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Studying edge geometry in transiently turbulent shear flows

Published online by Cambridge University Press:  23 April 2014

Matthew Chantry  and
Tobias M. Schneider
Matthew Chantry*
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Tobias M. Schneider
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*
†Email address for correspondence: matthew.chantry@bristol.ac.uk
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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.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 506 - 517
Copyright
© 2014 Cambridge University Press 

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