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On the short cylindrical waves due to a body heaving on water. I

Published online by Cambridge University Press:  24 October 2008

P. F. Rhodes-Robinson
P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, Victoria University of Wellington, New Zealand
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Abstract

In this paper we obtain the short-wave asymptotic value of the force coefficient for a heaving body partially immersed in the free surface of water which has finite constant depth. The body is required to intersect the free surface normally and have a vertical axis of symmetry. The motion of the water is thus axisymmetric with short outgoing cylindrical waves at a distance, and these must be calculated. For this we use a non-rigorous argument. The potential problem discussed is analogous to the two-dimensional problem afready investigated involving a heaving surface cylinder. Numerical values are obtained in the case of a half-immersed sphere in conclusion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 311 - 321
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Barakat, R.Vertical motion of a floating sphere in a sine-wave sea. J. Fluid Mech. 13 (1962), 540–556.CrossRefGoogle Scholar
(2)Barakat, R. Forced periodic heaving of a semi-immersed sphere. (Unpublished paper.)Google Scholar
(3)Havelock, T. H.Waves due to a floating sphere making periodic heaving oscillations. Proc. Roy. Soc. Ser. A 231 (1955), 1–7.Google Scholar
(4)Rhodes-Robinson, P. F.On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. I. Proc. Cambridge Philos. Soc. 67 (1970), 423–442.CrossRefGoogle Scholar
(5)Rhodes-Robinson, P. F.On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. II. Proc. Cambridge Philos. Soc. 67 (1970), 443–468.CrossRefGoogle Scholar
(6)Ursell, F.On the heaving motion of a circular cylinder on the surface of a fluid. Quart. J. Mech. Appl. Math. 2 (1949), 218–231.CrossRefGoogle Scholar
(7)Ursell, F.On the virtual mass and damping of floating bodies at zero speed ahead. Proc. Symp. Behaviour of Ships in a Seaway (1957), 374–387.Google Scholar
(8)Ursell, F. The periodic heaving motion of a half-immersed sphere: the analytic form of the velocity potential; long-wave asymptotics of the virtual-mass coefficient. (Unpublished paper.)Google Scholar
(9)Wang, S.The hydrodynamic forces and pressure distributions for an oscillating sphere in a fluid of finite depth (Technical Report, Department of Naval Architecture and Marine Engineering M.I.T., 1966).Google Scholar
(10)Yu, Y. S. and Ursell, F.Surface waves generated by an oscillating circular cylinder on water of finite depth: theory and experiment. J. Fluid Mech. 11 (1961), 529–551.CrossRefGoogle Scholar