Upstream influence

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Abstract
The phenomenon under investigation occurs in various flow systems characterized by being dispersive to small-amplitude waves, but such that phase and group velocities approach the same finite limit at extreme wavelengths: for example, water in an open channel, density-stratified fluid flowing between horizontal boundaries, and rotating fluid contained in a tube. It is well known in each of these examples that, when a solid body is moved steadily at a subcritical velocity (i.e. less than the long-wave limit) relative to the undisturbed fluid, the body experiences resistance accountable to the continual development of a pattern of waves on the leeward side. But in these circumstances there is a second effect, upstream influence, consisting of a disturbance in the form of a uniform long wave that extends to a steadily increasing distance ahead of the body; and this has for some time been the subject of a controversy, particularly with regard to the question whether or not it is always present. The aim of the paper is to establish the principle that this second effect is inevitably coexistent with the first, being an essential component of the mechanism of wave resistance.

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