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Critical threshold in pipe flow transition. (English) Zbl 1221.76096
Summary: This study provides a numerical characterization of the basin of attraction of the laminar Hagen-Poiseuille flow by measuring the minimal amplitude of a perturbation required to trigger transition. For pressure-driven pipe flow, the analysis presented here covers autonomous and impulsive scenarios where either the flow is perturbed with an initial disturbance with a well-defined norm or perturbed by means of local impulsive forcing that mimics injections through the pipe wall. In both the cases, the exploration is carried out for a wide range of Reynolds numbers by means of a computational method that numerically resolves the transitional dynamics. For \(Re ~ O(10^{4})\), the present work provides critical amplitudes that decay as \(Re^{ - 3/2}\) and \(Re^{ - 1}\) for the autonomous and impulsive scenarios, respectively. For \(R\)e=2875, accurate threshold amplitudes are found for constant mass-flux pipe by means of a shooting method that provides critical trajectories that never relaminarize or trigger transition. These transient states are used as initial guesses in a damped Newton-Krylov method formulated to find periodic travelling wave solutions that either travel downstream or exhibit a helicoidal advection.

MSC:
76F06 Transition to turbulence
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