Spatio-temporal aspects of chaotic stirring: optimizing injection in the aperiodic wake of a blade

The present study focuses on the chaotic advection characteristics of aperiodic wakes behind stirring blades at low Reynolds numbers. Accurate numerical solutions of the flow are acquired and found to exhibit temporally chaotic characteristics, since interrogation of recorded time series shows positive Lyapunov exponents. The correlation of vortical mechanisms and their evolution in parameter space, along with the intensity of chaotic mixing, for various locations of release of tracers is discussed. The effect of major and minor vortical formations is illustrated by various Lagrangian depictions of this flow. More in-depth understanding of the mechanisms that drive the chaotic advection is obtained through the isolation of saddle-type stagnation points in the Eulerian velocity fields. The tracking of deformations of the structure of such points yields controlling sets for the chaotic advection, corresponding to finite time stable and unstable manifolds correlated with these trajectories.