Contribution of large-scale motions to the Reynolds shear stress in turbulent pipe flows

Direct numerical simulation data for turbulent pipe flows with Reτ = 544, 934, and 3008 were used to investigate the contribution of large-scale motions (LSMs) to the Reynolds shear stress. The relationship between viscous force (d2U+/dy+2,VF) and turbulent inertia (d〈−u′v′〉+/dy+,TI) results in a transition from the inner length scale to the intermediate length scale in the meso-layer. The acceleration force of the LSMs is balanced by the deceleration force of the small-scale motions (SSMs), which makes the zero TI at the wall-normal location of the maximum Reynolds shear stress (ym+). As the Reynolds number increases, the enhanced acceleration force of the LSMs expands the nearly zero TI region. The constant-stress layer is formed in the neighborhood of the zero TI, having the relatively strong VF. For sufficiently high Reynolds number flows, the log law is established beyond the meso-layer due to the fact that VF loses its leading order. The role of the LSMs in the wall-scaling behavior of ym+ is examined.