利用Lagrangian 描述方式來進行理論解析與試驗研究，至今已有一系
列之發展。但對於諸多軌跡試驗者，雖有量測質點運動軌跡，然因受水槽
長度不夠常有反射波的干擾和模擬水粒子的顆粒其粒徑與密度等因素，迄
今仍無法於前進波與同向及反向流交會流場中，得到較完整的質點運動軌
跡之試驗量測的量化資料。為了探究波與流交會流場中的真實運動，遂進
行質點運動軌跡試驗研究。
本文選用直徑大小為1mm 之圓形塑膠顆粒(聚苯乙烯)來模擬水粒子
質點，搭配高速攝影機拍攝觀察波與流同向及反向交會流場中之質點運動
特性，進行一系列定性化及定量化試驗。資料處理上則採影像處理的方式
擷取與定位質點軌跡座標，改善攝影機所造成的網格變形與扭曲，減少人
為判定點位上之誤差，以獲取較往昔更佳的軌跡曲線。
由本文試驗結果得知只要有波浪存在，則流場中的質點運動皆會出現
交叉迴旋式的而非封閉的運動軌跡。於前進波與同向(水平)均勻流交會的
流場中之質點運動軌跡則是有更拉開的幅度。當波谷處的總水平流速等於
零時，則位在波谷處之質點運動軌跡甚至出現尖點軌跡。而於前進波與反
向(水平)均勻流交會的流場中之質點運動軌跡，則呈現與波與流同向交會
及等深無流時不同的結果而有上下顛倒的相反情形。此系列結果與陳(1994)
及許、陳(2006)以理論解析至第三階結果相比，具有相當一致的運動情形。
且其質點運動軌跡重現高程的運動週期皆大於波浪本身者，並隨波浪尖銳
度變大而增大，試驗之質量傳輸速度皆與理論本身相同，質點運動之水平
速度與重直運動速度皆與理論者重合。誤差探討上各理論與試驗量值之比
值均在10%以內，顯示試驗研究與陳(1994)與許、陳(2006)之理論解析相當
吻合。

There is a long terms of developement for academics theoretical analyzing and
experimental researching by using the Lagrangian method. But for such trajectory
experimentalists still have interference with reflected waves because of the length of
the water tank is too short or the diameter and the density of the simulate particle , in
spite of measuring the trajectory of the fluid particle have done. For there is no quite
completed quantification data for the trajectory of fluid particle, this study is aiming at
researching the truly movement of the flow field under wave-current interaction by
trajectory measuring.
This research choosing the simulate particle’s diameter for 1 mm , collocating
with a high-speed vedio camera to record the particle’s moving characteristics while
the wave-current interaction occured, to proceed a series of qualitative and
quantitative testing. And to comple with all these data and improve the modification
by using Image Processing to derive and orientate the coordinates .
According to the experimental results of the flow field,it has proved that mass
transport occured at the same-depth and no-flow condition through the wave
progressing direction.The trajectory of the fluid particle of wave-current interaction
in co-flow , its curve presenting the cross-convolution increasing and even presenting
the cuspidal locus. And the trajectory of the fluid particle of wave-current interaction
in inverse –flow is opposite to the trajectory of the no-flow movement. The results of
the experiment is quite accord with to the 3rd order the theoretical analyzing of Chen
（1994）and Shu、Chen（2006）。The fluid particle reproducting the moving period
of the high-elevation is greater than the wave’s and increasing by the sharpness of the
wave.
The mass transport velocity is the same theory results ,and decreased deviation
of artificiality in estimating particle position.
According to the ratio of the experimental results, root mean square of error Ex
and total mass transport displacement. The experimental results compared to the
theoretical results obtained by Chen (1994)and Hsu、Chen(2006) has the similar
results as well.

摘要.............................................................................................I
ABSTRACT ............................................................................. II
目 錄......................................................................................IV
圖目錄.......................................................................................X
表目錄................................................................................XVIII
第一章 緒論.............................................................................. 1
1-1 研究目的.....................................................................................1
1-2 文獻回顧......................................................................................2
1-3 研究方法及本文架構...............................................................11
第二章 波動系統描述與解析................................................ 13
2-1 等深水中非旋轉性自由表面前進重力波之座標系統描述....13
2-1-1 等深水中非旋轉性自由表面前進重力波之控制方程.................14
2-1-2 等深水中非旋轉性自由表面前進重力波至第三階解.................15
2-2 Lagrangian 系統下三維波與流交會流場之理論解析..........17
2-2-1 波流場的控制方程..........................................................................18
2-2-2 波與流交會流場至第三階解..........................................................19
第三章 實驗設備與佈置及方法............................................ 24
3-1 實驗設備...................................................................................24
3-1-1 基本設備..........................................................................................24
3-1-2 攝影裝置..........................................................................................28
3-1-3 水粒子模擬......................................................................................29
3-2 實驗佈置...................................................................................32
3-3 實驗方法與步驟.......................................................................33
3-4 實驗條件...................................................................................36
第四章 影像位差校正及影像辨識與座標轉換.................... 37
4-1 影像位差之探討與校正...........................................................38
4-1-1 影像位差之探討.............................................................................38
4-1-2 影像位差之校正..............................................................................41
4-2 影像辨識處理...........................................................................44
4-2-1 邊緣強度.........................................................................................46
4-2-2 影像二值化.....................................................................................46
4-2-3 濾除雜訊.........................................................................................46
4-2-4 控制點(即格點)的擷取..................................................................46
4-2-5 擬合曲線.........................................................................................47
4-3 影像座標之轉換.......................................................................47
4-4 實際校正後的情形....................................................................48
第五章 試驗結果、分析與討論............................................ 50
5-1 試驗結果分析...........................................................................54
5-1-1 試驗困難所在及解決......................................................................54
5-1-2 等深無流情形..................................................................................55
5-1-3 波與流交會情形.............................................................................56
5-2 試驗與理論比對.......................................................................58
5-2-1 質點運動軌跡比較.........................................................................58
5-2-3 波浪週期Tw 與水粒子運動(或重現高程)週期 TL ........................58
5-2-4 質點運動速度.................................................................................59
5-2-5 軌跡尖點出現的條件.....................................................................59
第六章 結論與建議................................................................ 97
6-1 結論...........................................................................................97
6-2 建議...........................................................................................98
參考文獻.................................................................................. 99
附錄一 實驗條件下之各時序列位置座標值...................... 104
附錄二 雙曲線正切函數TANH 之圖形............................. 157

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