Spherical vortices in rotating fluids

Scase, Matthew M.; Terry, Helen L.

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.

Citation

Scase, M. M., & Terry, H. L. (2018). Spherical vortices in rotating fluids. Journal of Fluid Mechanics, 846, Article R4-1-R4-12. https://doi.org/10.1017/jfm.2018.334

• 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
• Contract Date: Apr 16, 2018