**4. Discussion**

We investigated transient turbulence and the transition to sustained turbulence in a high-radius-ratio Taylor–Couette experiment. The presented lifetime measurements confirm the transient nature of turbulent stripes and show that their decay is memoryless in agreement with the study by Borrero et al. [16] for a smaller Taylor–Couette setup and more generally with transitional turbulence in other shear flows. At lower Reynolds numbers the lifetimes are shorter than the equilibrium time of the flow to adapt to the reduction in Reynolds number, but distributions remain exponential unlike in pipe flow where at low Reynolds numbers the tails deviated from exponential [14]. Our system area is more than 10 times larger than previous Couette and Taylor–Couette experiments, which enables us to approach the critical point much closer without suffering from finite size effects. Whereas such studies in smaller aspect ratio Couette flow had suggested a discontinuous drop form considerably larger turbulent fractions in our case the scaling is continuous, consistent with a second-order phase transition. Our observation of a continuous phase transition is also in line with recent studies of Waleffe flow [28] and of channel flow (see Figure 9a of [46]). An even closer approach to the critical point also leads to a sudden drop in turbulent fraction in the present case. As the critical point is approached length scales diverge and once typical laminar gap sizes exceed the system size the flow relaminarizes. Finite size effects can therefore be mistaken for a discontinuous transition. To resolve this question and to potentially obtain critical exponents, would require an even larger system size which sets a challenge for future experiments. Because of the long laminar gaps separating stripes in the vicinity of the critical point, and of the results of simulations and experiments of quasi-one-dimensional Couette flow [26,38] and Waleffe flow [28], we estimate that order of 1000 gap width are needed in the azimuthal and axial directions to probe for scale invariant flow patterns sufficiently close to the critical point. Such a study would however require cylinders manufactured to considerably higher precision than the already very precise ones used in the present study.

**Author Contributions:** The experiments and analyses was performed by K.A. and the work was conceptualized by K.A. and B.H. Both authors wrote the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Central Research Development Fund of the University of Bremen grant number ZF04B /2019/FB04 Avila\_Kerstin ("Independent Project for Postdocs").

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** Shreyas Jalikop is acknowledged for recording some of the lifetime measurements.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
