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|Title:||The unsteady flow due to an impulsively rotated sphere|
|Citation:||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015; 471(2181):20150299-1-20150299-20|
|Sophie A.W. Calabretto, Benjamin Levy, James P. Denier and Trent W. Mattner|
|Abstract:||We consider the flow induced by a sphere, contained in an otherwise quiescent body of fluid, that is suddenly imparted with angular momentum. This classical problem is known to exhibit a finite-time singularity in the boundary-layer equations, due to the viscous boundary layer, induced by the sudden rotation, colliding at the sphere's equator. We consider this flow from the perspective of the post-collision dynamics, showing that the collision gives rises to a radial jet headed by a swirling toroidal starting vortex pair. The starting vortex propagates away from the sphere and, in doing so, loses angular momentum. The jet, in turn, develops an absolute instability which propagates back towards the sphere's equator. The starting vortex pair detaches from the jet and expands as a coherent (non-swirling) toroidal vortex pair. We also present results of some new experiments which show good qualitative agreement with our computational results.|
|Keywords:||radial jets; toroidal vortex; unsteady boundary layers; rotating spheres|
|Rights:||© 2015 The Author(s) Published by the Royal Society. All rights reserved.|
|Appears in Collections:||Mathematical Sciences publications|
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