- Widnall, S.E. and Bliss, D.B. and Chon-Yin Tsai, The instability of short waves on a vortex ring,
J. Fluid Mech. (UK), vol. 66
pp. 35 - 47 .
(last updated on 2007/04/09)
A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here