Wall-attached structures of streamwise velocity fluctuations in turbulent pipe flow*

The wall-attached structures of streamwise velocity fluctuations (u) are investigated using direct numerical simulation data of turbulent pipe flow at Re_τ ≈ 930 and 3000. The attached clusters of u are extracted in instantaneous flow fields. At Re_τ ≈ 3000, the attached structures exist over a broad range leading to the presence of the linear relationship between the streamwise length and height (l_y) for the taller structures (l_y⁺ > 400). The width of the objects follows the linear law over 100 < l_y⁺ < R⁺. The population density of the attached structures is inversely proportional to l_y over 0.3 < l_y/R < 0.6, reminiscent of the distribution of hierarchy scales. The streamwise velocity is reconstructed through the superposition of these structures. The log-law indicator function shows a plateau over 164 (≈ 3Re_τ^1/2) < y⁺ < 0.18R⁺ for the positive u, whereas no flat region for the negative u. The magnitude of the wall-shear stress for the positive u is approximately ten times larger than that for the negative u, representing that the logarithmic region observed in the positive u is attributed to high local Re_τ.