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Far-field representation for the vertical force on a floating structure

Published online by Cambridge University Press:  16 October 2012

M. McIver
M. McIver*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
*
†Email address for correspondence: m.mciver@lboro.ac.uk
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Abstract

Equations are derived that relate the vertical hydrodynamic force on two- and three-dimensional structures that are floating in a fluid of infinite depth to the far-field dipole coefficient in the velocity potential. By an application of Green’s theorem to the radiation or scattering potential and a suitable test potential, the heave added mass, the heave damping and the vertical exciting force are shown to be expressible in terms of the dipole coefficient in the relevant potential. The results add to the known reciprocity relations, which relate quantities such as the damping and the exciting force to the amplitude of the far-field radiated wave. The expressions are valid at all frequencies, and their high- and low-frequency asymptotics are investigated.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 661 - 670
Copyright
©2012 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
FitzGerald, C. J. & McIver, P. 2010 Passive trapped modes in the water-wave problem for a floating structure. J. Fluid Mech. 657, 456–477.CrossRefGoogle Scholar
Greenhow, M. 1986 High- and low-frequency asymptotic consequences of the Kramers–Kronig relations. J. Engng Maths 20, 293–306.Google Scholar
Havelock, T. H. 1955 Waves due to a sphere making periodic heaving oscillations. Proc. R. Soc. Lond. A 231, 1–7.Google Scholar
Kotik, J. & Mangulis, V. 1962 On the Kramers–Kronig relations for ship motions. Intl Shipbuilding Prog. 9 (97), 361–368.Google Scholar
Kuznetsov, N., Maz’ja, V. & Vainberg, B. 2002 Linear Water Waves – A Mathematical Approach. Cambridge University Press.Google Scholar
Leppington, F. G. 1973 On the radiation and scattering of short surface waves. Part 2. J. Fluid Mech. 59 (1), 129–146.Google Scholar
Linton, C. M. & McIver, P. 2001 Handbook of Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC.Google Scholar
Maruo, H. 1960 The drift of a body floating on waves. J. Ship Res. 4, 1–10.Google Scholar
McIver, P. 1994 Low-frequency asymptotics of hydrodynamic forces on fixed and floating structures. In Ocean Waves Engineering (ed. Rahman, M.), pp. 1–49. Computational Mechanics Publications.Google Scholar
McIver, P. & McIver, M. 2006 Trapped modes in the water-wave problem for a freely floating structure. J. Fluid Mech. 558, 53–67.Google Scholar
McIver, P. & McIver, M. 2007 Motion trapping structures in the three-dimensional water-wave problem. J. Engng Maths 58, 67–75.CrossRefGoogle Scholar
Newman, J. N. 1967 The drift force and moment on ships in waves. J. Ship Res. 6, 10–17.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.Google Scholar
Rhodes-Robinson, P. F. 1970 On the short-wave asymptotic motion due to a cylinder heaving on water of finite depth. I. Proc. Camb. Phil. Soc. 67, 423–444.Google Scholar
Sclavounos, P. D. 2012 Nonlinear impulse of ocean waves on floating bodies. J. Fluid Mech. 697, 316–335.Google Scholar
Ursell, F. 1949 On the heaving motion of a circular cylinder on the surface of a fluid. Q. J. Mech. Appl. Maths 2, 218–231.Google Scholar
Ursell, F. 1964 The decay of the free motion of a floating body. J. Fluid Mech. 19, 305–319.Google Scholar
Ursell, F. 1968 The expansion of water-wave potentials at great distances. Proc. Camb. Phil. Soc. 64, 811–826.Google Scholar