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中文摘要：
基于Galerkin方法，得到了方腔内高黏度流体上下盖振动拖动下的瞬时速度场近似解析解．建立了混合过程的动力学方程，采用4阶Runge-Kutta方法进行示踪剂数值积分追踪，得到了示踪剂构型随时间的变化．流场表现出对初始位置的敏感特性，证实了方腔内周期性混沌的存在．经过一定的时间后，同一位置出发的不同取向的流体微元，其界面拉伸增长随时间达到渐近分布，并随时间呈指数规律增长，长度之比不再发生变化．不同初始位置的示踪剂界面拉伸表现出自相似行为，示踪剂界面的几何特征也表现出了这种自相似性．
英文摘要：
Based on the Galerkin method, the approximate analytical solution to the transient velocity field is obtained for the high-viscosity fluid in a square cavity driven by the vibration of upper and bottom lids. Then, a dynamic equation describing the mixing process is proposed and the configuration variation of the tracer with time is obtained via the front tracking of passive tracer that numerically integrated by the fourth-order Runge-Kutta scheme. It is found that there exists periodic chaos in the square cavity because the flow field is sensitive to the initial position of particles, that when the micro-elements of fluid with different initial orientations are advected from the same initial position, the interface tension approaches to an asymptotical distribution mode and displays an exponential growth with the time, while the length ratio keeps constant, and that not only the interface tension of the tracers advected from different initial positions but also the geometrical configurations of tracer interfaces display a self-similarity.
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