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International Journal of Fluid Mechanics Research

ISSN Print: 1064-2277
ISSN Online: 2152-5102

International Journal of Fluid Mechanics Research


pages 618-630

Dynamics of a Viscous Vortex Ring

F. Kaplanski
Department of Aeromechanics, Estonian Energy Research Institute, Tallinn, Estonia
U. Rudi
Department of Aeromechanics, Estonian Energy Research Institute, Tallinn, Estonia

ABSTRACT

The evolution of a viscous vortex ring through the use of the earlier obtained solution of the Stokes equations in the form of time-dependent vorticity distribution is studied. In the long-time limit this distribution transforms into the classical self-similar Phillips' distribution and for t 0 it reduces to a delta-function. Also, this distribution satisfies the condition of the total impulse conservation and for early times its leading-order approximation inside the viscous vortex core is described by the Oseen-Lamb vortices. The integral transforms method is used to derive the corresponding stream function and the translation velocity of the ring. The obtained stream function behaves similarly to the vorticity distribution: at large times it transforms into Phillips' result and for t 0 it reduces to a circular line vortex. The predicted velocity agrees with the asymptotic drift velocity at t → ∞, the Saffman result for the rings with small cross-sections, and with the available experimental data.