Schmidt number effects on turbulent transport with uniform mean scalar gradient

Abstract

We study by direct numerical simulations the effects of Schmidt number (Sc) on passive scalars mixed by forced isotropic and homogeneous turbulence. The scalar field is maintained statistically stationary by a uniform mean gradient. We consider the scaling of spectra, structure functions, local isotropy and intermittency. For moderately diffusive scalars with Sc=1/8 and 1, the Taylor-scale Reynolds number of the flow is either 140 or 240. A modest inertial-convective range is obtained in the spectrum, with a one-dimensional Obukhov–Corrsin constant of about 0.4, consistent with experimental data. However, the presence of a spectral bump makes a firm assessment somewhat difficult. The viscous-diffusive range is universal when scaled by Obukhov–Corrsin variables. In a second set of simulations we keep the Taylor-microscale Reynolds number fixed at 38 but vary Sc from 1/4 to 64 (a range of over two decades), roughly by factors of 2. We observe a gradual evolution of a −1 roll-off in the viscous-convective region as Sc increases, consistent with Batchelor’s predictions. In the viscous-diffusive range the spectra follow Kraichnan’s form well, with a coefficient that depends weakly on Sc. The breakdown of local isotropy manifests itself through differences between structure functions with separation distances in directions parallel and perpendicular to the mean scalar gradient, as well as via finite values of odd-order moments of scalar gradient fluctuations and of mixed velocity-scalar gradient correlations. However, all these indicators show, to varying degrees, an increasing tendency to isotropy with increasing Sc. The moments of scalar gradients and the scalar dissipation rate peak at Sc≈4. The intermittency exponent for the scale-range between the Kolmogorov and Batchelor scales is found to decrease with Sc, suggesting qualitative consistency with previous dye experiments in water [Sc=O(1000)].