ
目錄 Ⅳ
圖目錄 Ⅵ
表目錄 Ⅷ
符號說明 Ⅸ
第一章 緒論 1
1-1 研究動機 1
1-2 前人研究 2
1-3 研究方法 4
1-4 本文組織 4
第二章 理論分析 6
2-1 建立控制方程式 6
2-2 無因次化處理 7
2-3 邊界條件和初始條件 8
第三章 數值方法 13
3-1 計算網格的配置 13
3-2 控制方程的離散化 13
3-3 離散化控制方程式的解 18
3-3-1 SIMPLER 演算法 18
3-3-2 加速方程組收斂的方法 21
3-4 邊界及計算網格的處理 22
3-4-1 自由液面上速度及壓力的計算 22
3-4-2 自由液面位置及計算網格的處理 25
3-4-3 底部邊界層計算網格的處理 26
3-5 計算流程 27
第四章 數值計算結果與討論 29
4-1 數值計算資料的取得與富立葉分析 29
4-2 水位波形歸於零軸之處理 30
4-3 光滑底床上邊界層臨界雷諾數 的界定 30
4-4 波浪底部邊界層之數值計算結果 31
4-4-1 底床至自由液面數值模擬結果之驗證 33
4-4-2 線性波邊界層數值模擬結果之驗證 37
4-4-3 非線性波邊界層數值模擬結果之驗證 39
4-4-4 本數值模式與實驗結果之驗證 41
4-4-5 波浪邊界層內水平速度隨Ur數之變化 44
4-4-6 水位和底床剪應力隨Ur數之變化 45
4-4-7 邊界層內各高程最大水平速度相位差隨Ur數之變化 47
4-4-8 底部摩擦係數 與雷諾數的關係 48
4-4-9 波浪參考邊界層厚度之探討 50
4-5 孤立波邊界層特性之探討 52
第五章 結論與建議 55
5-1 結論 55
5-2 建議 56
參考文獻 57

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