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 [approximate]P1/3(L/U), where the Péclet number P=LU/κ (L,U and κ 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 [approximate] L2/κ. 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 κ, but exceeds it if the streamlines are not circular. Expressions are also given for flow fields that are oscillatory rather than steady.(Published Online April 20 2006)
(Received October 19 1982)
(Revised March 9 1983)