The Velocity of Viscous Vortex Rings

  • P. G. Saffman


The motion of vortex rings of small cross section is considered. A formula is given for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core and an arbitrary circumferential velocity. A definition of velocity is given for the unsteady diffusing ring in a viscous fluid, and the speed is found by the method used for rings in ideal fluids.


Diffusion Equation Vortex Ring Viscous Fluid Tangential Velocity Ideal Fluid 
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  1. Lamb, H., (1932), Hydrodynamics, Cambridge University PressGoogle Scholar
  2. Saffman, P. G., (1970), Studies in App. Math. 49, 371.MATHGoogle Scholar
  3. Tung, C. and Ting, L., (1967), Phys. Fluids, 10, 901.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • P. G. Saffman
    • 1
  1. 1.California Institute of TechnologyUSA

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