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On Deep-water Two-dimensional Waves produced by any given Initiating Disturbance

Published online by Cambridge University Press:  15 September 2014

Lord Kelvin
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Extract

§ 1. Consider frictionless water in a straight canal, infinitely long and infinitely deep, with vertical sides. Let it be disturbed from rest by any change of pressure on the surface, uniform in every line perpendicular to the plane sides, and left to itself under constant air pressure. It is required to find the displacement and velocity of every particle of the water at any future time. Our initial condition will be fully specified by a given normal component velocity, and a normal component displacement, at every part of the surface.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 25 , Issue 1 , 1906 , pp. 185 - 196
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

note * page 186 A very easy way of effecting the realisations in (6) and (9) is by aid of De Moivre's theorem with, for one angle concerned in it, χ ═ tan−1x/z; and another angle ═gt 2x/4(z 2+x 2).

note * page 196 (Œuvres, vol. i. note xvi. p. 193.