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

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 is addressed by analyzing data from a field experiment in which 16 sonic anemometers were deployed in a four by four grid. The experiment was held in July 2002 at the Surface Layer Turbulence and Environmental Science Test ( SLTEST) facility in the Utah West Desert. The full SGS stress tensor and its parameterizations using both two-and three-dimensional filterings are obtained. Comparisons are given between two- and three-dimensional filterings 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 it is observed 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 wavenumber than those computed with a two- dimensional filter. The PDFs and spectra of the stresses calculated with two- and three-dimensional filters can be made to collapse by reducing the three-dimensional filter scale according to Delta(3-D) = 0.84 Delta(2-D). Geometric alignment analyses are performed for the SGS heat flux, SGS stress, and filtered strain rate for the cases of stable, near-neutral, and unstable atmospheric stabilities. Under unstable and near-neutral atmospheric stability, two- dimensional filtering yields acceptable results; however, under stable atmospheric stability, a new approach is recommended and delineated.