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On the transient nature of localized pipe flow turbulence

Published online by Cambridge University Press:  08 March 2010

MARC AVILA ,
ASHLEY P. WILLIS  and
BJÖRN HOF
MARC AVILA*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
ASHLEY P. WILLIS
Affiliation:
Laboratoire d'Hydrodynamique, École Polytechnique, 91128 Palaiseau, France
BJÖRN HOF
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarizes, raising the question of whether it is transient in nature or becomes sustained at a critical threshold. We present extensive numerical simulations and a detailed statistical analysis of the lifetime data, in order to shed light on the sources of the discrepancies present in the literature. The results are in excellent quantitative agreement with recent experiments and show that turbulent lifetimes increase super-exponentially with Reynolds number. In addition, we provide evidence for a lower bound below which there are no meta-stable characteristics of the transients, i.e. the relaminarization process is no longer memoryless.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 646 , 10 March 2010 , pp. 127 - 136
Copyright
Copyright © Cambridge University Press 2010

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