This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method to direct numerical simulation (DNS) of a turbulent channel flow at Re$_tau$=180 using two different forcing strategies that are designed to separately assess the anisotropy and nonlocality of momentum mixing. In the first strategy, the leading term of the Kramers-Moyal expansion of the eddy viscosity operator is quantified where the macroscopic forcing is employed to reveal all 81 tensorial coefficients that essentially represent the local-limit eddy viscosity. The results indicate: (1) eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both mean strain rate and mean rotation rate tensors, and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity operator is considered as an integration kernel representing the nonlocal influence of mean gradients on the Reynolds stresses. Considering the average of this kernel in the homogeneous directions, the macroscopic forcing is designed to reveal the nonlocal effects in the wall-normal direction for all 9 components of the Reynolds stresses. Our results indicate that while the shear component of the Reynolds stress is reasonably controlled by the local mean gradients, other components of the Reynolds stress are highly nonlocal. These two analyses provide accurate verification data for quantitative testing of anisotropy and nonlocality effects in turbulence closure models.
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