A nonlocal algebraic tensor model for Reynolds-stress closures*

Reynolds-stress closure modeling has been playing a major role in applied computational fluid dynamics and remains a challenging issue in complex shear flows. Here we report a new closure strategy for Reynolds stresses based on two-point correlation, which accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gradient tensor. The present model represents complete anisotropy with tensor coefficients, and provides a prior knowledge for separation of general and universal constants from closure coefficients, holding promise to deduce a real constitutive relationship for Reynolds stresses. These constants represent intrinsic similarities of different turbulent flows. Comparative analysis with prior linear and nonlinear eddy-viscosity models shows that the proposed model is able to capture more physical details of complex turbulent flows. Further detailed tests are made in fully-developed turbulent channel flow where nonlocal effects are expected to be important. This model provides improved predictions for Reynolds stresses and corrects log-layer mismatch.