The effect of the presence of inertial-convective and viscous-convective subranges on the statistics of a passive scalar in Homogeneous Isotropic Turbulence in air and water

An assumption common to many approaches to understanding and modeling turbulent mixing is that the statistics of a passive scalar at small length scales will approach the analogous statistics of the velocity field as the scale separation increases between the flow-specific outer scales and the small scales of interest.  However, it is well recognized that differences in the scalar and velocity dynamics prevent the overall statistics of the two being identically the same, even at either high Reynolds number or high Schmidt number individually.  Because of limitations in laboratory measurements, direct numerical simulations (DNSs), and measurements of the ocean and atmosphere, it is difficult to obtain data in which the Reynolds number is high enough for an inertial-convective subrange, and the Schmidt number is simultaneously high enough for a clear viscous-convective subrange.  We hypothesize that when both subranges exist, then there is sufficient scale separation in the velocity field for its statistics to be approximately universal, and also sufficient additional scale separation for the scalar to relax so that its small-scale statistics approach those of the velocity.  We explore this hypothesis with DNS resolved on up to 14256×14256×14256 grid points, Taylor Reynolds number Re_λ=633, and Schmidt number Sc = [0.1, 0.7, 1.0, 7.0].  For high Reynolds number with Schmidt number less than unity, a viscous-convective subrange does not exist and we find that small-scale isotropy, the intermittency exponent, and the probability density function (PDF) of the scalar dissipation rate are all much different from the analogous velocity statistics, as reported widely in literature. However, when the Schmidt number is greater than unity at high Reynolds number, the velocity and scalar statistics are similar. This suggests that at high Reynolds numbers, the modelling assumption of similarity between velocity and scalar statistics is valid for mixing in water, but not in air.