On the Magnitude and Variability of Subgrid-Scale Eddy-Diffusion Coefficients in the Atmospheric Surface Layer

Abstract

Eddy-viscosity closures for large eddy simulations (LES) of atmospheric boundary layer dynamics include a parameter (Smagorinsky constant cs), which depends upon physical parameters, such as distance to the ground, atmospheric stability, and strain. A field study [Horizontal Arrays Turbulence Study (HATS)] specifically designed to measure turbulence quantities of interest in LES, such as the parameter cs, is conducted. The instrumentation consists of two vertically separated horizontal arrays of 3D sonic anemometers, placed in the atmospheric surface layer. From 2D filtering and differentiating the velocity fields, subgrid-scale (SGS) and resolved quantities are computed. The parameter cs is obtained from the data by matching measured and modeled SGS dissipations under various flow conditions. Results indicate that cs is reduced near the ground, and also decreases rapidly with increasing stability in stable atmospheric conditions. A simple fit that parameterizes the data is proposed. The variability from one sample to another is studied by means of the probability density function (pdf) of cs. The pdfs show a most preferred value, which is essentially independent of the timescale used for statistical averaging. The width of the pdfs decreases with increasing averaging time, for unstable and neutral stability conditions. For stable conditions, the relative variability of the coefficient remains strong even for long averaging times, indicative of strong intermittency. In unstable conditions, cs is fairly independent of local strain-rate magnitude, supporting the basic scaling of the Smagorinsky eddy viscosity. For stable conditions, a transition occurs between small local strain-rate magnitudes, where cs is nearly constant, and high local strain-rate magnitudes, where cs decreases appreciably. The results suggest that when the filter scale approaches the local integral scale of turbulence (height above the ground or Obukhov length), one needs to include the friction velocity as relevant velocity to scale the eddy viscosity, in addition to the standard velocity scale of the Smagorinsky model based on filtered strain-rate magnitude. The analysis is repeated for the SGS heat flux, and for the associated eddy-diffusion coefficient (PrT–1cs2) and Prandtl number (PrT). The latter is found to depend only very weakly on stability, but it increases with decreasing distance from the ground.