Lamination, stretching, and mixing in cat's eyes flip sequences with varying periods

Abstract

This article explores the lamination, stretching, and mixing produced by sequences cyclically permuting a cat's eyes flow structure to stir the flow. Such sequences are experimentally driven by electromagnetic forces. Their intensity is kept constant between experiments while the duration of the forcing cycles varies over a decade. Mixing observations show that the mixing processes evolve from a seesaw stirring for short cycles (due to the regular rotation of the principal direction of the cat's eyes flow structures) to a cat's eyes stirring where the seesaw stirring is complemented by the rolling occurring within eddies. The transition from seesaw stirring to cat's eyes stirring is related to the persisting of the cat's eyes flow structure during one turnover time before it is flipped. Reference cases such as steady and random forcing configurations complement this exploration for comparison with the cat's eyes flip sequences. It is shown that cat's eyes flip sequences are efficient and possess baker-like mixing properties with an exponential growth for the length of interfaces and their lamination. The exponential coefficients of the stretching and lamination rates are conserved when varying the duration of the mixing cycles and using the generic cat's eyes flow turnover time as the reference of time to build these exponents. In particular, the stretching coefficients can be assumed as nearly constant when compared to the topological entropy which varies over a decade. This is attributed to the ability of the cat's eyes flip sequences to integrate lamination during the stirring sequences. This integration of the lamination compensates the reduction of flow's unsteadiness when increasing the duration of the mixing cycles so as to conserve a good stirring and mixing performance. Therefore, the lamination, stretching, and mixing of the cat's eyes flip sequences are robust to changes of the cycles’ duration.

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