Waves of spanwise velocity imposed at the walls of a plane turbulent channelflow are studied by Direct Numerical Simulations. We consider sinusoidal wavesof spanwise velocity which vary in time and are modulated in space along thestreamwise direction. The phase speed may be null, positive or negative, sothat the waves may be either stationary or traveling forward or backward in thedirection of the mean flow. Such a forcing includes as particular cases twoknown techniques for reducing friction drag: the oscillating wall technique (atraveling wave with infinite phase speed) and the recently proposed steadydistribution of spanwise velocity (a wave with zero phase speed). The traveling waves alter the friction drag significantly. Waves which slowlytravel forward produce a large reduction of drag, that can relaminarize theflow at low values of the Reynolds number. Faster waves yield a totallydifferent outcome, i.e. drag increase. Even faster waves produce a dragreduction effect again. Backward-traveling waves instead lead to drag reductionat any speed. The traveling waves, when they reduce drag, operate in similar fashion to theoscillating wall, with an improved energetic efficiency. Drag increase isobserved when the waves travel at a speed comparable with that of theconvecting near-wall turbulence structures. A diagram illustrating thedifferent flow behaviors is presented.
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