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Spherical vortices in rotating fluids

Published online by Cambridge University Press:  08 May 2018

M. M. Scase Open the ORCID record for M. M. Scase [Opens in a new window]  and
H. L. Terry
M. M. Scase*
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
H. L. Terry
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
*
†Email address for correspondence: matthew.scase@nottingham.ac.uk
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Abstract

A popular model for a generic fat-cored vortex ring or eddy is Hill’s spherical vortex (Phil. Trans. R. Soc. A, vol. 185, 1894, pp. 213–245). 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, pp. 117–129). 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.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , R4
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Copyright
© 2018 Cambridge University Press 

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