Mixing measures for a two-dimensional chaotic Stokes flow

Abstract

The effectiveness of a large number of protocols for mixing in a two-dimensional chaotic Stokes flow, according to a variety of measures, is investigated. The degree to which the various mixing measures are correlated is computed, and while no single protocol simultaneously optimises all measures, it is found that a small subset of the protocols perform well against most measures. However, it is difficult to elicit general rules for selecting effective protocols: for example, superficially similar protocols are found to exhibit considerably different mixing capabilities. The results presented here suggest that the selection of effective protocols by `sieving' (i.e., by successively eliminating candidate protocols that fail increasingly discerning mixing measures) may be ineffective in practice.