Anisotropy in large eddy simulations determined from SO(3) symmetry group

The issue of small-scale anisotropy in the context of eddy-viscosity-type subgrid-scale models is discussed in the present work. Recent developments in turbulence research suggest that anisotropy from large spatial scales is felt far into the inertial subrange of turbulence. This is of particular importance for subgrid-scale models of large eddy simulations. To address this issue, we present solutions of the random-phase Kolmogorov flow at moderate Reynolds numbers using direct numerical simulations and large eddy simulations with four subgrid-scale models: the Smagorinsky, the dynamic, the dynamic Clark, and the tensor-diffusivity models. The degree of anisotropy at different scales is analysed by decomposing the structure function into their irreducible representation of the SO(3) symmetry group. The results suggest that the dynamic model and the dynamic Clark model reproduce the statistical behaviour reasonably well, even in the anisotropic sectors at small length scales.