# On the stability of vortex rings

@article{Widnall1973OnTS, title={On the stability of vortex rings}, author={Sheila Evans Widnall and John P. Sullivan}, journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences}, year={1973}, volume={332}, pages={335 - 353} }

The stability of vortex rings is investigated both theoretically and experimentally. The theoretical analysis considers the stability of the vortex-filament ring of small but finite core size in an inviscid fluid to small sinusoidal displacements of its centreline. The effect of the vorticity distribution within the finite vortex core on the self-induced motion of each element of the vortex filament is calculated on the basis of the results presented previously by Widnall, Bliss & Zalay (1970…

## 268 Citations

### The instability of the thin vortex ring of constant vorticity

- Physics, Environmental SciencePhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
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### Experimental study of the instability of vortex rings

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- 2002

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### The evolution of an elliptic vortex ring

- PhysicsJournal of Fluid Mechanics
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### Dynamics and Instability of a Vortex Ring Impinging on a Wall

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- 2015

Dynamics and instability of a vortex ring impinging on a wall were investigated by means of large eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various…

### The linear stability of swirling vortex rings

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The stability of vortex rings with an azimuthal component of velocity is investigated numerically for various combinations of ring wavenumber and swirl magnitude. The vortex rings are equilibrated…

### Numerical stability analysis of a vortex ring with swirl

- PhysicsJournal of Fluid Mechanics
- 2019

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is…

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- 2004

This paper presents the results of an experimental investigation of the effects of a piston vortex on the vorticity evolution of a vortex ring. The rings are produced by the roll-up of a shear layer…

### Dynamics and stability of a vortex ring impacting a solid boundary

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- 1995

Direct numerical simulations were used to study the dynamics of a vortex ring impacting a wall at normal incidence. The boundary layer formed as the ring approaches the wall undergoes separation and…

### Numerical Study of the Instability and Flow Transition in a Vortex-Ring/Wall Interaction

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- 2016

Instability and fl w transition of a vortex ring impinging on a wall were investigated by means of large-eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings.…

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