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Lagrangian approach to laminar–turbulent interfaces in transitional pipe flow

Published online by Cambridge University Press:  16 April 2013

Markus Holzner ,
Baofang Song ,
Marc Avila  and
Björn Hof
Markus Holzner*
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
Baofang Song
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
Marc Avila
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 4, 91058 Erlangen, Germany
Björn Hof
Affiliation:
Max Planck Institute for Dynamics and Self-Organisation, Bunsenstraße 10, 37073 Göttingen, Germany
*
†Email address for correspondence: holzner@ifu.baug.ethz.ch
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Abstract

Transition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar–turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.

JFM classification

Instability: Instability Nonlinear Dynamical Systems: Pattern formation Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 140 - 162
Copyright
©2013 Cambridge University Press 

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