In order that streamline motion should be possible such motion must be a stable state, so that, if we suppose that by some means a surface of discontinuity be initiated, the conditions must be such that the form of motion so produced is unstable.
Let us suppose that we have (Fig. 10) a streamline body made in two halves, and that the rear half, or run, be temporarily removed; then a surface of discontinuity will be developed, as indicated in the figure. Let now the detached portion be replaced. Then the question arises. What are the changed conditions that will interfere with the permanence of the discontinuous system of flow, as depicted in the figure?
If, in the first place, the fluid be taken as inviscid, and if,
Fig. 10.
for the purpose of argument, we assume that the system of flow indicated in the figure is possible in an inviscid fluid, then it is evident that when the run is replaced we shall not have disturbed the conditions of flow, for our operations have been confined to the dead water region, where the fluid is at rest relatively to the body. Consequently the discontinuous system of flow will persist. That is to say, under the supposed conditions streamline motion is either unstable or is at best a condition of neutral equilibrium. Let us next introduce viscosity as a factor. The conditions are now altered, for the fluid in the dead-water region is no longer motionless, but is in active circulation, and the introduction of the rear half of the body obstructs the free path of the fluid, so that, as the outer layers of the dead-water are carried away by the viscous
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