Chaotic Mixing in a Torus Map

Details Chaotic Mixing in a Torus Map Chaotic Mixing in a Torus Map

2002-11-21

arxiv.org/abs/nlin/0211036v2

Chaos 13, 502-507 (2003)

Nonlinear Sciences

Chaotic Dynamics

12 pages, 4 figures. RevTeX4 and psfrag macros. Final version

Scientific paper

10.1063/1.1568833

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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