The effect of filter dimension on the components of the subgrid-scale stress and tensor alignments in the atmospheric surface layer

Chad Higgins(1,3), Charles Meneveau(2,3) and Marc B. Parlange(4)

1 Department of Geography and Environmental Engineering 2 Department of Mechanical Engineering 3Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore MD 21218, EPFL Switzerland

ABSTRACT: In field experiments designed to study subgrid-scale parameterizations for Large Eddy Simulation, the flow field is often measured and then filtered in two-dimensional planes. This two dimensional filtering serves as a surrogate for three dimensional filtering. The question of whether this will yield accurate results in subgrid-scale (SGS) models has not yet been adequately addressed. In this paper, we answer this question by analyzing data from a July 2002 experiment in which sixteen sonic anemometers were deployed at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility in the Utah West Desert. We obtained the full SGS stress tensor and its parameterizations using both two and three-dimensional filtering. We present comparisons between two dimensional and three dimensional filtering of the field measurements based on probability density functions (pdfs) and energy spectra of the SGS stress elements. The pdfs reveal that quantities calculated with two dimensional filtering exhibit greater intermittency than those computed with three dimensional filtering at the same scale. From the spectra we observe that the different filtering methods result in similar behavior, but that spectra of SGS stress components computed with a three dimensional filter roll off at a slightly lower wave-number than those computed with a two dimensional filter. The pfds and spectra of the stresses calculated with two dimensional and three dimensional filters can be made to collapse by reducing the three dimensional filter scale according to Delta-3D = 0.84 x Delta-2D. Geometric alignment analyses are also performed with both two and three dimensional filtering for the cases of stable, near neutral, and unstable atmospheric stability. Under unstable and near neutral atmospheric stability two dimensional filtering yields acceptable results; however under stable atmospheric stability, we recommend and delineate a new approach.

(2007), J. Atmos. Ocean. Tech., 24, 360-375.

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