Examination of the linear algebraic subgrid-scale stress [LASS] model, combined with reconstruction of the subfilter-scale stress, for large-eddy simulation of the neutral atmospheric boundary layer

A number of authors have highlighted the features of the atmospheric boundary layer, including coherent structures and anisotropic turbulence (e.g., Dubos et al., J Atmos Sci 65, 2008, 2631ff). Biferale et al. (Eur J Mech B-Fluid 23, 2004, 401ff) cite the quantification of anisotropic effects in small-scale turbulence as a theoretical and practical challenge and a first-order question for near-wall large-eddy simulation [LES]. Sullivan et al. (J Fluid Mech 482, 2003, 101ff) show the anisotropy of turbulence in the Horizontal Array Turbulence Study [HATS] near-ground field data and support the use of mixed subfilter-scale models in LES. Mixed models are useful turbulence models, but a current weakness of their approach is that the subgrid-scale stress model is typically an eddy-viscosity model. Eddy-viscosity models cannot reproduce the observed anisotropy of the normal stresses and, in the simplest forms, cannot support the observed backscatter of energy.

We have developed a linear algebraic subgrid-scale stress [LASS] model, which includes production, dissipation, and pressure redistribution terms. Results of a large-eddy simulation of a neutrally-stratified boundary layer flow over a flat, rough surface indicate that the LASS model is a more physically complete subgrid-scale stress turbulence model that provides near-wall anisotropies that eddy-viscosity models do not, and yields proper shear stress values in the logarithmic layer.

Here we examine the performance of the combination of the LASS model with reconstruction, using the approximate deconvolution model [ADM], of the subfilter-scale stress (Chow et al., J Atmos Sci 62, 2005, 2058ff). For example, the addition of the Bardina term [reconstruction level 0 or ADM0] for the subfilter-scale stress to the LASS model improves compliance with the logarithmic law in the neutral boundary layer. In addition, there are insignificant differences in the vertical velocity patterns in horizontal planes between the LASS model with ADM0 and the Dynamic Wong-Lilly model with ADM5 (cf., Ludwig et al., J Appl Meteorol Clim 48, 2009, 1161ff). Differences in the vertical velocity patterns are most distinct in the near-wall region. In this area, most of the scales are subgrid, so higher levels of reconstruction appear to be unnecessary because the LASS model provides adequate information. While the LASS model alone does a good job of matching to the reported HATS near-wall anisotropies (Chen et al., J Fluid Mech 626, 2009, 149ff), the LASS model with ADM0 provides near-wall anisotropies that better correspond with the HATS data, especially the cross-stream component.

With our mixed model we are able to represent both anisotropy and energy backscatter at both the subfilter- and subgrid- scales. In our paper we will present, for example, an examination of the importance of these features as a function of distance from the ground.

Finally, the LASS model not only shows promise for turbulence modeling in complex terrain because higher levels of reconstruction are unnecessary, but it also shows great potential as a model for simulations within the “terra incognita”, where reconstruction of the subfilter stress is not feasible because of the proximity of the peak energy containing scale to the grid scale.