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Chaotic Mixing in a Torus Map

Jean-Luc Thiffeault·Stephen Childress
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Abstract

The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of constant scalar variance (for short times) to exponential decay (for long times). This transition is embodied in a short superexponential phase of decay. The asymptotic state in the exponential phase is an eigenfunction of the advection-diffusion operator, in which most of the scalar variance is concentrated at small scales, even though a large-scale mode sets the decay rate. The duration of the superexponential phase is proportional to the logarithm of the exponential decay rate; if the decay is slow enough then there is no superexponential phase at all.

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Jean-Luc Thiffeault, Stephen Childress. 2003-02-25. Chaotic Mixing in a Torus Map. https://doi.org/10.1063/1.1568833

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