The instability of the thin vortex ring of constant vorticity
Abstract
A theoretical study indicating that vortex rings at moderate Reynolds numbers are unstable to azimuthal bending waves is presented. Only the case of a thin vortex ring with a core of constant vorticity in an inviscid flow is examined. The disturbance flow and the mean flow of the vortex ring are derived as asymptotic solutions near the core; the stability analysis is developed completely for a certain class of bending waves that are unstable on a line filament in the presence of strain. The vortex ring is found to be always unstable for at least two wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate. Published experimental results are cited to support these conclusions.
- Publication:
-
Philosophical Transactions of the Royal Society of London Series A
- Pub Date:
- October 1977
- DOI:
- 10.1098/rsta.1977.0146
- Bibcode:
- 1977RSPTA.287..273W
- Keywords:
-
- Flow Stability;
- Vortex Rings;
- Vorticity;
- Wave Interaction;
- Asymptotic Methods;
- Differential Equations;
- Flow Distribution;
- Ideal Fluids;
- Potential Flow;
- Wave Equations;
- Fluid Mechanics and Heat Transfer