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 simulation, and is critical to model for a variety of applications, including turbulent mixing, turbulent reacting flows, and cloud microphysical processes. In the context of cloud turbulence, Lagrangian microphysics models often require information about the SGS supersaturation variance; thus the fidelity of the SGS model plays a critical role for numerically simulated cloud droplet growth. Using data collected turbulent Rayleigh-Benard convection in the Michigan Technological University Pi chamber (aspect ratio Γ = 2) for Rayleigh numbers Ra ~ 10⁸-10⁹, we perform a priori tests of the SGS supersaturation variance. Data from a spatial array of ten thermistors is spatially filtered and used to calculate the true SGS variance, a gradient model, and a scale similarity model for three dimensionless filter widths. While the gradient model exhibits low correlations (ρ ~ 0.2), the similarity model is highly correlated (ρ ~ 0.8) with the true SGS variance and exhibits good local performance in terms of joint probability density functions. Implications for large eddy simulations of cloud turbulence will be discussed.