本文報告在國內第一座（ 公尺）鋼架玻璃水槽中，於總水深 的條件下，以淡、鹽水依密度分層佈置的兩層流體，從事孤立內波產生、傳遞及斜坡上反射之一連串基礎試驗研究之成果。在水槽的右端為可控制垂直升降的氣動式閘板，最左端放置一面可調整角度的斜板，實驗時使用六種單斜坡（角度分別為 、 、 、 、 及 ）；上層淡水密度 ，水層厚度 ；下層鹽水密度 ，水層厚度 ，布氏參數 。佈置水體系統時，需先由水槽底部注入淡水達到 厚度，再以定水頭方式，混合好的鹽水，由水槽底部水孔緩慢注入，自底部抬升淡水水層，直至水槽內總水深達 為止。再利用微馬達抽取造波區閘板兩側淡水，製造造波區位能差 。當閘板抽起，由閘板兩側淡、鹽水的位能差 促成水體翻轉，產生下沈型或上舉型孤立內波，往水槽中央及左側傳遞。本實驗利用五支超音波計記錄淡、鹽水層界面之波動，一根密度剖面計記錄分層水體的垂直密度剖面及定點密度變化，兩支電容式波高計記錄水體表面波動及使用數位式攝錄影機拍攝實驗過程，提供觀察及分析內波運動所需畫面。
水槽內的上下層水深比 、造波區位能差 及斜坡角度 ，為實驗主要的控制變因，在各種不同的條件配合之下，從事孤立內波在等深底床的傳遞、在單斜坡上的發展及反射試驗，探討上舉型與下沈型孤立內波的物理特性。深度參數 為影響孤立內波振幅、波速及波形的主要因素，當深度參數愈大，振幅愈大、波速愈慢、孤立波形愈顯著。由實驗結果與理論模式比較，顯示KdV理論能精確地描述小振幅孤立內波的物理特性；mKdV理論則符合大振幅孤立內波的物理特性。在不考慮流體黏滯力的情況下，底床摩擦力與斜坡上的碎波機制是孤立內波在水槽傳遞時，影響能量消散的兩個重要因素。孤立內波在傳遞中因底床摩擦力造成的振幅衰減，大約是每傳遞六公尺振幅高度衰減10%。本研究報告亦陳述兩種碎波機制可能引致淡、鹽水水體的巨大混和及局部渦旋，因而造成能量的消散。當入射內波能量或振幅較大時，其振幅或能量反射率隨入射振幅或能量增加而減少，此時可將底床摩擦力影響的振幅或能量反射率視為常數。若進一步考慮碎波機制對反射率的關係，推論反射率隨入射波振幅或能量增加而呈拋物線方式衰減，本報告提出碎波的反射率經驗公式，與實驗結果比較，趨勢非常吻合。藉由此經驗公式，可將底部摩擦力及破碎機制引起的孤立內波振幅或能量反射率 及 ，以簡易的入射波振幅或能量大小I換算，得迅速預測內波反射率R之值。
在天然的湖泊環境中，孤立內波以各種型式出現，如下沈型、上舉型及不規則波群，且湖畔的傾斜角度多以陡峭地形為主。針對內波在傾斜坡度地形上的能量消散，本研究報告所討論之各種實驗成果，應可當作研究湖泊水文的參考。

Laboratory experiments were conducted to investigate the propagation of internal solitary waves on a uniform slope in a two-layered free surface fluid system. The laboratory facilities employed in this study is the first in Taiwan, which include a stainless steel wave flume (dimensions: 12 meters long with cross-section 0.5 m wide and 0.7m deep) and experimental apparatus for generating and measuring internal waves. The flume incorporates a movable vertical gate at one end for generating internal solitary waves, and a uniform slope (either θ = 30o, 50o, 60o, 90o, 120o or 130o) at the other end. The upper layer had fresh water with density ρ1 (999kg/m3), to a depth H1; the lower layer was saline brine density ρ2 (1030 kg/m3), which was slowly filled into the flume to a depth of H2 by gravity through several openings at the bottom of the flume, Boussinesq parameter . A mini pump was used to remove a small quantity of fresh water from one side of the vertical gate to another side. By creating a prescribed difference ηo in the interface levels on either side of the gate beforehand, internal solitary wave was generated by the mechanism of overturning the brine and fresh water behind the movable gate. Five ultrasonic probes at equidistant distance recorded the interface fluctuations, one density probe measured the change of density at the interface, while two electrical capacitance gauges for the free surface displacements likely to occur. Digital cameras were also used to record the motions of internal wave in the flume and on the slope for further analysis.

