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On the radiation and scattering of short surface waves. Part 3

Published online by Cambridge University Press:  29 March 2006

F. G. Leppington
F. G. Leppington
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The radiation properties of partially immersed three-dimensional bodies, in time-periodic motion, are examined in the short-wave asymptotic limit ε → 0, where ε is a non-dimensional wavelength. The method of matched expansions is used to specify an outer approximation, away from the surface wave region, and an inner approximation where the potential, in the vicinity of the obstacle and free surface, depends only on the local geometry. Finally, the radially spreading surface wave field is estimated by ray-theory arguments. Explicit details are given for the heaving and rolling of a circular dock and for the heaving motion of a hemisphere. Some speculations are made regarding the scattering properties of such obstacles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 147 - 157
Copyright
© 1973 Cambridge University Press

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References

Holford, R. L. 1964 Proc. Camb. Phil. Soc. 60, 957, 985.
Keller, J. B. 1956 I.R.E. Trans. Antennas Propag. AP 4, 312.
Keller, J. B., Lewis, R. M. & Seckler, B. D. 1956 Comm. Pure Appl. Math. 9, 207.
Kim, W. D. 1963a J. Ship Res. 7, 7.
Kim, W. D. 1963b J. Fluid Mech. 17, 607.
Leppington, F. G. 1972 J. Fluid Mech. 56, 101.
Leppington, F. G. 1973 J. Fluid Mech. 59, 129.
Maccamy, R. C. 1961 J. Ship Res. 5, 34.
Sneddon, I. N. 1966 Mixed Boundary Value Problems in Potential Theory. North-Holland.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Watson, G. N. 1944 Theory of Bessel Functions. Cambridge University Press.