Control of stretching rate in time-periodic chaotic flows

Abstract

In this study we consider a method for enhancement of mixing in time-periodic laminar flows. The stretching rate along unstable manifold of the chaotic flow is considered as a quantitative criterion of mixing quality. Optimal control theory is applied for improving the stretching rate in a prototypic cavity flow. It is demonstrated that the optimal flow field tends to stretch the infinitesimally small vectors that are distributed along the material interface. The higher is the length of a vector at the final moment of time the more effective is the stretching along this vector. It is shown that a high stretching rate does not imply uniformity of mixing. In the periodic flows with the relatively short periods the chaotic region does not span over the entire flow, and the increase of a stretching rate in the chaotic region leads to expansion of regular islands. Thus, the proposed method for enhancement of mixing is applicable for the flows without regular unmixed islands.