New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully turbulent flows

Abstract

By measuring concentration fluctuations of a dye with very fine spatial and temporal resolution in typical unconfined turbulent water flows, we obtain the fractal dimension characteristic of the scalar interface in the range between Kolmogorov and Batchelor scales. We use one-dimensional intersection methods and invoke Taylor's hypothesis, but both of them are amply justified. We obtain a theoretical estimate for the fractal dimension by modifying our earlier arguments for finite (though large) Schmidt number effects. Finally, the multifractal characteristics of the scalar dissipation rate in the same scale range are also presented.