QUANTIFICATION OF MIXING IN APERIODIC CHAOTIC FLOWS

Most previous studies of mixing in deterministic flows have focused on time-periodic or spatially-periodic flows. In contrast, mixing proces ses in aperiodic flows have been considerably less studied. Four proce dures are used in this paper to generate well-characterized aperiodic flows. These procedures are applied to the cavity flow and to a two-di mensional mapping with a sinusoidal velocity profile. Mixing in period ic and aperiodic flows is quantitatively compared. Since most of the a vailable analytical tools developed in the context of periodic systems (Poincare sections, periodic points and their associated manifolds) a re poorly suited for the analysis of aperiodic systems, comparisons ar e based on measures, such as the structure and statistics of the stret ching field and the rate of tracer spreading, that apply to both perio dic and aperiodic systems. Aperiodicity enhances mixing enormously. Ap eriodic perturbations generate widespread chaos under conditions where periodic flows generate minimal or no chaos. The average rate of stre tching of material elements can be increased several orders of magnitu de in brief intervals corresponding to just 10-20 periods of the perio dic flow. The spatial distribution of stretching is much more uniform for aperiodic systems than for periodic ones, and tracers spread much more rapidly and uniformly.