Fluid stirrings in a circular cavity with various driven boundaries

The present study deals with the complicated phenomena of fluid stirrings for the Stokes flows in a circular cavity. Two belts set on the boundary and periodically rotated with varied speeds construct the model flows. By means of the manipulations, the chaotic fluid stirrings prevail. Rather than to compute the finite-Lyapunov exponent in a local sense, a large number of fluid filaments are traced to quantitatively evaluate the averaged fluid stretch-rates in the cavity. Based on the results, several figures are provided to pre-estimate the overall fluid quantities that will be yielded when the installations and the rotations of the belts are specified. In general, the belts counter-rotated out of phase with longer periods are beneficial to the fluid stirrings. On the other hand, the variations of the fluid stretches with the belt installations are ambiguous. The maximum of the averaged fluid stretch-rates is about of 960 and 1.6 for the minimum.