the direction of the translation is at right angles to the plane containing their centres.
A vortex filament in the neighbourhood of a plane boundary surface behaves as if it can see its own reflection, that is, as if such reflection were another vortex filament.
A vortex ring may be looked upon as the analogue of a vortex pair in three dimensions, i.e., the mutual interaction of its parts results in a motion of translation, the translation taking place at right angles to the plane of the ring.
Two concentric co-axial vortex rings tend to behave as two similarly rotating filaments, i.e., revolve round one another; the consequence of such a motion under the changed conditions is that the two rings alternately overtake and pass through one another, the process being repeated and going on indefinitely. Rings behaving in this way are sometimes said to play "leap-frog."
Groups of filaments or rings behave in a similar manner to pairs: thus a group of rings may play "leap-frog" collectively so long as the total number of rings does not exceed a certain maximum; congregations of vortex filaments likewise by their mutual interaction move as part of a concerted system, like waltzers in a ball-room; when the number exceeds a certain maximum the whole system consists of a number of lesser groups.
In general, beyond the special features above described, the motion and behaviour of vortices and vortex rings presents much in common with that of solid bodies; thus two vortex rings on impact bounce off from one another like two perfectly elastic solids, and we have the Vortex Atom theory first propounded by Lord Kelvin (Sir William Thomson), and subsequently extended by Professor J. J. Thomson (ref. "Motion of Vortex Rings," Macmillan, 1883).[1]
- ↑ The present description of vortices and vortex motion is a bare statement of the most elementary facts of the subject. Most of that which is known will be found in the writings of Helmholtz, Kelvin, and J. J. Thomson, and a mathematical resumé, with copious references, in Lamb's "Hydrodynamics," Chap. VII.
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