Mechanism of drag reduction by pre-determined spatio-temporally periodic control of wall turbulence

We evaluate pre-determined controls with temporally- and spatially-periodic spanwise velocity inputs at the wall in a fully developed turbulent channel flow. The spatially-periodic control generally achieves better performance than the temporally-periodic one, which is conventionally called the spanwise wall-oscillation control. Particular attention is paid to the Reynolds stress, which dominates the skin friction. We apply a conditional sampling technique in order to clarify the response of the Reynolds stress around a particular rotation direction of a longitudinal vortex to the spanwise control input. Quadrant analysis of the Reynolds stress shows that the phase-dependencies of Q2 and Q4 events around a longitudinal vortex are totally different. Based on this knowledge, the drag reduction mechanisms in the two controls are discussed.