Stokes' Mechanism of Drag Reduction

The mechanism of drag reduction due to span wise wall oscillation in a turbulent boundary layer is considered in this report. Published measurements and simulation data are analyzed in light of Stokes second problem. A kinematic vorticity reorientation hypothesis of drag reduction is first developed. It is shown that span wise oscillation seeds the near-wall region with oblique and skewed Stokes vorticity waves. They are attached to the wall and gradually align to the free stream direction away from it. The resulting Stokes layer has an attenuated nature compared to its laminar counterpart. The attenuation factor increases in the buffer and viscous sublayer as the wall is approached. The mean velocity profile at the condition of maximum drag reduction is similar to that due to polymer. The final mean state of maximum drag reduction due to turbulence suppression appears to be universal in nature. Finally, it is shown that the proposed kinematic drag reduction hypothesis describes the measurements significantly better than the current direct numerical simulation method.