Predicting chaotic dispersion with Eulerian symmetry measures: Wavy Taylor-vortex flow

In a recent investigation of particle transport in numerically computed wav y Taylor-vortex flow, Rudman estimated an effective axial diffusion coeffic ient, D-z, to characterize the enhanced mixing due to chaotic advection [AI ChE J. 44, 1015 (1998)]. We find that D-z is proportional to the product of two measures of symmetry deviation. The first is a measure of the average deviation of the flow from rotational symmetry, and the second is a measure of the average deviation from flexion-free flow (a flow where the curl of the vorticity is zero). Because these quantities are obtained directly from the velocity field, we call them Eulerian symmetry measures. Thus, we show that the macroscopic transport behavior in a flow can be quantified direct ly in terms of the velocity field and its gradients, and hence provides a c onnection between Eulerian and Lagrangian pictures of transport-a problem o f fundamental and widespread interest. (C) 2001 American Institute of Physi cs.