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An experimental and computational study of the post-collisional flow induced by an impulsively rotated sphere

Published online by Cambridge University Press:  25 October 2019

Sophie A. W. Calabretto Open the ORCID record for Sophie A. W. Calabretto [Opens in a new window] ,
James P. Denier Open the ORCID record for James P. Denier [Opens in a new window]  and
Benjamin Levy
Sophie A. W. Calabretto*
Affiliation:
Department of Mathematics and Statistics, Macquarie University, Sydney 2109, Australia
James P. Denier
Affiliation:
Department of Mathematics and Statistics, Macquarie University, Sydney 2109, Australia
Benjamin Levy*
Affiliation:
6 Lorne Street, Auckland 1010, New Zealand
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The unsteady flow due to a sphere, immersed in a quiescent fluid, and suddenly rotated, is a paradigm for the development of unsteady boundary layers and their collision. Such a collision arises when the boundary layers on the surface of the sphere are advected towards the equator, where they collide, serving to generate a radial jet. We present the first particle image velocimetry measurements of this collision process, the resulting starting vortex and development of the radial jet. Coupled with new computations, we demonstrate that the post-collision steady flow detaches smoothly from the sphere’s surface, in qualitative agreement with the analysis of Stewartson (Grenzschichtforschung/Boundary Layer Research (ed. H. Görtler), Springer, 1958, pp. 60–70), with no evidence of a recirculation zone, contrary to the conjectured structure of Smith & Duck (Q. J. Mech. Appl. Maths, vol. 20, 1977, pp. 143–156).

JFM classification

Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer receptivity Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 772 - 793
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Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

Formerly affiliated with Department of Engineering Science, University of Auckland, New Zealand.

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