Studying edge geometry in transiently turbulent shear flows

Matthew Chantry*, Tobias M. Schneider

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)

Abstract

In linearly stable shear flows at moderate Reynolds number, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories, we provide evidence that the edge of chaos does not separate state space globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.

Original languageEnglish
Pages (from-to)506-517
Number of pages12
JournalJournal of Fluid Mechanics
Volume747
DOIs
Publication statusPublished - May 2014

Keywords

  • instability
  • nonlinear dynamical systems
  • transition to turbulence
  • PLANE COUETTE-FLOW
  • TRANSITIONAL PIPE-FLOW
  • BOUNDARY
  • DYNAMICS
  • STATES
  • MODELS

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