title: Chaotic mixing in a torus map.
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.
authors.affiliation: Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA. jeanluc@mailaps.org
authors.forename: Jean-Luc
authors.initials: JL
authors.lastname: Thiffeault
authors.forename: Stephen
authors.initials: S
authors.lastname: Childress