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Transition to chaos in the wake of a rolling sphere

Published online by Cambridge University Press:  22 February 2012

A. Rao ,
P.-Y. Passaggia ,
H. Bolnot ,
M.C. Thompson ,
T. Leweke  and
K. Hourigan
A. Rao*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
P.-Y. Passaggia
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Équilibre (IRPHE), CNRS/Aix-Marseille Université, 13384 Marseille CEDEX 13, France
H. Bolnot
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Équilibre (IRPHE), CNRS/Aix-Marseille Université, 13384 Marseille CEDEX 13, France
M.C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
T. Leweke
Affiliation:
Institut de Recherche sur les Phénomènes Hors-Équilibre (IRPHE), CNRS/Aix-Marseille Université, 13384 Marseille CEDEX 13, France
K. Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia Division of Biological Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The wake of a sphere rolling along a wall at low Reynolds number is investigated numerically and experimentally. Two successive transitions are identified in this flow, as the Reynolds number is increased. The first leads to the periodic shedding of planar symmetric hairpin vortices. The second and previously unknown transition involves a loss of planar symmetry and a low-frequency lateral oscillation of the wake, exhibiting a surprising 7:3 resonance with the hairpin vortex shedding. The two transitions are characterized by dye visualizations and quantitative information obtained from numerical simulations, such as force coefficients and wake frequencies (Strouhal numbers). Both transitions are found to be supercritical. Further increasing the Reynolds number, the flow becomes progressively more disorganized and chaotic. Overall, the transition sequence for the rolling sphere is closer to the one for a non-rotating sphere in a free stream than to that of a non-rotating sphere close to a wall.

JFM classification

Nonlinear Dynamical Systems: Chaos Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 135 - 148
Copyright
Copyright © Cambridge University Press 2012

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