Persistent patterns in transient chaotic fluid mixing

Abstract

Chaotic advection^1,2,3 of a fluid can cause an initially inhomogeneous impurity (a passive scalar field) to develop complex spatial structure as the elements of the fluid are stretched and folded, even if the velocity field is periodic in time. The effect of chaotic advection on the transient mixing of impurities—the approach to homogeneity—has been explored theoretically and numerically^4,5,6,7,8. A particularly intriguing prediction is the development of persistent spatial patterns, whose amplitude (contrast) decays slowly with time but without change of form. Here we investigate these phenomena using an electromagnetically driven two-dimensional fluid layer in which one half is initially labelled by a fluorescent dye (the passive scalar). We observe the formation of structurally invariant but slowly decaying mixing patterns, and we show how the various statistical properties that characterize the dye concentration field evolve with time as mixing proceeds through many cycles. These results show quantitatively how advective stretching of the fluid elements and molecular diffusion work together to produce mixing of the impurity. We contrast the behaviour of time-period; c flows and identically forced but weakly turbulent flows at lower viscosity, where mixing is much more efficient.