*3.1. Lifetimes of Turbulent Stripes and Spots*

For the lifetimes measurements, the speed of the lids was held constant at *Re*lids = −800. The system was perturbed by rapidly accelerating the speed of the inner cylinder to *Rei* = 630. This excited at first a linear instability in the form of laminar spirals (see Figure 3a), which quickly evolved into an intermittent pattern of laminar-turbulent stripes (see Figure 3b). The flow was then given sufficient time to reach a statistical steady state pattern. The camera started to record the flow pattern 20 s before *Rei* was abruptly reduced to one of the six values indicated in the legend of Figure 5. The flow was continuously recorded until it relaminarised. Rather independently of the *Rei*, the turbulent fraction typically dropped monotonically within the first 20 s, as the flow adapted to the new *Rei*. Two examples of the corresponding spatio-temporal dynamics are shown in Figure 4, where the green line indicates the change of the *Rei* in time. Despite the apparently similar dynamics, the long time behavior of these two cases is very different, leading to different lifetimes, see Figure 2. The complete decay of turbulence was systematically detected by determining the time at which the moving average of the turbulent fraction dropped permanently below a threshold.

During most of the runtime, the axial extent of the turbulent stripes was shorter than the cylinder length. The stripes moved in the axial and azimuthal direction exhibited a rich dynamics, including growth, shrinkage, splitting, merging and decay. Interactions with the axial lids occurred frequently. Specifically, the decay occurred often close to the lids. We thus believe that end effects are likely to influence the turbulent dynamics despite the large axial aspect ratio of our setup.

The probability of survival of turbulence as a function of time is shown in Figure 5. For the two lowest *Rei* investigated the lifetimes are all shorter than 20 s, which corresponds to the time in which the (averaged) turbulent fraction continuously decreases without developing intrinsic dynamics. Therefore it is unclear wether the corresponding lifetimes are exponentially distributed or not in these two cases. A similar behavior was observed for the decay of puffs in pipe flow at low *Re* [14] in which the distribution deviated from an exponential one. However, in our measurements the distributions still seems to be exponential and for *Rei* > 507 the probability follows *P*(*t*) = 1 − exp[(*t* − *t*0)/τ, with the equilibration time *t*0≈ 20 s and τ the characteristic lifetime. This indicates that the decay of turbulence in this regime is a memoryless process, as reported for spatially extended plane Couette flow [8], quasi-one-dimensional [26,38] and moderate aspect-ratio [16] Taylor–Couette flows, and also for pipe flow [14] and quasi-one-dimensional channel flow [45].
