How rapidly is a passive scalar mixed within closed streamlines?

The homogenization of a passive ‘tracer ’ in a flow with closed mean streamlines occurs in two stages: first, a rapid phase dominated by shear-augmented diffusion over a time z @ ( L / U ) , where the €’Met number P = LU/K (L, U and K are lengthscale, velocity scale and diffusivity), in which initial values of the tracer are replaced by their (generalized) average about a streamline ; second, a slow phase requiring the full diffusion time x L 2 / K . The diffusion problem for the second phase, where tracer isopleths are held to streamlines by shear diffusion, involves a generalized diffusivity which is proportional to K , but exceeds i t if the streamlines are not circular. Expressions are also given for flow fields that are oscillatory rather than steady.