  Recent studies have brought into question the view that at sufficiently high
Reynolds number turbulence is an asymptotic state. We present the first direct
observation of the decay of turbulent states in Taylor-Couette flow with
lifetimes spanning five orders of magnitude. We also show that there is a
regime where Taylor-Couette flow shares many of the decay characteristics
observed in other shear flows, including Poisson statistics and the coexistence
of laminar and turbulent patches. Our data suggest that characteristic decay
times increase super-exponentially with increasing Reynolds number but remain
bounded in agreement with the most recent data from pipe flow and with a recent
theoretical model. This suggests that, contrary to the prevailing view,
turbulence in linearly stable shear flows may be generically transient.
