渦量動力學一直是流體力學中一門相當重要且基礎的研究課題。特別是在非線性方程的因素下，會產生多形式的差異解，多重解中包含穩定與不穩定狀態解，更是引起許多學者的廣泛研究探討。而這些問題的研究結果，可運用到許多工程問題的應用上，如薄膜覆蓋沈積的製程上。
本論文採用長寬比為1.96的二維的矩形體，其以具溫度梯度雙板反向平行等速移動來驅動流體去模擬薄膜覆蓋製程的流場的變化情況。首先採用連續法與線性穩定度分析於流場的探討上，以求得整個系統在特定的長寬比下，無溫度梯度流場隨對板移動速度的改變，並建構出整個系統的分歧圖，隨後加入各流場隨時間的穿遞變化，再次驗證流場穩定度，最後再加入溫度梯度對原流場的影響，對流場的散熱效應加以討論。
由連續法的計算結果，以Re為控制參數下，在雷諾數2000以下存在五種流場形態及其流場穩定度，其中三種形態為穩定流場，另發現在對稱性流場與非對稱性流場分界的pitch-fork分歧點，而在以Gr為控制參數下的計算結果，建構出流場形態隨溫度梯度強弱的轉變，再區分出穩定流場的存在區域，在穩定流場的熱傳遞效率比較上，cat’s eye flow明顯優於two-vortex flow。

The dynamics of vorticies is a fundamental topic in fluid mechanics. Due to nonlinear characters in governing equations, multiple flow solutions are found in a two dimensional cavity flow accompanied by heat transport. In particular, the instability problems of these multiple flow solutions always attract many scholar’s investigation. The results of the basic study on the stability analysis may find applications in engineering, e.g. the processes of film coating.
We use a cavity model of aspect ratio 1.96 in this study. The two lids on the top and the bottom of the cavity with temperature gradient move in opposite direction. A continuation method and linear stability analysis are used to obtain a comprehensive bifurcation diagram on the cavity flow and the flow transition process is used to confirm the flow stability. Finally, the flow with temperature gradient in the cavity is investigated.
Three symmetric flows and two asymmetric flows are found for different continuation parameter on Re. Three of them are stable flows. A pitch-fork bifurcation point is determined to distinguish between symmetric flow and asymmetric flow. For different continuation parameter on Gr, the heat transfer effect in cat’s eye flow is much stronger than two-vortex flow.

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