Drag reduction effect by a wave-like wall-normal body force in a turbulent channel flow

Skin-friction drag reduction effect of a wave-like wall-normal body force in a fully developed turbulent channel flow is investigated by means of direct numerical simulation. The flow rate is kept constant; the bulk Reynolds number is set at 5600, which corresponds to the friction Reynolds number of about 180 in the uncontrolled flow. An exponential decay of the wall-normal body force is assumed so that the body force acts in the regions near the walls only. The friction drag is found to decrease when the wave travels in the upstream direction at slower wavespeeds than the bulk-mean velocity; the maximum drag reduction rate of about 40% is achieved in the case of a stationary control input. The net energy saving rate, however, is found to be mostly negative and, if positive, subtle. Visualization of the flow field shows attenuation of streamwise vortical structures and existence of spanwise roller-like vortices. The spanwise roller-like vortices are found to produce a negative Reynolds shear stress in the regions near the walls, which contributes to the reduction of friction drag. A linear analysis reveals that the spanwise roller-like vortices are well described by a linearized Navier-Stokes equation.