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On the short-wave asymptotic motion due to a cylinder heavinǵ on water of finite depth. I

Published online by Cambridge University Press:  24 October 2008

P. F. Rhodes-Robinson
P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

This paper is a first investigation into the short-wave asymptotic motion due to a cylinder heaving on water of finite constant depth, and we present a non-rigorous method for an arbitrary smooth cylinder which intersects the free surface normally. The reduction of the potential problem by the use of two auxifiary potentials, introduced by the subtraction of formal solutions constructed from the limit potential, enables us to find (i) an integral expression, by using a subsidiary approximate Green's function, for the potential in the far field which is evaluated after making plausible assumptions about the asymptotic value of the first auxiliary potential on the cylinder and below the free surface; and (ii) a form for the virtual mass, using the second auxiliary potential whose value on the cylinder is deduced from that of the first to which it is related. Thus we obtain the asymptotic evaluation of the coefficients describing the wave-making and virtual mass of the heaving cylinder, which depend on the limit potential and have no formal dependence on the depth of the bottom.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 423 - 442
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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