| 摘要: | 異重流又名為GRAVITY CURRENTS或DENSITY CURRENTS，是因密度差 異所形成的流動現象。流體溫度的變化、溶解或懸浮的物質如鹽及泥沙，皆會造成 密度的差異而產生流動現象。近年來，在台灣異重流的研究與水庫的操作和維護緊 密相關。夾帶懸浮泥沙的入流進入水庫，即因密度較大而在水庫底部形成異重流往 下游方向運移。 瞭解異重流在斜坡上的運動特性，可以有效幫助水庫水利排沙的操作，中國 小浪底水庫操作即是一個具體的例子。目前，異重流在斜坡上運動的研究可分為連 續入流與不連續入流兩類。連續入流的情況下，也可能會形成類似不連續入流所產 生的流況。因此研究計畫預訂從不連續之異重流在斜坡上運動著手，探討異重流在 此情況中之運動特性，最主要觀察異重流運移的速度以及與清水混合、分離的情形， 並與目前之理論低階模型做一具體驗證。 現階段廣泛使用之不連續異重流在斜坡運動的低階模型是由Beghin, Hopfinger, and Britter (1981 J. Fluid Mech.)所發展的熱體理論(thermal theory)。此一 模型的適用性近年來亦引發許多的學術探討，因為原始的熱體理論無法定量的準 確描述異重流在斜坡上的運動特性。筆者於2008年觀察異重流在斜坡的運動情形 引進一新的捲出量化參數，並以數學理論證明此參數所代表之異重流物理現象足 以解釋原始的熱體理論所無法定量準確描述的缺憾。 此研究計畫即從此新觀點上出發，預定以直接數值模擬及水槽實驗兩種方法 來驗證異重流在斜坡上運動的特性、提供最新的研究資料用以量化此參數、探討此 參數所代表之物理特性在異重流運動中的變化、及研究影響此物理特性的各種成因。 研究之成果可提供更準確之異重流低階模型，此模型將適用於大區域異重流運動 之評估及沉砂淤積運移之估算。 直接數值模擬為目前流體力學研究已知最準確的計算概念，利用龐大的計算 資源，避免使用紊流模型，直接數值解析連續及動量方程，並含括紊流中巨觀及 微觀的尺度。直接數模提供可信度最高的計算資料，並經常用來校正低階模式或實 驗結果比較。本研究第一步預定採用最高精度之譜方法來進行異重流直接數模計算， 計算結果可用來分析流動現象、量化參數、提供水槽實驗設計之參考。 異重流之水槽實驗為目前廣泛使用觀察異重流特性的方法。利用染色劑的透光 度，可以定量的描述異重流的運動特性，包括速度、混合、捲出等物理量。此實驗之 關鍵在製作一透明水槽、提供均勻投射光源、建立影像擷取分析程式。目前影像分析 的部分筆者得到劍橋大學的技術協助，願意提供使用此一分析軟體。本計畫第二步 即為進行水槽實驗，定量觀察異重流運動特性，並與直接數值模擬結果進行比較。 目前異重流的研究在台灣產、學界引起高度的興趣。高精度之直接數值模擬和 透光水槽實驗皆為目前國際力學界研究此課題最先進之方法。此一研究計畫可以突 破異重流在斜坡上運動之原始理論的缺憾，提供最新之數值及物理實驗數據佐證， 建立更準確及適用之低階模型供業界參考，提供學生學習此先進方法並與國際學 者有互動交流的機會。 Gravity currents, also known as density currents, are buoyancy-driven flows generated by a density difference. The density difference can be due to a temperature differential, dissolved or suspended materials, e.g. salt and sediments. In recent years, the research in gravity currents has drawn significant attention concerning the operation and sedimentation management of reservoirs in Taiwan. Understanding the characteristics of gravity currents on sloping boundaries can effectively improve the operation and sedimentation removal in reservoirs, e.g. the success of Xiaolangdi reservoir in China. Up to this point, the research of gravity currents on sloping boundaries can be divided into two categories based on the inflow condition, i.e. continuous buoyancy inflow and instantaneous (discontinuous) buoyancy release. Even in the continuous inflow case, occasionally the gravity currents generated can be similar to the discontinuous case. Therefore, we start the project with discontinuous gravity currents on sloping boundaries. The focus will be on the characteristics of gravity currents on sloping boundaries, including the front velocity, entrainment, detrainment, and comparison against the low-dimension thermal theory. The broadly used thermal theory was developed by Beghin, Hopfinger, and Britter (1981 J. Fluid Mech.). However, the original thermal theory has drawn attention recently since it cannot accurately predict the gravity current motion; in fact, it only qualitatively captures different phases of motion. I (Dai and Garcia 2008 Dynamics of Atmospheres and Oceans) have observed the gravity currents on sloping boundaries and introduced a new parameterization, and have proved theoretically that the mechanics represented by the new parameterization explains the quantitative difference between the original thermal theory and the experiments. The project is based on the aforementioned epiphany and followed by the Direct Numerical Simulations (DNS) and gravity current experiment in a transparent flume (dye experiment). Using these two methods we will acquire the latest data for verification of gravity current motion on sloping boundaries. More specifically, we may quantify the parameters in the low-dimension thermal theory and study how these parameters are influenced by other conditions. The research will provide an accurate lowdimension model for gravity currents on sloping boundaries, which is suitable for large-scale modeling of gravity currents and the prediction of associated accumulation and transportation of sediments. DNS depends heavily on computational resources without modeling of turbulence and provide the most accurate computational data often used for verification of low-dimension models and comparison with experiments. As the first part of the project, we are planning to implement the DNS of gravity currents on sloping boundaries with spectral methods. The data will be used for the analysis of flow characteristics, parameterization, and design of the transparent flume. The second part of the project is on the gravity current experiments in a transparent flume (dye experiment). The dye experiment is widely used for the observation of gravity currents and provides quantitative measures for the flow characteristics. The keystones in the experiment are the flume, uniform and seamless lighting, and the image processing software. I have the courteous permission from the Cambridge University to use their gravity current software. The acquisition of the flume and lighting is requested in the project. The experimental data will be compared against the findings from DNS. The research of gravity currents has drawn significant attention in Taiwan, both industry-wise and in academia. DNS and dye experiment are the two widely used advanced tools in the gravity current research community. The proposed project will make a breakthrough on the modeling of gravity currents on sloping boundaries. The data and improved low-dimensional model will provide evidence for the theoretical innovation and assist the large-scale modeling of gravity currents in reservoirs. The project will also allow the students to learn research skills and interact with internationally recognized scholars. |
