本文主旨在以 Lagrangian描述方式，來解析二度空間中，行進在緩斜坡底床上的規則前進重力波之波動流場；並以一系列的試驗研究，來驗證在Lagrangian描述方式下的解析解之適足性。接著，進一步將本文的解析解，應用至該波動流場的極限情況--碎波，發現此解析解在碎波特性的判斷比一般的經驗式，更為準確。
就細節而言，在Lagrangian方式探究緩斜坡底床上的非線性前進波傳遞問題，本文引入導致水深變化因素的底床坡度α，及保有波浪非線性特性的深海波浪尖銳度ε兩個重要參數，進行系統化之雙攝動展開，以解析此非線性理論至O(ε^3α^0) 階次量。其次，本文以試驗研究的方式來量測(1)．水粒子運動軌跡，(2)．淺化過程中持續變化的波形，(3)．向岸傳遞連續演化至碎波的波速；以此三個波動場之物理特性，來驗證本文解析的真確性。本文理論的極限為恰發生碎波時，應用K.S.P. 指標，即u/Cw=1 來判斷碎波，因此可得本文解析解之碎波波高、碎波水深、波速變化等特性。
本文之解析解滿足自由表面常壓條件與垂直斷面處總質量傳輸量平衡式。本解析解可描述在緩斜坡底床上前進波的波動場，由深水至臨近碎波點的波形、水粒子運動軌跡及波速…等動力特性；在應用本文理論於描述碎波的過程中發現，本文解析解所得之碎波特性與試驗結果比較，兩者相當符合。而且由於本文對底床坡度α攝動展開，故在較陡坡情況較往昔學者的經驗式適用。

The purpose of this thesis is applying Lagrangian approach to analyze shoreward progressive waves over a gently sloping bottom. A series of laboratorial experiments were executed to validate the analytical results. Then, the theory is extended to the prediction of wave breaking and the resulting breaking criteria are shown to be more accurate than regression formula in the literature.
In the analysis, a two-parameter perturbation were used that employs both bottom slope α and wave steepness ε , and the solution is expanded up to the order. Based on this analytical solution, water particle trajectory, waveform and wave velocity in the shoaling process are calculated and their counterparts in the laboratorial experiment are recorded for comparison. Then, the analytical solution is used to derive the wave height, the water depth, and the wave velocity for a breaking wave where the Kinematic Stability Parameter (K.S.P.) u/Cw equaling one is adopted as the breaking criteria.
In deriving the O( ε^3α^0) solution, the following conditions are satisfied at each order: (a) The pressure on the free surface is constant, and (b) the mass flux is conserved at each vertical cross section. This solution can accurately describe the waveform, the water particle trajectory and the wave velocity all the way from the deep water to the breaking point, as is shown by the comparison with the laboratorial experiments. The perturbation with respect to the bottom slope α is included and the flow at the bottom is consistent with the sloping bottom condition. Consequently, the present analytical solution can provide better breaking criteria than previous regression formula, especially in the case of large sloping angles.

目錄
誌謝 I
中文摘要 II
英文摘要 Ⅲ
目錄 Ⅴ
表目錄 Ⅶ
圖目錄 Ⅷ
符號說明 XI
第1章、 緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 2
1-3 本文組織架構 6
第2章、 波動系統之描述 7
2-1 控制方程式及邊界條件 7
2-2前進波動系統化攝動展開之理論解析 9
第3章、理論解析 21
3-1 ε^m α^n m+n=1 階解 21
3-1-1 ε^1 α^0階解 21
3-2 ε^m α^n m+n=2 階解 24
3-2-1 ε^1 α^1階解 24
3-2-2 ε^2 α^0階解 28
3-3 ε^m α^n m+n=3 階解 34
3-3-1 ε^1 α^2階解 34
3-3-2 ε^3 α^0階解 37
3-4分析與檢核 42
第4章、 試驗驗證 46
4-1試驗設備與儀器 46
4-2試驗配置 51
4-3試驗方法、步驟及條件 54
4-4試驗量測資料之處理 56
4-5 緩斜坡底床上波浪水位的變化 60
4-6沿緩斜坡底床上前進波中質點的運動軌跡量測分析
與理論印證 65
4-7緩斜坡底床上前進波波速(位相速度)量測分析
與理論印證 70
第5章、 結果與討論 76
5-1 緩斜坡底床上波形的演化 76
5-2質點運動軌跡及波速 79
5-3波浪碎波特性 82
第6章、 結論與建議 87
6-1 結論 87
6-2 建議 89
參考文獻 90
附錄A: 緩斜坡底床上Csae 2~9水位變化圖 98
附錄B: 試驗之質點軌跡的時序列資料 122

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