Transition in localized pipe flow turbulence.

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar flow from turbulent intermittency. For Reynolds numbers ranging from Re=1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For Re< or =2000 the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For Re> or =2200, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.