Laboratory test on internal solitary wave were arranged from one of the combinations using different layer thickness ratios H1/H2, interface differences ηo, density ratios ρ1/ρ2, and bottom slopes θ. In addition to internal solitary wave reflection from a uniform slope, laboratory investigations included internal wave propagation on a rigid impermeable bottom and evolution on a uniform slope. Keeping the total water depth in the flume at H = 40cm, an increase in the depth parameter |H2-H1|/H produced large internal wave amplitude, reduced phase velocity, and enhanced soliton feature. From the experimental result analyzed, it suggests that the Korteweg-de Vries (KdV) theory fits solitary waves of small amplitude, and the modified KdV is suitable for large amplituded waves. Considering wave motion in an inviscid fluid, the dissipation of internal solitary waves propagating in a flume may occur through bottom friction and wave breaking. Subjected to bottom friction alone, the amplitude of most internal solitary waves in the experiments decayed approximate by 10% over a journey of 6 meters. Two types of wave breaking mechanism were found to produce strong mixing and local vortex in the fluid, causing significant energy losses. For internal solitary waves of large amplitudes, reflection coefficient for wave amplitude or energy decreased, as amplitude or energy increased. Under this condition, however, the reflection coefficient due to bottom friction may be assumed as constant. Using the experimental results obtained, empirical equation is now proposed to account for wave dissipation due to for non-breaking internal waves. The equation indicates that decrease in reflection coefficient as wave amplitude or energy increases may be expressed using a second order polynomial. Overall, experimental results suggest that good agreement can be found between experimental data and the empirical equation so derived. Upon assuming the wave reflection coefficient is solely dependent on the incoming wave amplitude or energy, prediction for reflection coefficient can be calculated in a straight forward manner.

Either large-scale, high-frequency internal wave motion or internal solitary waves have been observed in natural lakes. The observed rapid decay of internal wave energy after severe breaking events seemed to be mostly due to dissipation on various sloping boundaries in a lake. From the basic laboratory experiments on internal wave reflection from various single slopes, the results many benefit provide researchers to promote further research on practical applications related to limnology.

謝誌 i
中文摘要 ii
英文摘要 iv
目錄 vi
圖目錄 ix
表目錄 xii
符號表 xiii

第一章 緒論
1.1前言 1
1.2研究目的 2
1.3本文架構 3

第二章 文獻回顧
2.1前言 5
2.2南海內波現場調查 6
2.3理論解析 9
2.3.1前言 9
2.3.2線性內波 9
2.3.3孤立內波 10
2.4實驗室研究 12
2.5內波生成、傳遞與消散
2.5.1前言 15
2.5.2水體的分層 15
2.5.3內波的結構 16
2.5.4內波的生成 18
2.5.5內波的運動與傳遞 19
2.5.6內波的消散 21
2.6內波在斜坡邊界上的反應
2.6.1前言 21
2.6.2溯升與溯降 22
2.6.3破碎 23
2.6.4沈積物傳輸 24
2.7內波反射
2.7.1前言 24
2.7.2內波反射的物理機制 25
2.7.3內波的反射率 26

第三章 實驗配置與方法
3.1實驗方法 28
3.2實驗佈置 32
3.3實驗條件 35
3.4實驗方法與步驟 38

第四章 實驗結果與討論
4.1實驗數據整理 45
4.1.1測波儀器組量得之內波及表面波波高值 45
4.1.2孤立內波特徵參數 49
4.1.3內波影像處理 53
4.1.4溯升與溯降 54
4.2實驗數據結果 55
4.3內波生成與傳遞 58
4.3.1實驗水體密度剖面 58
4.3.2孤立內波生成 59
4.3.3孤立內波波形 68
4.3.4孤立內波振幅 71
4.3.5孤立內波波速 73
4.3.6實驗波形與波形理論比較 75
4.3.7孤立內波振幅的衰減 82
4.3.8孤立內波對表面波的影響 84
4.4內波傳遞至斜坡邊界的反應 85
4.4.1孤立內波在斜坡上的現象 85
4.4.2溯升與溯降高度 97
4.4.3孤立內波的反射 99

第五章 結論與建議
5.1結論 109
5.2建議 111

參考文獻 113
附錄 實驗設備圖片集

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