discontinuity will spring from the ends in the manner shown, and these surfaces, constituting at first a Helmholtz vortex sheet, will break up into a number of vortex filaments which conceivably become the vortex cores discussed in Chap. IV, with reference to Figs. 83—86.
This view must at present be regarded as tentative, and is not altogether in agreement with the explanation put forward in the chapter to which reference has been made; it is highly suggestive, however, and on that account requires to be recorded; thus if we examine the wing of a bird we find that the middle portion is of a very characteristic arched section, but towards the extremities the arching is very much less pronounced; in fact, the form becomes such as might easily become the seat of discontinuity. This observation applies more particularly to the soaring birds, which in all respects constitute the best criterion.
If the view put forward in § 106 is correct, as to the cause of the noise made by bodies in rapid motion, then the " whirring " noise made by the wing of a bird in flight is a direct proof of the existence of discontinuity.
Of the two explanations of the genesis of the vortex continuations offered here and in Chap. IV., it is not necessary that either should be in error. The previous explanation also opens out a possibility that must not be lost sight of as bearing on the phenomenon now under discussion.
Let us suppose that the two air streams passing under and over the aerofoil find themselves when they meet at the trailing edge possessed of different velocities. Then their common surface would constitute a surface of discontinuity which might in itself fulfil the requirements of theory. But such a condition is impossible in an irrotational mass of fluid, for where there is a difference of velocity there is also a difference of pressure; and the fluid in the periptery is certainly irrotational in the sense of the argument.[1] But let us modify the supposition and take
- ↑ The continuity of the system of flow cut by a path taken round the aerofoil at some distance away, from one side to the other of the supposed surface of discontinuity, points to this conclusion; the motion in the region traversed by such a path would be sensibly irrotational.
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