Preservation of statistical properties in Large Eddy Simulation of shear turbulence

We discuss how large-eddy simulation (LES) can be properly employed to predict the statistics of the resolved velocity fluctuations in shear turbulence. To this purpose an a posteriori comparison of LES data against filtered direct numerical simulation (DNS) is used to establish the necessary conditions that the filter scale LF Must satisfy to achieve the preservation of the statistical properties of the resolved field. In this context, by exploiting the physical role of the shear scale L(S), the Karman-Howarth equation allows for the assessment of LES data in terms of scale-by-scale energy production, energy transfer and subgrid energy fluxes. Even higher-order statistical properties of the resolved scales such as the probability density function of longitudinal velocity increments are well reproduced, provided the relative position of the filter scale with respect to the shear scale is properly selected. We consider here the homogeneous shear flow as the simplest non-trivial flow which fully retains the basic mechanism of turbulent kinetic energy production typical of any shear flow, with the advantage that spatial homogeneity implies a well-defined value of the shear scale while numerical difficulties related to resolution requirements in the near wall region are avoided.