Suboptimal control for drag reduction via suppression of near-wall Reynolds shear stress

We propose a new suboptimal control law for drag reduction in wall-turbulence, which requires the streamwise wall-shear signal only. The cost function is designed to reduce the near-wall Reynolds shear stress that is directly related to the turbulent skin friction drag. The suboptimal solution to minimize the cost function is analytically derived by using the procedure proposed by Lee et al. [J. Fluid Mech. 358 (1998) 245]. Direct numerical simulation of turbulent pipe flow shows that the friction drag can be successfully reduced by the derived control law. Moreover, the sign of Reynolds shear stress in the near-wall layer is found to be reversed with the present control.