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Field experimental study of dynamic Smagorinsky models in the atmospheric surface layer
ABSTRACT: An analysis of dynamic Smagorinsky models is performed based on the HATS (Horizontal Array Turbulence Study) data set. In the experiment, two vertically separated horizontal arrays of fourteen 3d sonic anemometers were placed in the atmospheric surface layer. Subgrid-scale (SGS) and resolved quantities are derived from 2d filtering at a filter scale D and differentiation of filtered velocity fields. In a previous study (Kleissl et al. 2003), the Smagorinsky coefficient c_s^D was computed directly from these data and found to depend on atmospheric stability and height above the ground. In the present study we examine the scale-invariant dynamic model (Germano et al. 1991) and the scale-dependent dynamic model (Port\'{e}-Agel et al. 2000b) and test their accuracy in predicting c_s^D and its dependencies on stability and height above the ground. The Germano identity uses a test filter at aD (in this study we use a=1.75). 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 D 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 a^2D to deduce dependence of c_s^D on filtering scale. This model gives excellent predictions of c_s^D and its dependence upon stability and height. J. Atmos. Sci. (2004), 61, 2296-2307. or full pdf article -- ( © AMS, see http://www.ametsoc.org/AMS/) |
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