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The motion of a buoyant vortex filament

Published online by Cambridge University Press:  19 October 2018

Ching Chang Open the ORCID record for Ching Chang [Opens in a new window]  and
Stefan G. Llewellyn Smith Open the ORCID record for Stefan G. Llewellyn Smith [Opens in a new window]
Ching Chang*
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Stefan G. Llewellyn Smith
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA Scripps Institution of Oceanography, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0213, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond. A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , R1
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Copyright
© 2018 Cambridge University Press 

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