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Spherical vortices in rotating fluids

Scase, Matthew M.; Terry, Helen L.

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Authors

Helen L. Terry



Abstract

A popular model for a generic fat-cored vortex ring or eddy is Hill's spherical vortex (Phil. Trans. Roy. Soc. A vol. 185, 1894, p. 213). This well-known solution of the Euler equations may be considered a special case of the doubly-infinite family of swirling spherical vortices identified by Moffatt (J. Fluid Mech. vol. 35(1), 1969, p. 117). Here we find exact solutions for such spherical vortices propagating steadily along the axis of a rotating ideal fluid. The boundary of the spherical vortex swirls in such a way as to exactly cancel out the background rotation of the system. The flow external to the spherical vortex exhibits fully nonlinear inertial wave motion. We show that above a critical rotation rate, closed streamlines may form in this outer fluid region and hence carry fluid along with the spherical vortex. As the rotation rate is further increased, further concentric 'sibling' vortex rings are formed.

Journal Article Type Article
Acceptance Date Apr 15, 2018
Online Publication Date May 8, 2018
Publication Date Jul 10, 2018
Deposit Date Apr 16, 2018
Publicly Available Date Nov 9, 2018
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 846
Article Number R4-1-R4-12
DOI https://doi.org/10.1017/jfm.2018.334
Keywords Waves, rotating fluids
Public URL https://nottingham-repository.worktribe.com/output/946126
Publisher URL https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/spherical-vortices-in-rotating-fluids/29FD940CF485394602C09F4AEC2AB6CA

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