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How rapidly is a passive scalar mixed within closed streamlines?

Published online by Cambridge University Press:  20 April 2006

P. B. Rhines  and
W. R. Young
P. B. Rhines
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
W. R. Young
Affiliation:
University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, La Jolla, California 92093
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Abstract

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 ≈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 ≈ 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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 133 , August 1983 , pp. 133 - 145
Copyright
© 1983 Cambridge University Press

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