Kelvin waves are helical displacements of the vortex core as shown in the figure:

• Onset of rotating turbulence
  In this movie, a lattice of quantised vortices created by rotating the container about the vertical direction is destabilised by a small normal flow parallel to the rotation. Notice how the Kelvin waves grow in amplitude, until they trigger vortex reconnections, hence turbulence.
• Kelvin waves on a vortex ring
  This movie shows a circular vortex ring (left), a vortex ring with small amplitude kelvin waves (middle), and a vortex ring with large amplitude Kelvin waves (right). The effect of the Kelvin waves is to slow down the ring. If the amplitude of the Kelvin waves is sufficiently large, the vortex ring can even travel backwards (right).

References:

• Rotating superfluid turbulence
  by M. Tsubota, T. Araki and C F. Barenghi
  Phys. Rev. Lett. 90, 205301 (2003)
• Instability of vortex array and transition to turbulence in rotating helium II
  by M. Tsubota, C F. Barenghi, T. Araki and A. Mitani
  Phys. Rev. B 69, 134515 (2004)
• Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves,
  by C.F. Barenghi, R. Hanninen and M. Tsubota,
  Phys. Rev.. E 74 046303 (2006)