When a weakly diffusing passive impurity is introduced into a
turbulent flow, regions of high concentration are stretched and
folded repeatedly. This process creates thin striations with large
concentration gradients that enhance diffusion, so that uniformity is
achieved at the smallest scales. More than 30 years ago, Batchelor
predicted that the spatial power spectrum of the impurity should show
a region proportional to the inverse of the wavenumber k. We
studied the mixing of a passive scalar in two dimensional turbulence
in part to test this prediction. The flow is established in a thin
buoyant layer that is electromagnetically forced by an array of
permanent magnets. Mixing is studied by introducing a dye solution on
one side and extracting the mixed solution at the other. An image
corresponding to the dye mixing is shown.
Strong deviations are observed from the predicted 1/k scaling.
Ben Williams won the Apker Award of the American Physical Society for his work on this problem. A long paper has appeared in Physics of Fluids 9, 2061-80 (1997).
Last updated 10/31/98