APPENDIX III.
A NOTE ON DISCONTINUOUS MOTION.
In § 101 allusion has been made to the instability of a surface of kinetic discontinuity in an inviscid fluid, and at the same time the impossibility of such a surface breaking up into finite vortex filaments is pointed out.
Helmholtz[1] has suggested that the instability takes the form of a development of convolutions of the surface of discontinuity or surface of gyration. He says:—
"An infinitely extended plane surface uniformly covered with parallel straight [infinitesimal] vortical filaments might indeed continue stable, but where the least flexure occurs at any time the surface curls itself round in ever narrowing spiral coils, which continually involve more and more distant parts of the surface in their vortex."
It is, unfortunately, not easy to form a clear picture of the continued transition that the above implies, or even of the resulting system of flow. There would appear to be no doubt, however, that Helmholtz's view is substantially correct.
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- ↑ "Sensations of Tone," Appendix VII., B II.
