MIXING IN GLOBALLY CHAOTIC FLOWS - A SELF-SIMILAR PROCESS

The first half of this paper reviews mixing in chaotic flows. The sine -flow is employed as a two dimensional example to demonstrate techniqu es used for characterizing mixing behavior. Several manifestations of self-similarity are readily apparent. The results of tracer mixing sim ulations demonstrate a self-similar, iterative development of partiall y mixed structures in the flow. The spatial distribution of mixing int ensities present in the flow is examined via computation of stretching . The probability density function (PDF) of the logarithm of stretchin g values reveals a Gaussian distribution over the central spectrum of stretching intensities for the globally chaotic case, but contains two peaks for a case with coexisting chaotic and regular regions: a broad Gaussian peak for higher stretching values, corresponding to the chao tic region, and a sharp peak of low stretching values corresponding to the regular regions. The self-similar stretching distributions can be collapsed to a single invariant distribution using an appropriate sca ling based on the central limit theorem. The folding processes in the flow are examined through curvature calculations; PDFs for curvature c ollapse to time invariant self-similar distributions without the need for scaling. Direct computation of the striation thickness distributio n (STD) provides the most fundamental (and computationally most expens ive) measure of mixing; STDs develop a self-similar form that can be c ollapsed to an invariant distribution using a simple scaling. The seco nd half of the paper focuses on a real, three-dimensional mixing syste m: the Kenics static mixer. Two alternate configurations of the Kenics mixer were analyzed: one in which elements have alternating right-han ded and left-handed twist (R-L) and a second in which all elements hav e right-handed twist (R-R). Poincare sections as well as experiments i ndicate that the R-L configuration is globally chaotic, while the R-R configuration contains significant segregated, regular regions. Stretc hing histories of material elements in the two flows were computed, on ce again revealing self-similar distributions that can be collapsed to an invariant limit using a scaling based on the central limit theorem .