supposing the viscosity to become less and less, endeavour to approach the conditions of the inviscid.
We have seen in § 117 that the lateral terminations of the aerofoil give rise to vortex cylinders, which trailing behind gradually dissipate their energy in the wake. Such a supposition presents no difficulty in viscous fluid, for the core of the vortex cylinders can then be formed of a mass of fluid in rotation.
Now we know that two parallel vortices, such as we have here, possessed of opposite rotation, in the first instance attract one another, and by their mutual interaction move through the fluid parallel to one another in the direction of motion of the fluid that lies between them (§ 93). Consequently in the present instance they will precess downwards as fast as they are formed, so that the aerofoil and its accompanying vortex train will appear somewhat as shown diagrammatically in elevation and plan in Fig. 79.
But if the dissipation of the vortex motion takes place sufficiently slowly, as when the viscosity of the fluid is not great, the vortices may persist until they reach the level of the ground. Under these circumstances one of two things will happen: either the vortices will spread apart as they approach the ground surface, each acting under the influence of its own "reflection" in the well known manner, or the ends of the vortices will attach themselves to the surface in the manner suggested by § 93.
If it be supposed that the aerofoil and its load were created in some upper region, and set in motion away from the earth's surface, the former assumption would be perhaps the most academically correct: if, however, we suppose the loaded aerofoil to be launched from the earth beneath, the vortices would naturally grow out from the surface, and would remain attached to the surface as they travel with the aerofoil to which they belong.
In the case of real fluids, the existence of these vortices can be traced experimentally by the employment of an aerofoil under
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