Vortex dynamics is at the heart
of the turbulence problem. Vortices have been described by various authors
as the “muscles and sinews” of turbulence and the “voice”
of the flow (since sound can be generated by vortex motion). Vortex phenomena
span an incredible range of scales: quantized vortices in helium II have
a core size of an Angstrom, tornados and waterspouts of ordinary human
scale, phenomena such as Jupiter’s red spot have planetary scales
and vortex motions are evident in entire galaxies.
Laboratory vortex rings share many common problems with all these flows.
The formation of ring vortices from the gun is an example of the rollup
of the boundary layer created by the piston. The lifetime of the rings
is determined by friction on the core, and by the growth of core instabilities.
Collisions with walls, free surfaces and other vortices have not been
systematically studied, but they involve topological changes owing to
vortex reconnections which are very fundamental to turbulent flows. Vortices
can “leapfrog” through each other, they can coalesce to one
vortex ring on collision, or they can scatter with possible exchange of
bits of line from each vortex. It has been anticipated from the time of
Kelvin that vortex rings might “link”, at least for a finite
time. This phenomenon has yet to be observed.
Waves can exist on the cores of vortex rings. Bending waves (or Kelvin
waves) can exist on even very thin cores of vortices. Relatively thick
cores with distributions of vorticity can have instabilities within the
cores themselves. Studies of these instabilities are scarce in number
and limited in scope.
Knowledge of vortex ring dynamics can help other problems: For example,
vortex loops or horseshoe vortices pinned to boundaries by roughness can
play a role in nucleation of other vortices and are important in their
own right. But it is safe to say that if we cannot understand vortex rings,
we shall have little opportunity to understand more complicated vortex
dynamics, and indeed turbulent flows in general.