Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/140

§ 93 § 93. Vortex Motion.—It is unnecessary in the present work to do more than give a general description of vortex motion and vortices, and discuss their properties so far as bearing on the present subject.

Reference has already been made to vortex motion in § 72, where the character of the motion in a vortex filament is dealt with, and it is shown that such a filament possesses rotation, and the relation area $$\times$$ angular velocity $$=$$ constant is established.

The most common form of vortex motion is found in the vortex ring, familiar from the easy manner in which such rings can be produced in smoke-laden air (the smoke being necessary to render the rings visible), either by ejecting tobacco smoke from the mouth or by employing a simple apparatus consisting of a box having a circular aperture on one side and a loose diaphragm on the other. Vortex rings of great size may frequently be seen when a salute is being fired from guns of large calibre.

The motion in a vortex ring resembles that of an umbrella ring being rolled on its stick, only the rotation is in the reverse direction—that is, as if the ring were being rolled inside a cylinder; the fluid is, so to speak, being eternally turned inside out, with a motion of translation superposed. The superposed translation is necessary to its equilibrium.

In real fluids the rotation is not concentrated at the axis as in the case discussed in § 72, but is distributed about the axial region or core. As a matter of convention in the perfect fluid, it is usual to suppose the core to be in a state of uniform rotation—that is, to have constant angular velocity, and the motion of the part external to the core to be cyclic and irrotational, there being no discontinuity at the surface of the core, the velocity $$(u\ v\ w)$$ being a continuous function of the position $$(x\ y\ z)$$.

By this convention the core behaves as a solid body, since in an inviscid fluid under no circumstances can its rotation be destroyed or transferred.

We might equally suppose the core to consist of a void space, a