Scale dependence and asymptotic very high Reynolds number spectral behavior of multiscale subgrid models

Abstract

This paper investigates the spectral response of recent multiscale subgrid models, all of eddy viscosity type, in large-eddy simulation (LES) of fully developed turbulence, from moderate to very high Reynolds (Re) number. The objective of this work is to provide useful results about the behavior of the subgrid scale (SGS) models and, in particular, their asymptotic behavior. Such information is indeed important for practitioners using LES to simulate truly high Reynolds number flows. Specifically, we consider LES of homogeneous isotropic turbulence at very high Re and where the LES cutoff (here the grid Δ) is taken well into the inertial range (i.e., Δ/η≥100 with η the Kolmogorov scale). Large LES grids (1283 and 2563) are also used in order to compare and attain the true asymptotic behavior of each SGS model, something not fully observable in LES on smaller grids. An analysis is also carried out to obtain the scale dependence of each model coefficient in the viscous range of turbulence using LES run on several grids and compared to direct numerical simulation. The results provide C for each model and for various Δ/η. A convenient fit then also provides C/C∞ as a function of Δ/η, where C∞ is the asymptotic coefficient. The comparisons are supported using the evolution of resolved energy (global and spectrum), resolved enstrophy, and effective dissipation. It is shown that the multiscale models acting on the high wavenumber part of the LES field are indeed able to provide a significant k−5/3 inertial subrange, yet it is always followed by an energy pileup effect also called “bottleneck.” This effect is also characterized for the various models.