|Abstract: ||異重流又名為密度流，是流體中因密度差異所產生的流動現象。流體溫度的變 化、溶解的物質，皆會造成密度的差異而形成流動現象。水庫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 清水大而形成異重流沉入水庫底部往下坡運動。相關異重流之學門廣泛，除水庫操 作外，物理海洋學、大氣科學中皆有涉及。 筆者於2010年榮幸獲得國科會補助研究計畫，然因奉派代表學校前往美國姐 妹校進行交流及訪問合作，無法簽約執行。本次提出的計畫為筆者近年來異重流研 究系列的延續，內容為探討布氏異重流與非布氏異重流在水平面以及在斜坡上之 運動行為。布氏異重流基本假設密度差異微小，其對於運動行為之影響僅限於密度 差所造成之驅動力。然而實際上水庫中之異重流密度差異經常可達清水密度之一至 二成以上，此密度差異對於異重流運動行為之影響在控制方程式中除驅動力外， 慣性項及非線性之擴散項皆不可忽略。 筆者在此課題上投入相當心力，目前已從理論證明傳統的低階模型有修正的 必要，並指出新的修正方向，為此類別異重流研究中之先驅(Dai, 2010)，並且成 功地使用直接數值模型探討布氏異重流在斜坡上的運動特性(Dai et al. 2011)。最終 極的目的是為要建立一適用大區域異重流估算的低階模型以便利實際操作使用。本 次申請計畫延續筆者目前之研究，第一年計畫使用直接數值模型擴大探討布氏異 重流在不同坡度、雷諾數、及不同起始重流體之幾何形狀下的運動情形；第二年計 畫完成修改平行計算程式以用於探討非布氏異重流在不同坡度、雷諾數下的運動特 性，及其與布氏異重流之差異；第三年計畫探討布氏與非布氏異重流在層化環境 下的運動行為。 為提供實驗數據參考驗證以及訓練研究生需要，本計畫亦規劃異重流之透明 水槽實驗。本次計畫中，預計第一年同時進行布氏異重流之實驗，持續探討坡度及 起始重流體之幾何形狀對流動的影響，並撰寫影像後處理程序來分析影像擷取軟 體得到的結果；第二年預計進行非布氏異重流之實驗，並與計算及第一年實驗結 果比較；第三年預計完成設計及進行異重流在層化環境中運動之實驗。|
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. in physical oceanography and in atmospheric sciences. The proposed project is a continuation of the works published by the author. The focus is to investigate the characteristics of Boussinesq and non-Boussinesq gravity currents on horizontal and sloping boundaries. Boussinesq approximation states that the density difference is sufficiently small that it only plays a role through the buoyancy forcing term; in non-Boussinesq flows the density difference has influence on the inertia and non-linear diffusion terms, in addition to the buoyancy forcing term. It is understood that in reservoirs the density difference can oftentimes reach as high as 10 to 20 percent of the density of water, therefore consideration of non-Boussinesq flows is deemed adequate. The author has shown in theory the direction for improvement of classic lowdimensional thermal theory for gravity currents (Dai, 2010) and the characteristics of gravity currents propagating on slopes in direct numerical simulations (Dai et al. 2011). The ultimate goal is to establish an improved low-dimensional gravity current model which is accurate and efficient for large scale modeling. The proposed study spans three years. During the first year, we will continue to use direct numerical simulations for Boussinesq gravity currents and the influence of bottom slope, Reynolds number, and initial aspect ratio of heavy fluid. In the meantime, modification of the code for non-Boussinesq gravity currents will begin. The code modification will be completed and fully tested during the second year and production runs for non-Boussinesq gravity currents will be carried out. During the third year, we aim at studying Boussinesq and non-Boussinesq gravity currents in stratified environments. The author has successfully built the code for Boussinesq gravity currents on a slope, therefore graduate students will be ably assisted and supervised and finish the proposed work in time. For validation and training purposes, it is also proposed to carry out Plexiglas flume experiments. Thanks to the funding and technical supports from NSC, Tamkang University, Cambridge, and UCSD, a gravity current laboratory is successfully built and preliminary test runs are underway. The flume experiments are planned in parallel to the computational works. During the first year, the post-processing tools for acquired images will also be completed.