Coarse Grained Scale of Turbulent Mixtures

What is the physical length scale which supports the concentration content in a stirred mixture? Among the length scales familiar in stirred mixtures is the dissipation scale which equilibrates substrate deformation and diffusive smearing rates. That scale is a decreasing function of the deformation rate and is, thus, a decreasing function of the Reynolds number in turbulent flows. Experiments show that the mixture concentration content is defined on a support whose elementary brick eta=LSc(-2/5) is much larger. It scales like the stirring scale L, depends on the Schmidt number Sc, and is independent of the Reynolds number. The above law is supported by measurements covering two decades in L and three decades in Sc. We suggest that this scale results from the aggregation of bundles of elementary stretched scalar sheets merging under large-scale substrate deformation.