| 摘要: | 異重流又名稱為GRAVITY CURRENTS，是流體中因密度差異所產生的流動 現象。流體溫度的變化、溶解或懸浮的物質，皆會造成密度的變化而形成流動現象。 目前，台灣水庫的水利排砂的操作和泥砂淤積的預測都與異重流的研究緊密相關。 懸浮泥沙的入流進入水庫，即因密度較大而形成異重流在水庫底部往下坡運動。利 用異重流幫助水庫水利排沙的操作，中國小浪底水庫即是一個具體的例子。 除水 庫操作外，有關異重流之學門廣泛，如物理海洋學中研究大陸棚因泥砂懸浮形成 之異重流產生的地形變化，以及大氣科學中研究溫度差異的氣團之運動行為。 筆者於2009年榮幸獲得國科會補助為期一年的異重流研究計畫，內容為探討 不連續入流的異重流在斜坡上運動的特性，目的為要建立一適用大區域異重流估 算的低階模型。計畫執行至今，已經從理論證明傳統的低階熱體模型(THERMAL THEORY)有修正的必要，主因模型中唯一之捲入參數不足完整描述此類異重流的 特性，筆者所指出加入新的捲出參數即補正傳統模型的缺憾，本創新概念為此類 異重流研究中之先驅(Dai & Garcia, 2010; Dai, 2010)。 本次申請計畫接續筆者所指出新的異重流觀點，除了從理論證明外，並從直 接數值模擬及水槽實驗兩種方法驗證並且量化所引入的新參數，在此名之為捲出 參數。本計畫重點將探討捲出參數隨底床坡度、雷諾數、及起始重流體之幾何形狀的 關係。本計畫之研究成果將可以幫助相關領域更瞭解不連續異重流的運動特性，其 中最具代表性的是量化的捲出參數隨不同環境條件下的變化關係。此關係不但在學 理上有創新的貢獻，更可以使低階的異重流模型便於實際應用。 直接數值模擬(DIRECT NUMERICAL SIMULATION)為目前異重流計算研究中 最準確的計算概念，解析異重流中最大及至最小的運動尺度，避免使用紊流模型， 提供可信度最高的數值實驗資料，來驗證低階模式並與實驗結果比較。2009年第 一階段的計畫，筆者與美國佛州大學異重流研究團隊合作，採用最高精度之譜方 法來進行異重流計算。目前適用於斜坡上異重流的平行計算及後處理程式已經由筆 者完成修改、編寫及測試，計算的結果印證筆者之理論證明(Dai et al. 2009)。本次 申請的計畫為期預計兩年，接續目前進行的工作。第一年預計將繼續修改並擴充計算及後處理程式來探討低密度異重流(BOUSSINESQ FLOW)在不同坡度、雷諾數、 及起始重流體之幾何形狀下的運動情形。直接數值計算的結果可以量化捲出參數、 並與實驗結果比較。第二年預計更進階修改計算程式以用於高密度之異重流(NONBOUSSINESQ FLOW)，並探討計算的結果並與低密度之異重流進行比較。 異重流之透明水槽實驗為目前學術研究上廣泛使用的方法。筆者榮幸得到英國 劍橋大學及美國加州大學的技術協助，已經完成同等級實驗硬體設備的採購及設 計製造，並進行初步的實驗測試。本次計畫預計兩年，第一年將進行低密度異重流 之實驗，探討坡度及起始重流體之幾何形狀對流動的影響，同時並撰寫影像後處 理程序用來分析影像擷取軟體得到的結果。第二年預計進行高密度異重流之實驗， 並預備利用顆粒顯影技巧測量異重流運動的速度場。水槽實驗得到的結果，可以驗 證直接數值模擬的正確性，更可提供率定捲出參數與其他變數關係的重要資料。此 研究之成果可建立更準確之異重流低階模型，與完整之參數關係供低階異重流運 動模擬之參考。 目前異重流的研究在台灣及國際間皆有高度的興趣。本研究計畫之精神為突破 傳統低階模型的限制，引入代表性的參數有效改進低階模型，並已得到此領域之 學者肯定。預計研究所得到之參數與其他變數的關係更能使改進的低階模型便於應 用在相關問題上。本研究所建立的低階模型，不僅適用在水庫的異重流問題，將可 應用於物理海洋、大氣科學等相關問題的基礎模型。另外，研究計畫所採用之數值 模擬數學方法和透明水槽定量實驗皆為當今研究最先進之方法，在計畫的過程中 使参與研究之學生得到訓練的機會，並使國內此領域之科學研究在國際上打開知 名度。
Gravity currents, also known as density currents, are flows driven by a density difference. The density difference can be attributed to a number of reasons: temperature differential and dissolved or suspended materials. As an example, the sedimentation of reservoirs in Taiwan is related to gravity currents. Gravity currents can also be controlled otherwise to remove sediments in a reservoir, and Xiaolangdi reservoir in China sets a good example in the field of hydraulics. In addition to operation of reservoirs, gravity currents find their applications in other disciplines, e.g. morphology in continental shelf and gravitational convection in atmospheric sciences. I am currently supported by the National Science Council of Taiwan to study the motion of gravity currents off a slope for a year. The focus is to investigate the characteristics of such gravity currents and to establish an accurate low-dimensional model good for convenient large scale modeling. To this point, I have shown that the class thermal theory needs to be improved, since the only parameter, entrainment coefficient, is not sufficient to describe the gravity current dynamics. The new introduced parameter, detrainment coefficient, makes up the deficiency of the original thermal theory (Dai and Garcia 2010; Dai 2010). This proposed study aims at continuing on the new perspective of gravity currents. In addition to theoretical modeling, it is proposed to verify the concept and quantify the introduced parameter using direct numerical simulations and Plexiglas flume experiments. The emphasis in this project will be on the relation between other parameters, such as the slope, Reynolds number, initial aspect ratio of dense fluid, and the gravity current dynamics. This relation will be new invented and will facilitate the applications of the improved low-dimensional model. The proposed project will use direct numerical simulations (DNS) of gravity currents and Plexiglas flume experiments. The time of project is proposed for 2 years. In the first year, we will modify the simulations to study the influence of slope, Reynolds number, and initial aspect ratio of dense fluid for Boussinesq gravity currents. At the same time, we will conduct flume experiments and finish analyzing the results. In the second year, we will study the non-Boussinesq gravity currents using flume experiments while preparing to conduct particle tracking velocimetry (PTV) and developing the code for DNS of non-Boussinesq gravity currents. The research will provide an accurate low-dimension model for gravity currents on sloping boundaries, and the results obtained from the numerical and experimental studies will benefit the applications of the improved lowdimensional model. The research of gravity currents draws much attention worldwide. The proposed project has improved the classic theory and introduced a new perspective of research. The results expected from the project not only will facilitate the applications of the improved low-dimensional model, but also will have impact on the study of gravity currents in reservoirs, continental shelf, and atmospheric dynamics by forming the basis of modeling. Finally, DNS and Plexiglas flume experiments are both state-ofthe- art methods for research in gravity currents. The proposed project will allow the participating students the opportunity to learn and interact with internationally recognized scholars. |
