垂直槽中受水平溫度與濃度梯度驅動的雙擴散不穩定性分析

Abstract

本文建立一套高的垂直槽且側向有溫度及濃度存在之系統，利用擁有濃度差異之流體與熱對流耦合之關係而產生的雙擴散對流效應。以往對自然對流的討論，不論是實驗或是數值模擬較多對於熱對流的注重討論，而鮮少有將溫度及濃度兩個因子加在一起討論的例子。故本文希望藉由在熱對流的情況下，加入濃度水平梯度，以觀察整個系統的變化及雙擴散對流的狀況。本文透過穩定性理論及MATLAB數值分析，收集數值並整理分析歸納出一系列的比較討論。 本研究旨在運用時間的線性穩定性理論，探討高垂直槽內，根據不同的普朗特數，路易斯數，溫度差及濃度差對此系統的不穩定性的影響。可以發現不管是固定普朗特數改變路易斯數，或是固定路易斯數改變普朗特數，得到的穩定性邊界圖皆會有三大區域，分別是溫度擴散區，濃度擴散區及鹽指區域。並可以看見鹽指區域顯而易見。 在得到三大區域的數據後，本研究著重分析三大區域隨著普朗特數及路易斯數的變化，更深入的研究三大區域波數的變化，並且在改變普朗特數時的溫度擴散區以及改變路易斯數的農度擴散區，皆發現波數的跳動，而這個跳動源自於波的型態的轉變，會由靜止穩態轉變為振盪型態。

This paper set up a system of high vertical slot imposed with horizontal thermal and salinity gradient.The Double-diffusion system coupling with different salinity and thermal convection.In the past, people discuss natural convection whether in experiment or in numerical,usually focus on thermal convection.Rarely focus on the interaction between thermal and salinity.Thus,this paper hope to observe how double diffusive affect the system by putting a horizontal salinity gradient into a thermal convection system.In this paper,we apply MATLAB numerical analysis and stability theory,gathering numerical values and analyzed the result we gain. We apply theory of linear stability and analyzed the effect of different Pr,Lewis number,temperature difference and concentration difference.We find that no matter we fixed Pr and changed Le,or fixed Le changed Pr,we can always get three region in temperature concentration map.They are respectively thermal dominant, salt-finger,salinity dominant.We can easily see the salt-finger area. After gathering the data of the former three region. We focus on how Pr and Le affect our temperature concentration map and the changes of wave number.We find that there is a jump of wave number when we change Pr in the thermal dominant area and change Le in the salinity dominant.This jump is derived from the changes of the wave type,from stationary mode to oscillatory mode.