Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/156

§ 104 It is by no means certain, however, that the Helmholtz system does actually represent the final form. Since the motion is a matter of infinitely slow development, it is probable that, in spite of the vanishing value of v, the fluid by which the dead water region is being developed will be set in motion just as in the case of a viscous fluid, the motion taking the form of a vortex ring on a core containing rotation, situated immediately in the wake of the plane or body. Such a system is quite in accord with hydrodynamic principles, but does not involve discontinuity and does not in itself give rise to resistance. It is a pregnant fact that, so long as the continuity of the system of flow is unimpaired, the pressure distribution for uniform motion is that of § 88, and resistance other than that directly due to viscosity is absent.

§ 105. Discontinuity in a Viscous Fluid.—It has already been pointed out that the surface of discontinuity in a viscid fluid must begin to degenerate as soon as formed, owing to the fact that a finite velocity between adjacent layers would betoken an infinite tangential stress. We could suppose the degeneration to take the form of a thickening of the discontinuity so that it becomes a stratum of fluid with a velocity gradient. We can alternatively and with every appearance of probability suppose that the surface becomes a stratum of turbulence. The latter would certainly agree more closely with observation.

Suppose we adopt the suggestion of Lord Kelvin and regard