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Flow past a sphere translating along the axis of a rotating fluid: revisiting numerically Maxworthy's experiments

Published online by Cambridge University Press:  19 July 2023

Tristan Aurégan Open the ORCID record for Tristan Aurégan [Opens in a new window] ,
Thomas Bonometti Open the ORCID record for Thomas Bonometti [Opens in a new window]  and
Jacques Magnaudet Open the ORCID record for Jacques Magnaudet [Opens in a new window]
Tristan Aurégan
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
Thomas Bonometti
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
Jacques Magnaudet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France
*
†Email address for correspondence: jacques.magnaudet@imft.fr
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Abstract

We compute the flow induced by the steady translation of a rigid sphere along the axis of a large cylindrical container filled with a low-viscosity fluid set in rigid-body rotation, the sphere being constrained to spin at the same rate as the undisturbed fluid. The parameter range covered by the simulations is similar to that explored experimentally by Maxworthy (J. Fluid Mech., vol. 40, 1970, pp. 453–479). We describe the salient features of the flow, especially the internal characteristics of the Taylor columns that form ahead of and behind the body and the inertial wave pattern, and determine the drag and torque acting on the sphere. Torque variations are found to obey two markedly different laws under rapid- and slow-rotation conditions. The corresponding scaling laws are predicted by examining the dominant balances governing the axial vorticity distribution in the body vicinity. Results for the drag agree well with the semi-empirical law proposed for inertialess regimes by Tanzosh & Stone (J. Fluid Mech., vol. 275, 1994, pp. 225–256). This law is found to apply even in regimes where inertial effects are large, provided that rotation effects are also large enough. Influence of axial confinement is shown to increase dramatically the drag in rapidly rotating configurations, and the container length has to be approximately a thousand times larger than the sphere for this influence to become negligibly small. The reported simulations establish that this confinement effect is at the origin of the long-standing discrepancy existing between Maxworthy's results and theoretical predictions.

JFM classification

Geophysical and Geological Flows: Rotating flows Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Quasi-geostrophic flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 967 , 25 July 2023 , A25
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

‡

Present address: Laboratoire de Physique et Mécanique des Milieux Hétérogènes, PMMH UMR 7636 CNRS ESPCI PSL, Univ. Paris Cité Sorbonne Université, Paris, France.

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