Influences of subgrid scale dynamics on resolvable scale statistics in large-eddy simulations

Recently, the epsilon-expansion and recursive renormalization group (RNG) theories as well as approximate inertial manifolds (AIM) have been exploited as means of systematically modeling subgrid scales in large-eddy simulations (LES). Although these theoretical approaches are rather complicated mathematically, their key approximations can be investigated using direct numerical simulations (DNS). In fact, the differences among these theories can be traced to whether they retain or neglect interactions between the subgrid-subgrid and subgrid-resolvable scales. In this paper, we focus on the influence of these two interactions on the evolution of the resolvable scales in LES: the effect(A) which keeps only the interactions between the small and large scales; and, the effect(B) which, on the other hand, keeps only the interactions among the subgrid-subgrid scales. The performance of these models is analyzed using the velocity fields of the direct numerical simulations. Specifically, our comparison is based on the analysis of the energy and enstrophy spectra, as well as higher-order statistics of the velocity and velocity derivatives. We found that the energy spectrum and higher-order statistics for the simulations with the effect(A) (referred to, hereafter, as model(A)) are in very good agreement with the filtered DNS. The comparison between the computations with effect(B) (referred to, hereafter, as model(B)) and the filtered DNS, however, is not satisfactory. Moreover, the decorrelation between the filtered DNS and model(A) is much slower than that of the filtered DNS and model(B). Therefore, we conclude that the model(A), taking into account the interactions between the subgrid and resolvable scales, is a faithful subgrid model for LES for the range of Reynolds numbers considered.