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

Abstract

Abstract The subgrid-scale (SGS) scalar variance represents the “unmixedness” of the unresolved small scales in large-eddy simulations (LES) of turbulent flows. 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 fluctuations in microphysics models. We present results from a priori tests of SGS scalar variance models using data collected in turbulent Rayleigh–Bénard convection in the Michigan Tech Pi chamber for Rayleigh numbers Ra ∼ 108–109. Data from an array of 10 thermistors were spatially filtered and used to calculate the true SGS scalar variance, a scale-similarity model, and a gradient model for dimensionless filter widths of h/Δ = 25, 14.3, and 10 (where h is the height of the chamber and Δ is the spatial filter width). The gradient model was found to have fairly low correlations (ρ ∼ 0.2), with the most probable values departing significantly 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 (ρ ∼ 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/Δ. The similarity model, which only requires an additional test filtering operation, is therefore a promising approach for modeling the SGS scalar variance in LES of cloud turbulence and other related flows.