- 學位論文
顆粒沈降於密度層化環境下的流體不穩定性探討
Study of instabilities of particle-laden fronts in continuously stratified environments
摘要
穩定分層環境中懸浮層的沉降現象普遍存在於海洋與環境流動之中，而沉降模式可分為沈降驅動或雙擴散不穩定現象，其中這兩種不穩定現象是由完全不同的機制引起的。在理論及數值文獻中，懸浮層的密度剖線及層化環境經常地被描述為一個誤差函數。由於懸浮層的誤差函數具有極窄的寬度，使得在沉降時會產生鼻子狀的密度剖線，並致使產生不穩定現象。然而，雖然可以在實驗室中獲得類似鼻子的輪廓，但在海洋環境中卻不容易觀察到。為了模擬海洋環境條件，本研究中的背景環境設置為線性且穩定的連續剖面，而懸浮層的剖面在界面處設置為不連續的。我們不僅通過使用線性穩定性分析推導出理論模態，而且總結沉降模式可以藉由整體密度比率來分類。沉積作用的發展過程可分為不穩定的第一階段和第二階段。對於第一階段的不穩定性，沉降模式可以很容易地根據主導模態和密度比率之間的關係分為三個型態，即瑞利-泰勒不穩定、過渡狀態和雙擴散對流。由於中性浮力高度的限制效果，第二階段的不穩定性是由羽尖兩側不同的背景梯度引起的，且在背景擴散率較小的情況下可以觀察到模態的顯著變化。另一方面，一個經過修改的尺度法則被提出來改善最終階段中沈降模式的分類。最後，我們還針對整個流體不穩定的階段作混合效率的討論。在含顆粒層中，具有大粒徑的顆粒可以在流體塊到達最大侵入高度之前提升混合效率。然而，最終的沉降模式主導了混合過程的效率，而最有效的混合過程是由雙擴散對流引起的。
並列摘要
The settling of suspension layers in stably stratified environments is ubiquitous in oceanic and environmental flows, and the pattern of the sedimentation can be classified as the settling-driven or double-diffusive instabilities, both instabilities are induced by totally different mechanisms. In theoretical and numerical literature, the density profiles of the suspension layer and the stratified environment are generally described as an error function. The nose-like profile, caused by the extremely thin width of the error function, is performed by the settling suspension layer, causing the instabilities. However, while the nose-like profile can be achieved in a laboratory, it can not be easily observed in an oceanic environment. To resemble the conditions of an oceanic environment, the background environment in the present study is set as a linearly and stably continuous profile, and the profile of the suspension layer is set to be discontinuous at the interface. We not only derive the theoretical mode by using linear stability analysis but also conclude that the sedimentation pattern can be classified by a bulk density ratio. The development process of the sedimentation can be divided into the first and second stages of the instabilities. For the first stage of the instabilities, the sedimentation pattern can easily be classified by the relationship between dominant mode and density ratio into three regimes, namely Rayleigh-Taylor instability, transition regime, and double-diffusive convection. Due to the confinement effect of the neutral buoyancy height, the second stage of the instabilities are induced by the different background gradient between both sides of the plumes＇tips, and the significant shift of the mode can be observed by the case with less background diffusivity. On the other hand, a modified scaling law is also proposed to improve the classification of the sedimentation pattern in the final stage. Finally, we discuss the mixing efficiency during the development process of the instabilities. The particle-laden layer with a large settling velocity can enhance the mixing efficiency before the fluid parcel reaches the maximum penetration height. However, the final pattern of the sedimentation dominates the efficiency of the mixing process, and the most efficient mixing process is induced by double-diffusive convection.
參考文獻
延伸閱讀
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