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 threedimensional 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 Δ3-D = 0.84Δ2-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.