Two-point stress–strain-rate correlation structure and non-local eddy viscosity in turbulent flows

By analysing the Karman–Howarth equation for filtered-velocity fields in turbulent flows, we show that the two-point correlation between the filtered strain-rate and subfilter stress tensors plays a central role in the evolution of filtered-velocity correlation functions. Two-point correlation-based statistical a priori tests thus enable rigorous and physically meaningful studies of turbulence models. Using data from direct numerical simulations of isotropic and channel flow turbulence, we show that local eddy-viscosity models fail to exhibit the long tails observed in the real subfilter stress–strain-rate correlation functions. Stronger non-local correlations may be achieved by defining the eddy-viscosity model based on fractional gradients of order $0