以實驗觀察異重流於線性層化環境的運動

Abstract

本論文探討異重流於線性層化環境之流動現象。藉由重流體與水槽高度比值 h/H 及層化強度值 R 兩項控制因子，擬進行37組不同初始條件之定界交換水槽試驗。研究中所使用的福祿數(internal Froude number)定義為 Fr=V/NH，在不同控制條件下將有所差異。當 Fr 小於臨界值 1/π，稱之為亞臨界流況，表示異重流傳遞速度相較於流場中內波傳遞速度慢，過程將受到內波顯著的交互作用影響，終而被其超越，發生異重流前端速度震盪之現象；反之，Fr>1/π 則稱之為超臨界流況，表示異重流傳遞速度相較流場中內波傳遞來的快，於異重流受重力驅動之傳遞過程中，預期不會發生被內波超越之現象。根據理論推導及實驗結果顯示，當重流體與線性環境流體間密度層化關係顯著情況下，可將其簡化為均質異重流問題進行探討。經無因次參數分析之結論，於線性層化異重流問題中，給定不同初始條件( ρ_c ,ρ_0 ,ρ_b , h/H )，將可透過回歸關係式求得福祿數，且由福祿數與各個無因次參數之分析結果，能進一步算出下列之實驗物理量：Ⅰ. 異重流於初始等速區段之前端速度 Ⅱ. 初估異重流於初始等速區段所維持之距離與時間關係 Ⅲ. 於亞臨界流況中，初始頭部與第二頭部之頭峰間距 Ⅳ. 當異重流脫離等速區段後，在與內波交互作用下，其頭部前端加速之次數 Ⅴ. 所有線性層化異重流於脫離等速區段當下之初始頭部高度。

This thesis examines phenomenon on gravity currents propagating into a linearly stratified ambient fluid within 37 various initial conditions of lock-exchange experiments. The given ratio of the depth of released heavy fluid (h) to total depth (H) and the magnitude of stratification (R) have been found that it will dominate the internal Froude number, Fr=V/NH , when gravity currents in the initial constant phase. For subcritical flow, i.e. Fr is less than the critical value 1/π , it means that the constant initial speed of propagation of heavy gravity currents is less than internal wave. And it resulted in an oscillation of the velocity of its leading edge. On the contrast, for supercritical flow, i.e. Fr>1/π , the phenomenon is opposite. And the velocity decay of the current front is monotonic for the geometries tested here. According to the theoretical derivation and the experimental results, in the limit of large R, the current would resemble one penetrating into a homogeneous ambient fluid to simplify the problem. From the dimensionless analysis results, the Froude number can be calculated from the relevant independent variables, ρ_c,〖 ρ〗_0,〖 ρ〗_(b )and h/H . Moreover, as we get the Fr, it is possible to forecast certain characteristic quantities in this study which listed below, including the constant initial speed of propagation, the initial constant phase distance (X_tr) and time (T_tr), the regime (λ) between the current peak in subcritical flow, the number of speed-up times of current after separating from constant phase, and the initial current height (a) when the velocity begins to decrease for all of lock-release gravity currents in a linearly stratified fluid.