Drag reduction in turbulent boundary layers by in-plane wall motion

Drag-reduction techniques capable of reducing the level of turbulent friction through wall-parallel movement of the wall are described, with special emphasis placed on spanwise movement. The discussion is confined to active open-loop control strategies, although feedback control is briefly mentioned with regard to peculiarities of spanwise sensing and/or actuation. Theoretical considerations are first given to explain why spanwise motion is expected to be particularly effective in skin-friction drag reduction. A review of the spanwise oscillating-wall technique is given next, with discussion of recent results and prospects. Last, waves of spanwise velocity are addressed, either spanwise- or streamwise-travelling. The latter include the oscillating wall as a special case. The generalized Stokes layer-i.e. the laminar, transverse oscillating boundary layer that develops under the action of the streamwise-travelling waves-is described, and its importance in determining turbulent drag reduction discussed. Finally, open issues like energetic efficiency and its dependence on Reynolds number are addressed.