Russell J. Donnelly
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Vortex Rings

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.


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