Chaotic advection in three-dimensional unsteady incompressible laminar flow

Abstract

We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows; the global dispersion of passive scalars in flows with two slow and one fast velocity components. We make a comprehensive study of the first model of an experimentally realizable flow to exhibit this {\it resonance-induced\/} dispersion: biaxial unsteady spherical Couette flow is a three-dimensional incompressible laminar flow with periodic time dependence derived analytically from the Navier--Stokes equations in the low-Reynolds-number limit.

Revised version, 24 pages, uuencoded gzip-compressed postscript file, submitted to J. Fluid Mech. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by request