How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from RayleighBenard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by threedimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs. PACS. 47.27.Cn Transition to turbulence – 47.27.nf Flows in pipes and nozzles – 47.10.Fg Dynamical systems methods