Role of wall-attached structures in frictional drag reduction by streamwise

The role of wall-attached structures in the frictional drag reduction by the Navier slip is explored. The wall-attached structures are extracted from the clusters of streamwise velocity fluctuations in a turbulent channel flow (\textit{Re}$_{\tau }=$ 470). The skin friction coefficient ($C_{f})$ is decreased by 35{\%}. A dataset of the no-slip condition (\textit{Re}$_{\tau }=$ 577) is also included for comparison. The wall-attached structures extend toward the upstream in the vicinity of the wall by the slip. The convection velocity of the wall-attached structures increases near the wall, leading to the wide influence on the inner region via roll-cell motions. The vortical structures circumscribing the wall-attached structures are attenuated, since the mean shear of the structures is decreased by the slip. The contribution of the wall-attached structures to $C_{f}$ is quantified through the skin friction decomposition, which can be derived from the mean vorticity equations. The advective vorticity transport and vortex stretching terms around the wall-attached structures are found to dominate the contributions to the frictional drag. The wall-attached structures are responsible for 53.2{\%} of the total reduction of $C_{f}$.