以實驗探討旋轉流體中泰勒渦柱與池盆渦漩交互影響

Abstract

本研究以水工實驗的方式，探討具背景渦度下，泰勒渦柱與池盆渦漩之交互影響。實驗中以吸入法產生渦漩，流場上下為固體邊界，在旋轉水槽底板中心有一吸水孔，在其上方上板處設置一圓柱，用以產生泰勒渦柱效應。針對當Rossby number(Ro = Uin/fR)與Ekman number (Ek = ν /fR2)遠小於一時，探討泰勒渦柱與艾克曼邊界層之關係，比較在不同圓柱高度(h/H)與不同圓柱排列方法，渦漩流場之特徵，以及在暫態時產生的雙眼牆現象。 研究發現流場處於地轉平衡中時，流場可分成三區域：地轉平衡區、上下邊界層區與中心渦柱區。並只以五種路徑流入吸水孔：(i)在底部Ekman layer之中，逆時針進入水孔，(ii) 在底部Ekman layer之中，且穿越泰勒柱之下邊緣後隨Ekman pumping流向孔洞，(iii)在底部Ekman layer之上緣，欲流入中央時被泰勒柱阻擋後往上攀升，之後隨著頂部Ekman layer進入中央渦柱，(iv)在頂部Ekman layer中，在遇到圓柱後先繞著圓周面向下流至端面，而後進入中央渦柱流入水孔，(v) 高於底部邊界層受到泰勒渦柱的影響，開始向上旋轉攀升到高於圓柱端面，之後到達圓柱端面受此處之下沉流而進入中央渦柱。而越高的圓柱高度能使泰勒渦柱對流場的影響較強。而在不同圓柱堆疊、排列的實驗中，確認了因泰勒渦柱而出現的外牆位置，以及以流體流經泰勒柱下方時的運動情況。在暫態的實驗中，發現NP型態的改變方式有明顯的雙眼牆現象。

The study is aimed to investigate interactions between a Taylor column and a bathtub vortex in a cylindrical rotating tank experimentally. The tank has a central drain-hole at the bottom boundary and a top-down cylinder which bring the Taylor column effect placed on the top boundary. We are interested in the case of prominent Taylor columns and Ekman layers, i.e., when both of Rossby number and Ekman number are much smaller then unity. We also examine the effect of the ratio of h/H and the effect of stacking several cylinders. It found that for the flow at geostrophic balance, the flow domain can be divided into three region: geostrophic bulk, Ekman layer and central vortex core. Moreover, there are formed five routes of exit flow patterns: (i) the fluid sneaks through the bottom Ekman layer and flows direct into the drain hole; (ii) the fluid sneaks through the bottom Ekman layer and subjects to Ekman pumping, and downwards to drain hole; (iii)the fluid moves up due to the Taylor column effect, a part of these sneaks through the bottom gap, then subjects to Ekman pumping, and downwards to drain hole; (iv)the fluid through the top Ekman layer and sneaks through the top gap to the dran-hole by downward central vortex core;(v) the fluid moves up due to the Taylor column effect, a part of these sneaks through the top gap, then follow the path(iv). Moreover, the effect of Taylor column depends on the height of cylinder. The position of the outer wall is confirmed by the experiment of stacking cylinder. The double eyewall is found obviously on the NP transition process.