Global finite amplitude perturbations in medium aspect ratio pipe flow

Abstract

Results of a numerical study on the finite amplitude global perturbations inducing transition to turbulence in pipe flow are reported. The aim of this analysis is to characterise the basin of attraction of the basic Hagen-Poiseuille flow (which is believed to be lineary stable for all Reynolds numbers Re) by means of the minimal amplitude of an initial global perturbation triggering transition. Subcritical transition in pipe flow is extremely sensitive to the shape of the initial perturbation. The analysis is focused on the streak breakdown transition scenario, by which the basic flow, perturbed with streamwise-independent disturbances of azimuthal wave number n = 1, develops transient streaks that are susceptible of being destabilised by much smaller streamwise-dependent perturbations. The numerical simulations cover a wide range of Reynolds numbers Re ∈ [2500, 104] and the transition dynamics are spectrally resolved by the numerical method. The threshold amplitude of perturbations seems to decrease with Re-3/2 within the studied range. © 2005 IOP Publishing Ltd.