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Radiation and diffraction of second-order surface waves by floating bodies

Published online by Cambridge University Press:  21 April 2006

P. D. Sclavounos
P. D. Sclavounos
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The paper studies the radiation and diffraction by floating bodies of deep-water bichromatic and bidirectional surface waves subject to the second-order free-surface condition. A theory is developed for the evaluation of the second-order velocity potential and wave forces valid for bodies of arbitrary geometry, which does not involve the evaluation of integrals over the free surface or require an increased accuracy in the solution of the linear problem. Explicit sum- and difference-frequency ‘Green functions’ are derived for the radiation and diffraction problems, obtained from the solution of initial-value problems that ensure they satisfy the proper radiation condition at infinity. The second-order velocity potential is expressed as the sum of a particular and a homogeneous component. The former satisfies the non-homogeneous free-surface condition and is expressed explicitly in terms of the second-order Green functions. The latter is subject to the homogeneous free-surface condition and enforces the body boundary condition by the solution of a linear problem. An analysis is carried out of the singular behaviour of the second-order potential near the intersection of the body boundary with the free surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 196 , November 1988 , pp. 65 - 91
Copyright
© 1988 Cambridge University Press

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References

Agnon, Y. & Mei, C. C. 1983 Slow drift motions by multiple-scale analysis. Intl Workshop on Ship and Platform Motions. Univ. Calif. Berkeley.
Faltinsen, O. M. & Loken, A. E. 1978 Drift forces and slowly-varying horizontal forces on a ship in waves. Proc. Symp. on Appl. Math. Dedicated to the Late Prof. Dr R. Timman, Delft, pp. 22–1.
John, F. 1950 On the motion of floating bodies II. Commun. Pure Appl. Maths 3, 45–101.Google Scholar
Lighthill, J. 1979 Waves and hydrodynamic loading. BOSS Conf. Univ. College London.
Molin, B. 1979 Second-order diffraction loads upon three dimensional bodies. Appl. Ocean Res. 1, 197–202.Google Scholar
Newman, J. N. 1983 Three-dimensional wave interactions with ships and platforms. Intl Workshop on Ship and Platform Motions. Univ. Calif. Berkeley.
Newman, J. N. 1985 Algorithms for the free-surface Green function. J. Engng Maths 19, 57–67.Google Scholar
Ogilvie, T. F. 1983 Second-order hydrodynamic effects on ocean platforms. Intl Workshop on Ship and Platform Motions. Univ. Calif. Berkeley.
Ogilvie, T. F. & Tuck, E. O. 1969 A rational strip theory for ship motions. Part 1. Rep. no. 013, Dept. of Nav. Archit, and Marine Engng, Univ. of Michigan, Ann Arbor.Google Scholar
Stoker, J. J. 1957 Water Waves. Interscience.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Stamford: The Parabolic Press.
Wang, P. F. 1987 The radiation condition in second-order wave-body interactions. PhD thesis, MIT, Dept of Ocean Engng 1987.
Wehausen, J. V. 1971 The motion of floating bodies. Ann. Rev. Fluid Mech. 3, 237–268.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. Hanbuch der Physik, vol. 9, pp. 446–778.Google Scholar
Yeung, R. W. 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395–442.Google Scholar