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The Velocity of Viscous Vortex Rings
Author(s) -
Saffman P. G.
Publication year - 1970
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1970494371
Subject(s) - vortex ring , vorticity , vortex , burgers vortex , mechanics , ring (chemistry) , ideal (ethics) , classical mechanics , perfect fluid , physics , motion (physics) , vorticity equation , diffusion , core (optical fiber) , vortex stretching , viscosity , mathematics , thermodynamics , optics , chemistry , philosophy , organic chemistry , epistemology
The motion of vortex rings of small cross section is considered. A formula is derived for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core. The effects of viscosity are then examined. A definition of the velocity of an unsteady diffusing ring is given and it is shown that the method used to calculate the ring speed in an ideal fluid can be extended to give the velocity of a vortex ring subject to viscous diffusion.