Modeling the Subgrid Scale Scalar Variance: a Priori Tests and Application to Supersaturation in Cloud Turbulence

The subgrid-scale (SGS) scalar variance represents the " unmixedness " of the unresolved small scales in large -eddy simulations (LES) of turbulent fl ows. Supersaturation variance can play an important role in the activation, growth, and evaporation of cloud droplets in a turbulent environment, and therefore efforts are being made to include SGS supersaturation fl uctuations in microphysics models. We present results from a priori tests of SGS scalar variance models using data collected in turbulent Rayleigh - B & eacute;nard convection in the Michigan Tech Pi chamber for Rayleigh numbers Ra 10 8 - 10 9 . Data from an array of 10 thermistors were spatially fi ltered and used to calculate the true SGS scalar variance, a scale -similarity model, and a gradient model for dimensionless fi lter widths of h / A = 25,14.3, and 10 (where h is the height of the chamber and A is the spatial fi lter width). The gradient model was found to have fairly low correlations ( p 0.2), with the most probable values departing signi fi cantly from the one-to-one line in joint probability density functions (JPDFs). However, the scale -similarity model was found to have good behavior in JPDFs and was highly correlated ( p 0.8) with the true SGS variance. Results of the a priori tests were robust across the parameter space considered, with little dependence on Ra and h / A. The similarity model, which only requires an additional test fi ltering operation, is therefore a promising approach for modeling the SGS scalar variance in LES of cloud turbulence and other related fl ows.