THE CURVATURE OF MATERIAL LINES IN A 3-DIMENSIONAL CHAOTIC FLOW

Folding of material filaments was examined computationally in the thre e-dimensional flow in a cylindrical duct with helical deflectors by tr acking the curvature of line elements in the flow. Two geometries were analyzed: a configuration in which the flow is globally chaotic, and an alternative geometry which has a mixture of chaotic and regular mot ion. The behavior of the curvature field in this complex flow geometry was in agreement with that previously observed for much simpler two-d imensional model flows [Phys. Fluids 8, 75 (1996)]. Curvature profiles along individual element trajectories indicate that an inverse relati onship exists between the rates of stretching and curvature. Material elements are compressed when they are folded. After an initial transie nt, the mean curvature oscillates within a finite range with a periodi city matching that of the flow geometry. The spatial structure of the curvature field becomes period-independent, and the probability densit y functions of curvature computed for different numbers of periods col lapse to an invariant, self-similar distribution without the need for scaling. (C) 1998 American Institute of Physics.