Laminar boundary layer separation and reattachment on a rotating sphere


A new model of the steady boundary layer flow around a rotating sphere is developed that includes the widely observed collision and subsequent eruption of boundary layers at the equator. This is derived following the Segalini & Garrett (J. Fluid Mech., vol. 818, 2017, pp. 288–318) asymptotic approach for large Reynolds numbers but replacing the Smith & Duck (Q. J. Mech. Appl. Maths, vol. 30, issue 2, 1977, pp. 143–156) correction with a higher-order version of the Stewartson (Grenzschichtforschung/Boundary Layer Research, 1958, pp. 59–71. Springer) model of the equatorial flow. The Stewartson model is then numerically solved, for the first time, via a geometric multigrid method that solves the steady planar Navier–Stokes equations in streamfunction-vorticity form on large rectangular domains in a quick and efficient manner. The results are then compared with a direct numerical simulation of the full unsteady problem using the Semtex software package where it is found that there is broad qualitative agreement, namely the separation and reattachment of the boundary layer at the equator. However, the presence of unobserved behaviour such as a large area of reverse flow seen at lower Reynolds numbers than those observed in other studies, and that the absolute error increases with Reynolds number suggest the model needs improvement to better capture the physical dynamics.

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Divisions: College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > Aston Fluids Group
Additional Information: Copyright © The Author(s), 2024. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Uncontrolled Keywords: boundary layer separation,rotating flows,computational methods
Publication ISSN: 1469-7645
Last Modified: 14 Jun 2024 07:36
Date Deposited: 08 Apr 2024 13:48
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Related URLs: ... 085BD278DDB3291 (Publisher URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2024-04-01
Published Online Date: 2024-04-01
Accepted Date: 2024-02-15
Authors: Smith, Benjamin J.
Hussain, Z.
Calabretto, S.A.W.
Garrett, S.J. (ORCID Profile 0000-0002-0671-160X)



Version: Published Version

License: Creative Commons Attribution

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