PT - JOURNAL ARTICLE
AU -
AU -
TI - On the stability of vortex rings
DP - 1973 Mar 27
TA - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
PG - 335--353
VI - 332
IP - 1590
4099 - http://rspa.royalsocietypublishing.org/content/332/1590/335.short
4100 - http://rspa.royalsocietypublishing.org/content/332/1590/335.full
SO - Proc R Soc Lond A Math Phys Sci1973 Mar 27; 332
AB - 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). The results of the analysis show that a vortex ring in an ideal fluid is almost always unstable. The number of waves around the perimeter in the unstable mode depends upon the size of the vortex core. For a given vortex core, only one mode is unstable and the smaller the vortex core, the larger the number of waves in the mode. The instability was investigated experimentally with vortex rings generated in air. A laser Doppler velocimeter was used to measure the velocity along the centreline of the ring and thus the circulation. The properties of the vortex core were inferred from the measurements of circulation, ring radius and velocity. The comparisons between theoretical predictions and experimental results show qualitative agreement in the prediction of the number of waves in the unstable mode and quantitative agreement in the prediction of the amplification rate in the early stages of growth.