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.