Spherical vortices in rotating fluids
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...
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| Format: | Article |
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Cambridge University Press
2018
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| Online Access: | https://eprints.nottingham.ac.uk/51153/ |
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| author | Scase, Matthew M. Terry, Helen L. |
| author_facet | Scase, Matthew M. Terry, Helen L. |
| author_sort | Scase, Matthew M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:19:38Z |
| format | Article |
| id | nottingham-51153 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:19:38Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-511532020-05-04T19:45:56Z https://eprints.nottingham.ac.uk/51153/ Spherical vortices in rotating fluids Scase, Matthew M. Terry, Helen L. 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. Cambridge University Press 2018-07-10 Article PeerReviewed Scase, Matthew M. and Terry, Helen L. (2018) Spherical vortices in rotating fluids. Journal of Fluid Mechanics, 846 . R4-1-R4-12. ISSN 1469-7645 Waves rotating fluids https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/spherical-vortices-in-rotating-fluids/29FD940CF485394602C09F4AEC2AB6CA doi:10.1017/jfm.2018.334 doi:10.1017/jfm.2018.334 |
| spellingShingle | Waves rotating fluids Scase, Matthew M. Terry, Helen L. Spherical vortices in rotating fluids |
| title | Spherical vortices in rotating fluids |
| title_full | Spherical vortices in rotating fluids |
| title_fullStr | Spherical vortices in rotating fluids |
| title_full_unstemmed | Spherical vortices in rotating fluids |
| title_short | Spherical vortices in rotating fluids |
| title_sort | spherical vortices in rotating fluids |
| topic | Waves rotating fluids |
| url | https://eprints.nottingham.ac.uk/51153/ https://eprints.nottingham.ac.uk/51153/ https://eprints.nottingham.ac.uk/51153/ |