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Updated: Jul 13, 2026

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
Published on: August 26, 2019
Turbulence transition and the edge of chaos in pipe flow
Tobias M Schneider1, Bruno Eckhardt, James A Yorke
1Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany.
Abstract:
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.
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