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 processes in aperiodic flows have been considerably less studied. Four procedures are used in this paper to generate well-characterized aperiodic flows. These procedures are applied to the cavity flow and to a two-dimensional mapping with a sinusoidal velocity profile. Mixing in periodic and aperiodic flows is quantitatively compared. Since most of the available analytical tools developed in the context of periodic systems (Poincare sections, periodic points and their associated manifolds) are poorly suited for the analysis of aperiodic systems, comparisons are based on measures, such as the structure and statistics of the stretching field and the rate of tracer spreading, that apply to both periodic and aperiodic systems. Aperiodicity enhances mixing enormously. Aperiodic perturbations generate widespread chaos under conditions where periodic flows generate minimal or no chaos. The average rate of stretching of material elements can be increased several orders of magnitude in brief intervals corresponding to just 10-20 periods of the periodic 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.