本文旨在探討波浪通過凹槽內部分層流體時，其分層流體之運動和演變行為。藉由物理實驗模型量測和數值模擬對此物理問題進行深入之研究。物理實驗模型量測主要是利用高解析度攝影分別擷取粒子和雷射染劑空間分布之影像，其影像再透過影像處理法分析，遂而得到瞬時流場和流體傳輸之空間分布結果; 數值模式則是利用三維數值模式 (TRUCHAS)，藉由求解黏性流體運動方程式(Navier-Stokes方程式) 以計算其數值流場。再利用流體體積法 (volume of fluid method) 模擬表面波運動、界面波運動和流體傳輸等行為。
在規則波通過凹槽內分層流體之實驗量測和數值模擬結果中，皆能觀察到兩種不同類型之界面波運動行為，分別為行進波型態 (traveling waves) 和部分駐波 (partial standing waves) 型態。藉由數值模式更進一步的分析，探討界面波不同運動型態之機制。分析結果可歸納為兩要點：1. 當凹槽背風和迎風邊壁上方自由液面之相位接近180度時，會使界面波運動呈現部分駐波型態2. 當部分駐波型態界面波運動達到內波共振條件時，則可能發生高於表面波振幅之部分駐波型態內波行為。此型態之內波運動會在界面波周圍引發較為劇烈之速度場，對於底床掏刷和結構物破壞深具影響性。此外，透過界面波和表面波頻率分析，可知表面波之非綫性效應對於界面波運動和振幅放大率之影響也為重要因子。
孤立波通過凹槽內分層流體時，造成的密度流演變行為亦透過物理實驗模型量測，以及數值模擬探討密度流傳輸行為和流場變化特性。當孤立波通過凹槽內分層流體時，凹槽迎風面邊壁周圍之密度流會被渦流帶出凹槽並朝自由液面方向移動。當增加凹槽內部流體的密度、降低入射波非綫性或縮小凹槽寬度，其密度流上升之高度皆會隨之降低。此外，當密度流之密度較大或入射波非綫性較低時，密度流會因重力影響而朝上游方向移動，形成類似異重流之型態。入射波非綫性和凹槽寬度之效應也可能使得渦流和密度流被限制於凹槽內部，而不會朝自由液面方向發展。此種因為波浪所造成的密度流演變之現象，是影響海洋中營養鹽、海洋生態和漁獲分布的因素之一。目前之數值模擬結果亦和實驗量測結果進行詳細的驗證以增進其模式可信性，並進一步利用數值模式考量更多非綫性波浪條件，最後透過量化分析的結果，對非綫性和密度差對於密度流傳輸之影響做更深入之探討。
本研究主要是針對波浪通過凹槽內部分層流體所致之內波運動、密度流傳輸和流場變化進行深入探討。透過高解析度的實驗量測和數值模擬配合兩個不同議題 (孤立波和規則波)，則能夠對此物理現象做詳細之論述且瞭解目前數值模式對此物理問題之適用性。期望對未來相關之工程問題能夠有所裨益。

This dissertation presents an investigation on the dynamic response of density-stratified fluid within a trench under water waves. For each topics of interest, numerical simulations are supported by carefully conducted experiments. In laboratory experiments, the free surface wave and interfacial motion are captured using a CCD camera and image processing. The dense fluid transport and flow field are measured by laser-induced fluorescence (LIF) and particle image velocimetry (PIV) techniques, respectively. The three-dimensional numerical model Truchas is employed to trace the interfacial motion, dense fluid transport using the volume of fluid method. Comparisons between measurements and numerical results are performed for the free surface elevation, interfacial motion, the dense fluid transport and flow field.
Regular waves over density-stratified fluid in a submarine trench is first investigated. Both the numerical and experimental results show two types of interfacial motion, namely, partial standing wave patterns and travelling wave patterns. The numerical model is then employed to study the mechanisms of the different modes of interfacial motions (partial standing/traveling waves) and their corresponding amplification factors (external/internal modes). It is shown that the partial standing wave patterns are easily generated when the motion of the surface waves is 180 degrees out of phase at the two sides of the trench. However, the existence of partial standing wave patterns does not mean partial standing internal waves occur. The partial standing internal waves are triggered as internal wave wavelengths reach resonant condition. Furthermore, the ratio of the interface wave height to the surface wave height decreases with wave nonlinearity, suggesting that the nonlinear effect may significantly change the interfacial wave motion. It is found that the excited pairs of counter-rotating vortices around the interfacial wave can induce a large velocity in the lower layer for the internal mode, indicating that bottom erosion can be enhanced in this manner.
Next, solitary wave over density-stratified fluid in a submarine trench are investigated. A new experiment was conducted to measure the dense fluid transport and flow field. The dense fluid transport and flow field characteristics are discussed in the experiments. The height of the transported dense fluid over the left trench wall decreases as the dense fluid density increases, wave nonlinearity decreases, or trench width decreases. Furthermore, the dense fluid can be transported toward the upstream of the trench when a denser fluid or lower wave nonlinearity is considered. Some dense fluid can be trapped inside the trench due to the effect of lee side trench wall under the high wave nonlinearity and narrower trench width. Comparisons between measurements and numerical results are performed for the free surface elevation and the dense fluid transport and flow field. Good agreements are obtained. The calibrated model is then used to examine the transport processes of the various dense fluids and quantitative analyses also demonstrate that either density of dense fluid or wave nonlinearity significantly affects.

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