viscosity of the fluid) is compared with the critical Reynolds numbers for stability or transition of the Stokes flow, although this analysis is obviously not rigorous in that we consider a space-averaged profile and not a purely laminar flow. Despite the wall velocity being as high as twice the centreline velocity, $Re_\delta = W_m^+\sqrt{T^+/\pi}$ is not high, since $T$ is low. For our data, $Re_\delta= 80-140$, which is lower than $\approx 1400$ found by @blennerhassett-bassom-2006 as the lowest critical Reynolds number for an oscillatory boundary layer between two parallel plates, and $\approx 550$ reported by @vittori-verzicco-1998 as their transition threshold.

However, these discrepancies do not limit the possibility of employing $S$ to study successfully the flow because all the relevant drag reduction features occurs for smaller $W_m^+$. Indeed, (i) $T_{op t,D}(D_m)$ approaches a constant value for $W_m^+>$25 (see Fig. 1 at page 259 in QR), (ii) the explored range of wall velocities has been $W_m^+<$16 in the previous experimental works and $W_m^+<$18 in the previous numerical works (except for a few cases at $W_m^+$=27 in QR), (iii) QR have found that the drag reduction does not change significantly with $W_m$ for $W_m^+>$20, which greatly simplifies the analysis and it implies 