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Short surface waves in the presence of a finite dock. I

Published online by Cambridge University Press:  24 October 2008

R. L. Holford
R. L. Holford
Affiliation:
University of Manchester
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Abstract

A long thin plate of finite width (a finite dock) extends over part of the otherwise free surface of a semi-infinite body of water under gravity and is given a forced heaving motion of small amplitude about this position. The solution of the boundary-value problem for the velocity potential of the resulting forced (two-dimensional) surface-wave motion may be reduced to that of an integral equation of the second kind for the value of the potential on the dock by means of an appropriate Green's function. There is an infinite number of choices for such a Green's function, and we show below how to construct one for which the kernel of the corresponding integral equation tends to zero with the ratio wavelength/dock-width. The integral equation may then be solved by iteration to calculate the short-wave asymptotics of the original wave-making problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 957 - 983
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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