Resolvent analysis of turbulent friction drag reduction by manipulation of mean velocity profile

In the present study, we numerically manipulate the mean velocity profile of a turbulent channel flow and assess the friction drag reduction performance by using resolvent analysis. Building on the implication obtained from Kühnen et al. (Nat. Phys., Vol. 14, 2017, pp. 386-390) that modifying mean velocity profile flat leads to significant drag reduction, we first introduce two functions for turbulent mean velocity, which can express flattened profiles: one is derived based on the turbulent viscosity model proposed by Reynolds & Tiederman (J. Fluid Mech., Vol. 658, 2010, pp. 336-382), and the other is based on the mean velocity profile of laminar flow. These functions are used as the mean velocity profile for the resolvent analysis, and the flatness of the resulting profiles is characterized by two different measures. As a result, we confirm that, friction drag reduction is achieved if the turbulent mean velocity profile is’flattened’. However, we also find that the flatness of the mean velocity profile in the center of the channel alone is not enough to evaluate the drag reduction performance.