the maximum wall velocity $W_m$. (A third parameter describing the oscillation is the peak-to-peak wall displacement $D_m$, which is $D_m = W_m T/\pi$ for a sinusoidal waveform.) @choi-xu-sung-2002 have correlated their drag reduction direct numerical simulation (DNS) data with $S$, which was found from physical arguments pertaining to the interaction between the spanwise laminar Stokes layer and the near-wall turbulence. A least-squares fit yielded a power-law expression for $S$. @quadrio-ricco-2004b (denoted by QR hereafter) have recently improved the analysis by @choi-xu-sung-2002 on the basis of a DNS dataset of a turbulent channel flow modified by the motion of both walls, for a Reynolds number $Re_\tau=200$ defined by the friction velocity of the natural turbulent flow and half the distance between the channel walls. The accuracy of their dataset brought to light a linear relation between the drag reduction and $S$, which was suggested to hold as long as $T$ remains smaller than a typical integral time scale of the wall turbulence.

The main objective of the present work is to investigate further the possibility of estimating the drag reduction through the parameter $S$. In QR the correlation analysis between $S$ and the drag reduction was carried out only with their 