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Turbulence transition and the edge of chaos in pipe flow

Tobias M Schneider·Bruno Eckhardt·James A Yorke
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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 \emph{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. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic 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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Tobias M Schneider, Bruno Eckhardt, James A Yorke. 2007-03-30. Turbulence transition and the edge of chaos in pipe flow. https://doi.org/10.1103/physrevlett.99.034502

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