**8. Summary**

An investigation into the intermittencies associated with the low- and high-drag events in turbulent channel flow has been conducted using experiments and DNS. For experiments, simultaneous measurements of streamwise velocity and wall shear stress are carried out to detect and characterise these intermittencies for *Re<sup>τ</sup>* between 70 and 250. DNS is carried out in a large computational box for *Re<sup>τ</sup>* = 70 and 85. The fraction of time spent in the intervals of low- and high-drag is found to be roughly independent of the Reynolds number for 70 ≤ *Re<sup>τ</sup>* ≤ 250 when the criteria for minimum time-duration is kept constant in inner units. The low- and high-drag events exhibit an exponential distribution of the frequency of their occurrence when studied as a function of the duration of their intervals. It is found that even for artificially constructed signals (up to the limit of Gaussian signal), there is a presence of spikes and dips in the ensemble-averaged data, if the same criteria is applied as used to detect a low- or high-drag event in the wall shear stress signals. This suggests that these spikes (or dips) might be the consequence of the conditional averaging of a time series data.

Streamwise velocity profiles, conditionally sampled during the low-drag events, get closer to Virk's MDR profile and the lower-branch of the nonlinear TW solutions for *<sup>y</sup>*<sup>+</sup> <sup>≈</sup> 20–35 at all studied Reynolds numbers. For 120 ≤ *Re<sup>τ</sup>* ≤ 250, in the log-law region, the conditional velocity profile is higher than the unconditional velocity profile with the slope of the profile higher during the low-drag events. Similarly, the conditional velocity profile is lower than the unconditional velocity profile with the slope of the profile being slightly lower during the high-drag events. A comparison of the conditional streamwise velocity profiles at *Re<sup>τ</sup>* = 180 and 250 with other drag reduction techniques is made. A good agreement between the profiles in the log-law region is observed. For *Reτ* = 70 and 85, in addition to the streamwise velocity, wall-normal velocity is also measured to investigate the behaviour of RSS. There is found to be an increase in the conditionally averaged RSS for *y*<sup>+</sup> - 10 during the low-drag events. This is observed to be due to a significant increase in the turbulence-generating Q2 motions during these low-drag events. The high-drag events are found to be associated with the Q4 events, although the RSS during these events remain fairly similar to the unconditional profile for *y*<sup>+</sup> -20.

**Author Contributions:** Conceptualisation, R.J.P., D.J.C.D. and M.D.G.; methodology, R.J.P., D.J.C.D. and H.C.-H.N.; software, R.A. and E.A.D.; validation, R.A.; formal analysis, R.A.; investigation, R.A.; resources, R.J.P., J.S.P.; data curation, R.A.; writing—original draft preparation, R.A. and E.A.D.; writing—review and editing, R.J.P., D.J.C.D., M.D.G., H.C.-H.N. and J.S.P.; visualisation, R.A.; supervision, R.J.P., D.J.C.D. and H.C.-H.N.; project administration, R.J.P., D.J.C.D. and H.C.-H.N.; funding acquisition, R.J.P. and J.S.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Air Force Office of Scientific Research through grant FA9550-16-1-0076.

**Acknowledgments:** This research was funded by the Air Force Office of Scientific Research (AFOSR) through grant FA9550-16-1-0076. M.D.G. acknowledges the financial support obtained from AFOSR through grant FA9550-18-1-0174. E.A.D. and J.S.P. gratefully acknowledge the financial support in part from the National Science Foundation through a grant OIA-1832976. We would like to thank Kevin Zeng (University of Wisconsin-Madison) for helping in transferring the flow fields computed in large computational boxes.

**Conflicts of Interest:** The authors declare no conflict of interest.
