Field Experimental Study of Dynamic Smagorinsky Models in the Atmospheric Surface Layer

Abstract

An analysis of dynamic Smagorinsky models is performed based on the Horizontal Array Turbulence Study (HATS) dataset. In the experiment, two vertically separated horizontal arrays of 14 three-dimensional sonic anemometers were placed in the atmospheric surface layer. Subgrid-scale (SGS) and resolved quantities are derived from 2D filtering at a filter scale ? and differentiation of filtered velocity fields. In a previous study the Smagorinsky coefficient c(?)s was computed directly from these data and found to depend on atmospheric stability and height above the ground. The present study examines the scale-invariant dynamic model of Germano et al. and the scale-dependent dynamic model of Porté-Agel et al. and tests their accuracy in predicting c(?)s and its dependencies on stability and height above the ground. The Germano identity uses a test filter at α? (in this study α = 1.75 is used). The coefficient is derived from various data test-filtered at this scale assuming that the Smagorinsky coefficient is scale invariant. The results show that the scale-invariant dynamic model severely underpredicts the coefficient and its trends whenever ? is similar to, or larger than, the large-scale limit of the inertial range (typically the smaller of the height above the ground z or the Obukhov length L). The scale-dependent dynamic model uses a second test filter at scale α2? to deduce dependence of c(?)s on the filtering scale. This model gives excellent predictions of c(?)s and its dependence upon stability and height.