Optimal sub-grid model for accurate determination of intermittent inertial range properties of turbulent flows

We present a study of the statistical properties of homogeneous and isotropic turbulence evolved by fully resolved direct numerical simulations (DNS) and by large eddy simulations (LES) equipped with different sub-grid-scales (SGS) models. We compare the effects produced on the high-order, multi-scales correlation functions by the well known Smagorinsky closure with the performances of a new model based on the introduction of a Lagrange multiplier which constraints exactly the turbulent energy spectrum scaling law to the Kolmogorov k^(-5/3) slope at high wavenumbers. Data from hyperviscous DNS are also analyzed. To identify the optimal model which maximizes the extension of the inertial range dynamics, we compare the statistics measured from LES and hyperviscous simulations with the statistics of DNS performed on a more refined grid. We also consider fine-tuning SGS models by "nudging" the smaller LES resolved scales from the dynamics obtained at the same scales in the inertial range of a higher resolution DNS.