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Transition in Localized Pipe Flow Turbulence

2009; American Physical Society; Volume: 103; Issue: 5 Linguagem: Inglês

10.1103/physrevlett.103.054502

1092-0145

Fernando Mellibovsky, Álvaro Meseguer, Tobias M. Schneider, Bruno Eckhardt,

Combustion and flame dynamics

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 $\mathrm{Re}=1800$ 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 $\mathrm{Re}\ensuremath{\le}2000$ the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For $\mathrm{Re}\ensuremath{\ge}2200$, 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.