A generalised stochastic backscatter model: large-eddy simulation of the neutral surface layer

The Smagorinsky subgrid model remains popular in large-eddy simulation (LES) modelling despite its failure to reproduce mean velocity shear within the atmospheric surface layer. Over-predictions as large as 100% are not uncommon, leading to local simulation degradation and potentially infecting scales further from the surface. Mason and Thomson achieved significant reduction in excessive velocity shear by adding stochastic accelerations on top of the Smagorinsky model to account for backscattered energy from the subgrid scales. However, neither this model nor its later implementation by Weinbrecht and Mason are able to ensure a physically appropriate spatial structure for the backscatter acceleration fields throughout the domain: with the Mason and Thomson model, the backscatter length scale and anisotropy depend on the local grid spacing and aspect ratio; with the Weinbrecht and Mason model, the backscatter is unavoidably isotropic with uniform length scale. We propose a new method for the generation of stochastic backscatter acceleration fields which utilises a grid-adaptive filter (GAF) capable with the capability of controlling spatial variations in the backscatter length scale and anisotropy, independently of the model grid. When applied to the atmospheric surface layer, this allows for the backscatter length scale to be reduced towards surfaces in the an appropriate manner, and the backscatter anisotropy to be varied in accordance with the physical anisotropy of the subgrid scales. The GAF model also has wider applicability as it may be used in cases where the LES filter width, and hence the backscatter length scale, varies spatially with local 3-D grid refinement. The GAF model is initially tested for the case of LES of the neutral atmospheric boundary layer, for grid aspect ratios ranging from α=∆x/∆z= 1 to 10, and found to give a reduction in maximum excessive mean velocity shear (from that obtained without backscatter) of around 80%, that is largely independent of α.