本文探討二度空間中於緩斜坡底床上，自由表面規則前進重力波由深水至淺水傳遞時因受水深淺化影響，使得波高變大波長變小波速變慢及波形變得不對稱。於波形演變期間，波峯區域部份的流體質點其水平速度分量會大於波速而逸出波面發生波浪碎波。引用Chen et al.(2005)之沿斜坡底床前進波的流場解，並將波浪碎波判定條件與碎波後流體質點以自由落體拋射運動方程式等條件納入，繼續來探討前進重力波於平緩斜坡底床上波浪碎波之後瞬間波形之連續演變趨勢情形。
本研究同時在國立成功大學水工試驗所斷面水槽（長21公尺、寬0.5公尺、高0.7公尺），採斜坡坡度 及 與水深37.6公分及40公分與週期0.8秒至3秒與波高4公分至8公分等條件進行實驗，並依據在不同碎波點處於水槽前佈設高速攝影機（MS55K2，解析度1280*1020，拍攝最大速率每秒1020張），並將高速攝影機所拍攝獲取影像照片資料經由校正格板(厚1mm， 面積0.9m×0.625m，格點間距5mm×5mm)轉換後，再與相同條件下之理論解析所得結果進行驗證比對。
藉由本文之理論解析與實驗驗證比對，可將波浪傳遞於斜坡底床上的淺化至碎波之後，呈現的捲波波形(plunging wave)或溢波波形(spilling wave)之波形變化演變趨勢情形予以清楚的描述，同時也證明了本文線性理論解析波浪碎波之後瞬間波形之變化是頗為準確的。再者，由於在波浪碎波之後其波形變化之理論解析甚少，故以本研究對於碎波後之波形變化及其波形捲曲包絡的程度及落下的情形，能用來預測描述海波碎波後之情形。
關鍵詞：平緩斜坡、碎波波形、拋射運動、捲波、溢波

This thesis discusses the plunging or spilling wave breaking profiles for the progressive water waves propagating on gentle sloping bottoms. Due to the shoaling effect, the wave height will increase and the wave length will shorten as well as the asymmetry of wave profile will appear. As the wave continues to move to the shore, the wave velocity will decrease and the wave profile will be pushed to steep in the vertical direction. As the slope of wave profile approaches to large, the horizontal velocity of the water particle at the wave crest will larger than wave phase velocity and the wave breaking will occur and move forward in the free-body projectile motion.The theoretical solution derived by Chen at al. (2005) for the progressive waves propagating on sloping bottoms, the wave breaking criteria and the equation of the particle projectile motion after the wave breaking are included to discuss the continuous variations of wave profile for the plunging or spilling breaking waves.
A laboratory experiment is conducted in order to validate the theoretical wave breaking profile on sloping bottoms with measures. Wave breaking profiles can be verified obtained by the theoretical solution and experimental measurements. The experimental measurements were carried out in a glass-walled wave tank, 21m×0.7m×0.5m, in Tainan Hydraulics Laboratory , National Cheng Kung University. A High-Speed camera was set up in front of the glass-wall at the different breaking point locations depending on the initial wave conditions. This method allows to successively capturing the wave breaking profiles. Images were captured by a High-Speed camera (MS55k2, Canadian Photonic Labs Inc.), which has a 1280*1080 pixel resolution and maximum framing rate 1020 frames per second (fps). A transparent acrylic-plastic sheet (0.9 m×0.625m) was calibrated at 1-mm intervals in 5 mm×5 mm grids. Its function is a virtual grid in the picture. The experiments were conducted at two different bottom slope ( ,1/20) and two different water depth (d=37.6m, 40.0cm) and various wave periods from =0.8sec~3.0sec). The range of incident wave heights were from 4 cm~8cm.
According to the comparison results between the theoretical solution and experimental data, the wave profile evolution of plunging or spilling breaking wave on sloping bottoms can be described. Meanwhile, it is also proved that the instantaneous wave profiles after the breaking wave is good agreement. The duration of the overturning wave is less known by the analytical solution. The present theory can well describe the wave shoaling, as well as the occurrence of breaking wave and wave overturning, similar to the plunging jet in the breaking water waves over sloping bottom. Comparing the sequence of computed wave breaking profiles with snapshots of breaking wave behavior over a sloping bottom captured by the high-speed camera shows a good agreement of the theoretical wave breaking profile with laboratory measurements. The breaker jet creating a forward moving jet is well observed in the present theoretical results. This indicates that the theoretical solution is accurate for modeling such post-breaking waves.
Keyword：free-body,projectile,waves breaking,plunging,spilling

論文審定書
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 xiii
第一章 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 4
第二章 波動系統描述 6
2-1 控制方程式及邊界條件 6
2-2 波動系統之理論解析 8
2-3 轉換至Lagrangian系統 14
第三章 前進波碎波後瞬間波形變化 21
3-1 前進波浪之碎波 21
3-2 前進波碎波特性分析討論 26
3-3 前進波碎波後瞬間波化 30
第四章 試驗驗證 34
4-1 試驗設備與儀器 34
4-2 試驗配置 39
4-3 試驗方法步驟及條件 40
4-4 試驗結果與討論 42
第五章 結論與建議 98
5-1 結論 98
5-2 建議 99
參考文獻 100

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