Kelvin waves are helical displacements of the vortex core as shown in
the figure:
A straight vortex (a) and a vortex with a Kelvin wave (b)
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).