本文利用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，建立黏性數值造波水槽，以探討微小振幅波及Stokes波中質量輸送的特性。水槽中的入射波浪由兩種方法產生，一是利用數值水槽中直推式造波板的運動;另一則是在水槽起始處，直接給定勢能理論的流速剖面及自由液面波形。兩種模式所求得之一階流速剖面及自由液面波形均與解析解無異。在確定數值模式的準確性後，本文針對底部邊界層附近及整個流場內的尤拉( Euler )質量傳輸速度及拉格朗日( Lagrange )質量傳輸速度，就數值解及理論解進行討論分析。而與實驗資料比對方面，採用Tsuchiya et al. (1980)所設計的開放性造波水槽(open wave flume)下所量測的實驗結果，與數值解的拉格朗日質量傳輸速和理論解的Stokes質量傳輸速度比較分析。最後就線性波、有限振幅波等不同入射波浪條件下，探討質量傳輸速度隨Ur數的變化。

In this study, a numerical scheme was developed to solve the unsteady, two-dimensional Navier-Stokes equations and the exact free surface boundary conditions for investigating the characteristics of the mass transport induce by the small-amplitude waves and the Stokes waves. The incident waves in the wave tank were produced by either setting up a piston-type wave maker in the computational domain or by providing the wave profile and the velocity profile from the potential theory at the left boundary of the computational domain. Both methods give the same results of the wave and flow fields, witch are shown to be consistent with the first-order analytical solutions. After having verified the accuracy of the model, the numerical of Eulerian and Lagrangian mass transport velocities in the boundary layer and in the whole velocity field were computed and compared with the corresponding analytical solutions. The numerical solution of Lagrange mass transport velocity and the analytical solution of Stokes mass transport velocity were also compared with the experimental data obtained by Tsuchiya et al. (1980) using an open wave flume. Finally, variation of mass transport velocity with Ursell number was investigated under different incident wave conditions.

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本文組織 5
第二章 理論分析 6
2-1數值造波水槽 6
2-1-1建立控制方程 6
2-1-2無因次化處理 7
2-1-3邊界條件和初始條件 8
2-2波浪質量傳輸速度之推導13
2-2-1邊界層內的尤拉質量傳輸速度13
2-2-2邊界層內的拉格朗日質量傳輸速度16
2-2-3內部流場的尤拉質量傳輸速度18
第三章 數值方法 20
3-1計算網格之配置 20
3-2邊界及計算網格的處理20
3-2-1自由液面上速度及壓力之計算20
3-2-2自由液面位置及計算網格的處理23
3-2-3底部邊界層網格處理 24
3-2-4下游邊界網格處理 26
3-3計算流程 27
第四章 結果與討論 29
4-1 數值方程式之驗證 29
4-1-1微小振幅波 31
4-1-2有限振幅波 36
4-2 微小振幅波質量傳輸速度之驗証40
4-2-1邊界層內尤拉質量傳輸速度41
4-2-2邊界層內拉格朗日質量傳輸速度45
4-2-3流場內尤拉質量傳輸速度47
4-2-4流場內拉格朗日質量傳輸速度49
4-3非線性波質量傳輸速度52
4-4本數值模式與實驗結果之比較55
4-5質量傳輸速度隨Ur數的變化57
第五章 結論與建議 59
5-1結論 59
參考文獻 61
自述 64

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