Universal properties of chaotic transport in the presence of diffusion

The combined, finite time effects of molecular diffusion and chaotic advect ion on a finite distribution of scalar are studied in the context of time p eriodic, recirculating flows with variable stirring frequency. Comparison o f two disparate frequencies with identical advective fluxes indicates that diffusive effects are enhanced for slower oscillations. By examining the ge ometry of the chaotic advection in both high and low frequency limits, the flux function and the width of the stochastic zone are found to have a univ ersal frequency dependence for a broad class of flows. Furthermore, such sy stems possess an adiabatic transport mechanism which results in the establi shment of a ''Lagrangian steady state,'' where only the asymptotically inva riant core remains after a single advective cycle. At higher frequencies, t ransport due to chaotic advection is confined to exchange along the perimet er of the recirculating region. The effects of molecular diffusion on the t otal transport are different in these two cases and it is argued and demons trated numerically that increasing the diffusion coefficient tin some presc ribed range) leads to a dramatic increase in the transport only for low fre quency stirring. The frequency dependence of the total, long time transport of a limited amount of scalar is more involved since faster stirring leads to smaller invariant core sizes. (C) 1999 American Institute of Physics. [ S1070-6631(99)04308-1].