**4. Conclusions**

In this paper, the subcritical transition of channel flow is studied experimentally and theoretically. A pressure turbulence intensity is defined to describe the pressure fluctuations, and it is found that both the pressure and the velocity turbulence intensities reach maxima at the same Reynolds number during the transition, where the turbulence fraction is about 0.6 and both the friction coefficient and the turbulence fraction increase abruptly with *Re*. The velocity defect of localized turbulent structure leads to a negative skewness, and for all tested cases, the smallest *Re* where the skewness of the midplane velocity starts to be negative is about 660. Since the onset of turbulence depends on not only the intensities but also the forms of initial or upstream disturbances, the high-order moments of fluctuations are better markers for the start of transition than the turbulence intensity or fluctuation kinetic energy, and hence should be considered in the future transition control strategies.

According to the experimental data, there exist maxima of the turbulence intensity and the forth-order moment of the midplane streamwise velocity and a negative minimum for the third-order moment. At the late stage of transition, the third-order moment decreases to a low level, and the turbulence intensity and the forth-order moment remain finite values. These phenomena are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit. In addition, different variation behaviors of the friction coefficient are explained by this model, as well, mainly in terms of the turbulence fraction and the aperiodic distribution of Reynolds stress in the localized turbulent structures, and the latter factor should be considered in the future transition modelling.

**Author Contributions:** Conceptualization, J.T. and S.X.; methodology, S.X. and J.T.; validation, J.L., Y.X., and M.L.; formal analysis, J.L., J.T., and Y.X.; data curation, J.L. and Y.X.; original draft preparation, J.T. and J.L.; supervision, J.T. and S.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grants Nos. 91752203, 11772173, and 11490553).

**Acknowledgments:** The authors would like to thank many cited authors for insightful discussions.

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