Turbulence transition and the edge of chaos in pipe flow

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.

4 pages, 5 figures

References in corpus (1)

• Statistical analysis of coherent structures in transitional pipe flow

Cited by in corpus (16)

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• An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar
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• On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
• Lifetime statistics in transitional pipe flow
• Subcritical dynamos in shear flows
• Laminar-turbulent separatrix in a boundary layer flow
• Understanding the sub-critical transition to turbulence in wall flows
• How does flow in a pipe become turbulent?
• Localization in a spanwise-extended model of plane Couette flow
• Deterministic and stochastic aspects of the transition to turbulence
• Streamwise decay of localized states in channel flow
• Turbulent transition in a truncated one-dimensional model for shear flow
• A spotlike edge state in plane Poiseuille flow