Based on vortex-velocity method, the control equations of laminar flow of high vicious fluid in a square cavity driven by the continuous periodic vibration motion of upper and bottom lids are derived. And then the numerical solution of the transient velocity field which is based on the superposition method is obtained by using the finite volume method. The motion of the passive tracer is numerically integrated by the fourth order adaptive Runge-Kutta scheme. The results show that when the frequency is below 0.1Hz, the mixing is controlled by the globally chaotic mixing. While the frequency increases to between 0.1 Hz and 0.5 Hz, the quasi-periodic islands occur in the region of chaotic motion. After the frequency exceeds 0.5Hz, the mixing degenerates into the regular laminar mixing. Through the contrasts of Poincaré sections, it is proved that the frequency not only has the effect on the scales of KAM islands, but also dominates the mixing transition from the globally chaotic mixing to the traditionally regular laminar mixing.
A 3D analytical model for vortex velocity field based on spiral streamline pattern