title: Increasing lifetimes and the growing saddles of shear flow turbulence.
abstract: In linearly stable shear flows, turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. 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. We present a mechanism by which the lifetimes increase: in the system's state space, turbulent motion is supported by a chaotic saddle. Inside this saddle a locally attracting periodic orbit is created and undergoes a traditional bifurcation sequence generating chaos. The formed new "turbulent bubble" is initially an attractor supporting persistent chaotic dynamics. Soon after its creation, it collides with its own boundary, by which it becomes leaky and dynamically connected with the surrounding structures. The complexity of the chaotic saddle that supports transient turbulence hence increases by incorporating the remnant of a new bubble. As a a result, the time it takes for a trajectory to leave the saddle and decay to the laminar state is increased. We demonstrate this phenomenon in plane Couette flow and show that characteristic lifetimes vary nonsmoothly and nonmonotonically with Reynolds number.
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany.
authors.forename: Tobias
authors.initials: T
authors.lastname: Kreilos
authors.affiliation: Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany and J.M. Burgerscentrum, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands.
authors.forename: Bruno
authors.initials: B
authors.lastname: Eckhardt
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany and Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
authors.forename: Tobias M
authors.initials: TM
authors.lastname: Schneider