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

Scott T. Salesky aSchool of Meteorology, University of Oklahoma, Norman, Oklahoma

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Kendra Gillis aSchool of Meteorology, University of Oklahoma, Norman, Oklahoma

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Jesse Anderson bDepartment of Physics, Michigan Technological University, Houghton, Michigan

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Ian Helman bDepartment of Physics, Michigan Technological University, Houghton, Michigan

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Will Cantrell bDepartment of Physics, Michigan Technological University, Houghton, Michigan

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Raymond A. Shaw bDepartment of Physics, Michigan Technological University, Houghton, Michigan

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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.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Scott T. Salesky, salesky@ou.edu

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.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Scott T. Salesky, salesky@ou.edu
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