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Published August 10, 2000 | public
Journal Article Open

A model for vortex ring formation in a starting buoyant plume


Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.'s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results.

Additional Information

"Reprinted with the permission of Cambridge University Press." (Received February 20 1999) (Revised March 3 2000) M. Shusser gratefully acknowledges the financial support provided by Lester Deutsch postdoctoral fellowship. We would like to thank Professor Johari for his critical review of this manuscript and providing some unpublished data.


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August 21, 2023
August 21, 2023