Uniform momentum zones for the logarithmic layer in turbulent pipe flow*

Wall-bounded turbulent flows are composed of spatial regions with relatively uniform streamwise velocity, known as uniform momentum zones (UMZs). These UMZs vary in size, and multiple UMZs coexist along the wall-normal direction in instantaneous flow fields. Although UMZs are essential coherent structures for understanding the multiscale phenomena and momentum transport in wall turbulence, there remains a question about which UMZs contribute to the logarithmic layer of wall turbulence. In this study, we explore relatively thick UMZs that span from the near-wall region and cross the logarithmic layer using the direct numerical simulation dataset of turbulent pipe flows at Reτ = 550-6000. The thickness of these UMZs is linearly proportional to the wall-normal distance, and the velocity jump across the shear layer between different UMZs scales with the friction velocity. The mean streamwise velocity profile is reconstructed from these UMZs, and it shows the existence of the logarithmic layer, which is supported by a clear plateau in the indicator function even in low Reτ. Additionally, the wall-normal turbulence intensity and the Reynolds shear stress profiles exhibit a region with constant values over the logarithmic layer. These findings indicate that the identified wall-attached UMZs directly contribute to the logarithmic layer and are important instantaneous structures that can explain the asymptotic behaviors of turbulence statistics predicted by Townsend's attached eddy hypothesis.