Numerical measurements of temporal and streamwise nonlocality in turbulent channel flow*

In contrast to the commonly used Boussinesq approximation, a purely local approximation, nonlocality refers to the dependence of Reynolds stresses at a given point on mean velocity gradients at all points in space and at previous times. Previous studies of nonlocality in turbulent channel flow (Park and Mani (2019), Hamba (2005)) have focused on quantifying nonlocality in the wall-normal direction. We present measurements of temporal nonlocality and nonlocality in the streamwise direction using direct numerical simulation (DNS) and the macroscopic forcing method (MFM) (Mani and Park (2021)). Our results demonstrate significant nonlocality in the streamwise direction as compared to the wall-normal direction, which may impact modeling of wall-bounded flows with strong mean velocity gradients in the streamwise direction such as separated boundary layers.