LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent channel flows. It is found from the comparisons that the LES with an eddy-viscosity sub-grid scale (SGS) model over-predicts the space-time correlations than the DNS. The overpredictions are further quantified by the integral scales of directional correlations and convection velocities. A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions. This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows. It suggests that enstrophy is crucial to the LES prediction of space-time correlations. The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.