  We provide analytical and numerical results concerning multi-scale
correlations between the resolved velocity field and the subgrid-scale (SGS)
stress-tensor in large eddy simulations (LES). Following previous studies for
Navier-Stokes equations (NSE), we derive the exact hierarchy of LES equations
governing the spatio-temporal evolution of velocity structure functions of any
order. The aim is to assess the influence of the sub-grid model on the inertial
range intermittency. We provide a series of predictions, within the
multifractal theory, for the scaling of correlation involving the SGS stress
and we compare them against numerical results from high-resolution Smagorinsky
LES and from a-priori filtered data generated from direct numerical simulations
(DNS). We find that LES data generally agree very well with filtered DNS
results and with the multifractal prediction for all leading terms in the
balance equations. Discrepancies are measured for some of the subleading terms
involving cross-correlation between resolved velocity increments and the SGS
tensor or the SGS energy transfer, suggesting that there must be room to
improve the SGS modelisation to further extend the inertial range properties
for any fixed LES resolution.
