本文主要目的係探討二度空間中，傳遞於等緩坡度 底床上之自由表面前進重力波問題。迥異前人所使用Eulerian系統下之控制方程式及邊界條件，本文完全直接以Lagrangian描述方法，導述出波動流場的所有控制方程式來對其做整體的解析。於波浪振幅線性階的考量下，把波浪場中各物理量對坡度 作一適當的攝動羃級數展開，且將所有的控制方程式演化成一系統化的至 階次模式，並由之解析出波動流場至 階解，當然可由此系統化的過程解析其至更高階解。因此，於波動流場中，對被參數 所標註的流體質點，其運動軌跡 與流場中的壓力 及流速勢函數 等，隨時空演變之特性可完全被闡述。並由理論分析得知，在任一波浪條件下，底床坡度對波浪變形以致破碎佔有相當大的影響。本文最後更以實驗數據與理論結果作一比對驗證。

　　The main purpose of this paper is to analyze the surface progressive gravity waves propagating on a gentle sloping beach in two dimension. Instead of using the method of Eulerian system by the previous investigators, we introduce the governing equations completely in the Lagrangian system directly. All the characteristics of the wave system is expressed by a suitable perturbation expansion in the bottom slope under linearizing the problem in wave amplitude, then all the governing equations are systematically expanded to order. The solution of the wave system is to be solved to second order , even to high order could also be obtained. Based on the obtained results, the velocity potential, pressure and motion of the fluid particle in the wave system in time and space is therefore presented, and we can see that the bottom slope is a main factor to screw the wave field to deform to break. Finally, the experimental result is cited to compare and verify.

中文摘要
英文摘要
圖目錄
符號說明
第一章 前言
第二章 理論推導
第三章 波浪的變形
第四章 結果與驗證
第五章 結論與建議
參考文獻
附錄A

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