  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.
