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Stokes’ paradox: creeping flow past a two-dimensional cylinder in an infinite domain

Published online by Cambridge University Press:  21 March 2017

Arzhang Khalili Open the ORCID record for Arzhang Khalili [Opens in a new window]  and
Bo Liu
Arzhang Khalili*
Affiliation:
Department of Biogeochemistry, Max Planck Institute for Marine Microbiology, 28359 Bremen, Germany Department of Physics and Earth Sciences, Jacobs University Bremen, 28759 Bremen, Germany
Bo Liu
Affiliation:
Department of Biogeochemistry, Max Planck Institute for Marine Microbiology, 28359 Bremen, Germany Geochemistry and Isotope Biogeochemistry Group, Marine Geology Department, Leibniz Institute for Baltic Sea Research (IOW), 18119 Warnemünde, Germany
*
†Email address for correspondence: akhalili@mpi-bremen.de
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Abstract

Finite container sizes in experiments and computer simulations impose artificial boundaries which do not exist when they are meant to mimic ambient fluid of infinite extent. We show here that this is the case with flows past an infinite cylinder placed in an infinite ambient fluid (Stokes’ paradox). Using a highly efficient and stable numerical method that is capable of handling computational domains several orders of magnitude larger than in previous studies, we provide a criterion for the minimum necessary extent around an object in order to provide accurate velocity and pressure fields, which are prerequisites for correct calculation of secondary quantities such as drag coefficient. The careful and extensive simulations performed suggest an improved relation for the drag coefficient as a function of Reynolds number, and identify the most suitable experimental data available in the literature.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Stokesian dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 374 - 387
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Copyright
© 2017 Cambridge University Press 

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