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Formation of coherent structures by fluid inertia in three-dimensional laminar flows

Published online by Cambridge University Press:  17 June 2010

Z. POURANSARI ,
M. F. M. SPEETJENS  and
H. J. H. CLERCX
Z. POURANSARI
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
M. F. M. SPEETJENS
Affiliation:
Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
H. J. H. CLERCX*
Affiliation:
Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
*
‡Email address for correspondence: [email protected]
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Abstract

Mixing under laminar flow conditions is key to a wide variety of industrial fluid systems of size extending from micrometres to metres. Profound insight into three-dimensional laminar mixing mechanisms is essential for better understanding of the behaviour of such systems and is in fact imperative for further advancement of (in particular, microscopic) mixing technology. This insight remains limited to date, however. The present study concentrates on a fundamental transport phenomenon relevant to laminar mixing: the formation and interaction of coherent structures in the web of three-dimensional paths of passive tracers due to fluid inertia. Such coherent structures geometrically determine the transport properties of the flow and thus their formation and topological structure are essential to three-dimensional mixing phenomena. The formation of coherent structures, its universal character and its impact upon three-dimensional transport properties is demonstrated by way of experimentally realizable time-periodic model flows. Key result is that fluid inertia induces partial disintegration of coherent structures of the non-inertial limit into chaotic regions and merger of surviving parts into intricate three-dimensional structures. This response to inertial perturbations, though exhibiting great diversity, follows a universal scenario and is therefore believed to reflect an essentially three-dimensional route to chaos. Furthermore, a first outlook towards experimental validation and investigation of the observed dynamics is made.

JFM classification

Mixing: Chaotic advection Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 654 , 10 July 2010 , pp. 5 - 34
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

†

Present address: Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden

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