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We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.
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Supplemental Video 1: Peristalsis at Reynolds 100 and wavelength 2π for three constrictions φ. The pressure field is shown by the colormap, the streamwise velocity is shown by velocity profiles. Passive particles tracers are present to emphasize the details of the flow motion. The wall deformation in the form of a traveling wave induces a flow from regions being constricted to regions being expanded: both forward and backward. The backward flow takes place in a constricted region, where viscosity opposes the motion. This results in pumping in the direction of the wave. Movie adapted with permission from Hœpffner & Fukagata (2009); copyright 2009 Cambridge University Press.
Supplemental Video 2: Blowing and suction at wave amplitude φ= 0.2 and wavelength 2π for three Reynolds numbers. The traveling wave of blowing and suction entrains particles in rotating trajectories. The backward part of this rotation takes place away from the wall, whereas the forward part of the rotation takes place close to the wall where viscosity opposes the motion. This results in pumping in the direction opposite to the wave. Movie adapted with permission from Hœpffner & Fukagata (2009); copyright 2009 Cambridge University Press.