Increasing lifetimes and the growing saddle of shear flow turbulence

In linearly stable shear flows turbulence spontaneously decays on a characteristic transient lifetime. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to sustained turbulence at a critical point has been discussed, yet the mechanism underlying the increase has not been understood. We present a mechanism by which the lifetimes increase: a locally attracting orbit forms a ``turbulent bubble'' via a route-to-chaos sequence of bifurcations, followed by a boundary crisis in which the chaotic attractor turns into a chaotic saddle. The complexity of the turbulence supporting saddle hence increases and it becomes more densely filled with unstable periodic orbits, increasing the time it takes for a trajectory to leave the saddle and decay to the laminar state. We demonstrate this phenomenon in the state space of plane Couette flow and show that characteristic lifetimes vary non-smoothly and non-monotonically with Reynolds number.