The Effect of Filter Dimension on the Subgrid-Scale Stress, Heat Flux, and Tensor Alignments in the Atmospheric Surface Layer

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 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 ⌬ 3ϪD ϭ 0.84⌬ 2ϪD . 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.

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

“…We analyzed the decay of TKE in the surface layer over a desert, using data from the SGS 2002 experiment (see Higgins et al 2007). These measurements were collected at the Surface Nieuwstadt and Brost (1986) model for k(t ) (dissipation term only) applied to the surface layer.…”

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

“…Even a coefficient that matches the dissipation rates on average cannot guarantee good results since it does not necessarily yield correct instantaneous energy dissipation or correct mean and instantaneous stresses and fluxes. Another important aspect is the alignment of the measured and modelled flux tensors (Clark et al 1979;Meneveau and Katz 2000;Higgins et al 2003Higgins et al , 2007 and the mean magnitude and the correlation of their individual components. The correlations of the measured and modelled fluxes and dissipations will be studied for both the Smagorinsky and the non-linear models; however, our focus here remains on understanding the SGS physics and answering the two questions introduced earlier, rather than testing the limits of a particular model.…”

“…1 to 3. The filtering operation needed in these equations was performed in two dimensions (which was found to be equivalent to filtering in three dimensions with a filter size reduced by about 16%- Higgins et al 2007). The 20 Hz data were first filtered in the vertical direction using a box filter of size 2dz = 1.3 m; this operation was applied separately to the upper three sonic-Licor pairs and to the lower ones as depicted in Fig.…”

“…To discriminate between the effects of filter anisotropy and filter size, we apply a correction for the anisotropy as proposed by Scotti et al (1993). To apply this correction, we compute the effective cross-stream width from Higgins et al (2007) who found that a 2D filter is equivalent to a 3D filter with a smaller effective size. Higgins et al (2007) conclude that 0.86 2D = 3D or 0.86( x z) 1/2 = ( x y z) 1/3 .…”

“…To apply this correction, we compute the effective cross-stream width from Higgins et al (2007) who found that a 2D filter is equivalent to a 3D filter with a smaller effective size. Higgins et al (2007) conclude that 0.86 2D = 3D or 0.86( x z) 1/2 = ( x y z) 1/3 . This finding can then be used to compute the effective y of a 3D filter that has the same x, z, and effective size of our 2D filter from y = 0.86 3 ( x z) 1/2 = 0.636( x z) 1/2 .…”