Scaling properties of differential molecular diffusion effects in turbulence

Scaling properties of a normalized concentration difference in a turbulent flow containing two scalars of unequal diffusivity are determined by similarity analysis and numerical simulation. Similarity hypotheses applied to the power spectrum of the normalized concentration difference, termed the differential diffusion, yield predicted dependences of the variance of the differential diffusion on the turbulence Reynolds number (Re) and on the Schmidt numbers (Sc) of the scalars. In particular, the variance is found to be proportional to Re−1/2. This and other predictions are supported by numerical simulations of multiple scalar mixing using a one-dimensional stochastic mixing model. The analysis and numerical results indicate fundamental distinctions between the physical mechanisms governing the scalar spectral cascade and those governing spectral transfer of the differential diffusion. The relationships of predicted scalings to passive mixing measurements that have been reported and to behaviors expected in reacting flow are noted.