就描述流體運動的兩種方式中，本文全然別於往昔學者研究所常用的Eulerian方式，對三度空間中之前進波與短峰波波動流場的描述，完全以Lagrangian的方式推導出其流場的所有控制方程式，再經由一適當的攝動解析法進行處理後，已將這些控制方程式演化成一套有系統的階次化模式，並由之求得前進波至第三階解與短峰波至第二階解。由此所得之解，更進一步地直接描述出流場內的運動特性，包括波形、波壓、流體質點運動軌跡與質量傳輸速度等。
於檢核本文結果的適足性上，成功的將短峰波解析結果退化至二度空間之單一前進波及駐波兩種特例情況，並與往昔學者之波形、波壓與流體質點的運動軌跡試驗比對，印證本文結果的正確性及一般性。

To differ from the usually applied Eulerian method for describing the motion of fluid, the governing equations complete in the Lagrangian form for describing three-dimensional progressive and short-crested waves system are derived in this paper. A systematical ordering expansion by an appropriate perturbation approximation is developed, and the exactly satisfactory solutions in a form of functional, up to third-order progressive waves and up to second-order short-crested waves, are obtained. The kinematic properties of the waves, including the surface profile, pressure, the paths of fluid particles, and the mass transport velocity, are then described directly.
The obtained solution for the short-crested waves system is successfully verified by reducing to two special cases, one is the two-dimensional simple progressive waves, and the other is the two-dimensional standing waves. Also, the analytical results are compared with experimental data including the surface profiles, the pressures and the paths of fluid particles for validation.

中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
圖目錄 Ⅴ
符號說明 XI
第一章 緒論 1
1.1 研究目的 1
1.2 文獻回顧 2
1.3 本文組織架構 4
第二章 波動系統之描述 5
2.1 單一自由表面前進重力波 5
2.1.1 波動流場的基本控制方程式 6
2.1.2 波動流場的邊界條件 12
2.2 短峰波 15
第三章 理論解析 17
3.1 單一自由表面前進重力波17
3.1.1 第一階解 30
3.1.2 第二階解 32
3.1.3 第三階解 38
3.2 短峰波 47
3.2.1 第一階解 48
3.2.2 第二階解 49
第四章 驗證比較及特性描述 59
4.1 理論印證 59
4.2 質量傳輸速度 66
4.3 波形 89
4.4 流體質點的運動軌跡 102
4.5 波壓 109
第五章 結論與建議 113
5.1 結論 113
5.2 建議 114
參考文獻 115
附錄A 118

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