Comparison between kinetic energy and passive scalar energy transfer in locally homogeneous isotropic turbulence

The general focus of this paper is on the mixing of a passive scalar for Sc = 1 (Sc is the Schmidt number) in decaying homogeneous isotropic turbulence for which the initial injections of turbulent energy and scalar variance are similar. The overall philosophy is to understand and predict the scalar behaviour, when the velocity field is determined, either completely (all the statistics are known) or through a minimal number of ingredients (the spectral slope in the restricted scaling range or RSR and the integral scale associated with the kinetic energy). The particular interest is on the scalar variance transfer, in comparison with the kinetic energy transfer. For several locally isotropic decaying-type flows (grid turbulence, jets), the experimental evidence suggests that the scalar variance transfer is closer to the asymptotic value of 4/3 than its kinetic energy counterpart. An analytical explanation is provided for this peculiar behaviour. In particular, the scalar variance transfer is modelled as the variance transferred at scale r, during a characteristic time resulting from the strain exercised by all scales larger than (or equal to) r. This model is supported adequately by experimental data in grid turbulence. (C) 2011 Elsevier B.V. All rights reserved.