連續入流之異重流在平面斜坡運動與分析

Abstract

本論文探討連續入流之異重流於底床坡度0度到15度上進行三維運動之實驗。當重流體被釋放於一斜面時，異重流流域形貌會類似於橢圓之形狀，由於在主流方向受重力驅動，並且在側向方向與環境流體混合，異重流會沿著斜坡運動並往側邊進行擴散。異重流前端之擴散形式取決於初始浮力通量、底床坡度以及重流體與環境流體間之密度差，在我們的實驗中，密度差設定在5.2%，屬於Non-Boussinesq之流動型態，藉由因次分析理論來說明異重流之流動特性。有趣的是，當底床坡度在6度以上時，角度對無因次參數π1=b/xf影響相對較小，始終處於相同的階數，其中b為異重流最大寬度，xf為異重流最前端之位置。另外，可以根據xf~b或是xf~〖((∆p/ρ0)g)〗^(-3/5)之關係做線性回歸得到虛擬原點之位置，而虛擬原點位置會隨著流量增大往上游移動。此外，角度對頭部高度成長及前端速度的影響比初始浮力通量還要來的大，但流量增加對於異重流側向的擴散有重要的影響。

Experiments for unconfined 3D gravity currents produced from continuous inflows propagating down an inclined bottom 0˚≦θ≦15˚ have been investigated. While the denser fluid is released propagating on the sloping surface, a gravity plume analogous to the elliptical shape is generated. The plume travels downslope and spreads laterally due to the gravitational force in streamwise direction and the entrainment in spanwise direction. The formation of front spreading depends on the initiating buoyancy flux, the slope of the bottom and the density difference between the heavy fluid and the ambient fluid. In our experiment the relative density difference is specified as the Non-Boussinesq flow regime, nearly 5.2%. Theoretical expressions were carried out to demonstrate the flow characteristics in experiments based on the dimensional analysis. Interestingly, on θ≧6˚ the effect of slope angle is relatively minimal, as indicated by the shape factor, π1=b⁄xf , that is consistently at the same order, where b is the maximum width of spreading plume and xf is location of effluent front. It is also known that the location of inlet point source, i.e. the virtual origin, could be determined based on linear regressions from the plot of xf~b or from the power-law relations between front location and relative density, xf~〖((∆p/ρ0 )g)〗^(-3/5). The location of virtual origin becomes further upstream as the flow rate increases. Additionally, from the relation xf~h, where h is the thickness of current head, it is noted that the growth of head thickness and the front velocity have a profound effect on the bottom slope rather than the buoyancy flux. With respect to the evolving flow motion, our results also showed that the growth of lateral spreading was dominated by the inlet flow rate.