狹長矩形穴槽潛流流體之混沌攪拌

Chaotic fluid stirrings with creeping flows in a very long rectangular cavity

本研究利用既有流場速度理論解與數值積分技術，探討狹長矩形穴槽內流體之慢速攪拌，計算結果可以清楚呈現流體質線之時變歷程。雖然本文主張之數學分析僅能獲得局部解，無法適用於整個流域，惟結果仍可清楚呈現穴槽中心附近複雜之流型。當穴槽二短板做週期式來回滑動時，流體質團(線)可同時承受摺疊、彎曲、延展三種作用，且週期愈長此等作用愈劇，有助於流體做混沌攪拌。

The present study aims to investigate a slow fluid stirring in a very long rectangular cavity. The theoretical solutions of the velocity field that had been obtained previously and numerical integrations were used. Based on the results of computation, the evolutions of the fluid materials are clearly reported. Although only the local solutions have been found that can not be applied on entire flow domain by virtue of the mathematical analysis, the complicated flow patterns near the center of the cavity are still clearly illustrated. When the two shorter ends are periodically slid back and forth, the fluid materials are transported featuring phenomena of folding, bending and stretching. Furthermore, longer periods of the protocols of the sliding velocity variation are observed to favorably create chaotic fluid stirrings with the enhancements of the three actions mentioned previously.