Reynolds number effect on wall turbulence: toward effective feedback control

Direct numerical simulation of turbulent channel flow at Reτ=110–650 is made in order to assess the feedback control algorithms which have been proposed for reducing skin friction. The effectiveness of the existing control schemes is decreased with increasing the Reynolds number from Reτ=110 to 300. It is found, through the Karhunen–Loeve (KL) decomposition of turbulent fluctuations, that the KL modes at 15<y+<30, which correspond to longitudinal vortices and near-wall streaky structures, play a dominant role in the production of turbulence and wall shear stress at Reτ=110. At Reτ=300, however, the KL modes at 30<y+<75 also make appreciable contribution to the wall shear stress generation. The regeneration mechanism of the near-wall vortices is related to the nonlinear interaction between the KL modes at 15<y+<30 and those at 30<y+<75.