下坡之異重流又稱為downflow，可以觀察到大規模不穩定發生在高坡度而且在低坡度不存在劇烈的不穩定。根據線性穩定度分析，我們發現兩個不穩定的現象在0°<θ<90°。上方的不穩定是在小角度的地方，而下方的不穩定則發生在高角度的部分，存在一個過渡的角度θ_E≈0.04°，越過這個角度不穩定就會變換。而我們的研究結果與之前的文章有些符合。臨界雷諾數，當低於該值流體是穩定的。坡底的作用力有兩個，一個是，在重力在下坡方向的分力是驅動downflow，另一個則是重力發生在法線方向，可以達到分層的效果。因此減小坡度可以達到更明顯的分層效果，而導致臨界雷諾數提高。當downflow傳播在足夠低坡度的運動過程中，低驅動力且分層效果強化可能使downflow轉換成另外一個狀態而且不容易維持流體的擾動，這便是異重流的最終階段。

Gravity currents transport on the slope, also called downflow. We can observe a larger scale instability on the high slope, and on the low slope there is no violent instability. According to the linear stability analysis, we find two branches of the stability at  . The upper branch occurs at the low slopes and lower branch occurs at the high slopes. There exists a transitional slope angle,  . Over this angle, the instability will be transitional. Our research conclusion conforms with previously reports. At lower Critical Reynolds number, the flows will be stable. Gravity plays a dual role. On one hand, the downslope component of gravity acts as the driving force for downflows. On the other hand, the wall-normal component of gravity acts for the stratification effect. Therefore, decreasing slope angles can be cause stronger stratification effect and increase critical Reynolds numbers. When a downflow propagates onto a sufficiently low slope angle, the low driving force and intensified stratification effect would make the downflow less prone to sustain a turbulent state of flow, which ultimately leads to the final stage of a gravity current event.

目錄	        1
圖目錄	        2
第一章 緒論	3
1.1 前言	        3
1.2 研究動機與目的	4
第二章 文獻回顧	5
第三章 研究方法	8
3.1線性穩定分析	8
3.1.1基流	11
3.1.2擾動方程	13
3.2 數值方法	16
第四章 結果與分析	19
第五章 結論與建議	25
5.1結論	        25
5.2總結	        27
參考文獻	        28
附錄	        32
圖3.1   downflow的模型圖	         9
圖3.2   穩態速度和剪應力曲線圖	12
圖4.1   downflow的中性穩定曲線	21
圖4.2   各角度的臨界雷諾數	        22
圖4.3   成長速率與波數的關係圖	23
圖4.4   特徵方程式 u' 和 w'	24

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