Multiscale properties of Large Eddy Simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations be-tween the resolved velocity field and the subgrid-scale (SGS) stress-tensor in largeeddy simulations (LES). Following previous studies for Navier-Stokes equations(NSE), we derive the exact hierarchy of LES equations governing the spatio-temporalevolution of velocity structure functions of any order. The aim is to assess the influ-ence of the sub-grid model on the inertial range intermittency. We provide a seriesof predictions, within the multifractal theory, for the scaling of correlation involvingthe SGS stress and we compare them against numerical results from high-resolutionSmagorinsky LES and froma-priorifiltered data generated from direct numericalsimulations (DNS). We find that LES data generally agree very well with filteredDNS results and with the multifractal prediction for all leading terms in the balanceequations. Discrepancies are measured for some of the subleading terms involvingcross-correlation between resolved velocity increments and the SGS tensor or theSGS energy transfer, suggesting that there must be room to improve the SGS mod-elisation to further extend the inertial range properties for any fixed LES resolutio