Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897199 | Physica D: Nonlinear Phenomena | 2008 | 8 Pages |
Abstract
We show how the ideas of topology and variational principle, opened up by Euler, facilitate the calculation of motion of vortex rings. Kelvin-Benjamin's principle, as generalised to three dimensions, states that a steady distribution of vorticity, relative to a moving frame, is the state that maximizes the total kinetic energy, under the constraint of constant hydrodynamic impulse, on an iso-vortical sheet. By adapting this principle, combined with an asymptotic solution of the Euler equations, we make an extension of Fraenkel-Saffman's formula for the translation velocity of an axisymmetric vortex ring to third order in a small parameter, the ratio of the core radius to the ring radius. Saffman's formula for a viscous vortex ring is also extended to third order.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Y. Fukumoto, H.K. Moffatt,