**5. Conclusions**

The transitional regime of pPf has been investigated numerically in large periodic domains. The transitional regime is composed of two sub-regimes each demarcated by a distinct behavior. The *patterning regime* is characterized, for 50 ď *ReG <sup>τ</sup>* ď 90, by a constant value of *Cf* « 0.01 and by a propagation downstream at approximately the mean bulk velocity ă *ub* ą. For lower *ReG <sup>τ</sup>* all the way down to the critical point close to *ReG <sup>τ</sup>* ď 36, independent turbulent bands define a regime analogous to the puff regime of cylindrical pipe flow. The patterns are shown to exhibit a near constant angle of inclination *θ* " 25˝ ˘ 2.5˝ for 60 ď *ReG <sup>τ</sup>* ď 90, which increases with reducing *ReG <sup>τ</sup>*. Both sub-regimes can be classified as spatiotemporally intermittent, as demonstrated by the exponential tails of the distribution of laminar gaps. The statistics of the local fields *τ* and *ub* reinforce the feeling that a fruitful analogy with first order phase transitions could be developed, but the later remains to be made more precise and exploited.

**Author Contributions:** Conceptualization, Y.D. and O.D.; methodology, P.V.K., Y.D. and O.D.; data curation, P.V.K.; original draft preparation, Y.D. and P.V.K.; visualization, P.V.K.; supervision, Y.D. and O.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This study was made possible using computational resources from IDRIS (Institut du Développement et des Ressources en Informatique Scientifique) and the support of its staff. We would like to acknowledge and thank the entire team of *channelflow.ch* for building the code and making it open source. The authors would also like to thank Takahiro Tsukahara, Kazuki Takeda, Jalel Chergui, Florian Reetz, Rob Poole, Rishav Agrawal, Laurette S. Tuckerman, and Sebastian Gomé for valuable discussions and technical input.

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