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Global relationships between two-dimensional water wave potentials

  • M. McIver (a1)


When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.



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Davis, A. M. J. 1976 A relation between the radiation and scattering of surface waves by axisymmetric bodies. J. Fluid Mech. 76, 8588.
Evans, D. V. 1970 Diffraction of water waves by a submerged vertical plate. J. Fluid Mech. 40, 433451.
Evans, D. V. 1974 A note on the total reflexion or transmission of surface waves in the presence of parallel obstacles. J. Fluid Mech. 28, 353370.
Haskind, M. D. 1957 The exciting forces and wetting of ships in waves, (In Russian). Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, 7, 6579. English translation available as David Taylor Model Basin Translation, No. 307.
Heins, A. E. 1950 Water waves over a channel of finite depth with a submerged plane barrier. Can. J. Maths 2, 210222.
Hulme, A. 1984 Some applications of Maz'ja's uniqueness theorem to a class of linear water wave problems. Math. Proc. Comb. Phil. Soc. 95, 165174.
John, F. 1948 Waves in the presence of an inclined barrier. Commun. Pure Appl. Maths 1, 149200.
John, F. 1950 On the motion of floating bodies II. Commun. Pure Appl. Maths 3, 45101.
Linton, C. M. 1991 Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Engng 18, 6174.
MacCamy, R. C. & Fuchs, R. A. 1954 Wave forces on a pile: a diffraction theory. Tech. Memo. 69, US Army Board, US Army Corp. of Engng.
Martin, P. A. & Dixon, A. G. 1983 The scattering of regular surface waves by a fixed half-immersed, circular cylinder. Appl. Ocean Res. 5, 1323.
Maruo, H. 1960 The drift of a body floating in waves. J. Ship Res. 4, 110.
Maz'ja, V. G. 1978 Solvability of the problem on the oscillations of a fluid containing a submerged body. J. Soviet Maths 10 8689 (In English).
McIver, M. 1992 Second-order oscillatory forces on a body in waves. Appl. Ocean Res. 14, 325332.
McIver, M. 1996 An example of non-uniqueness in the two-dimensional linear water wave problem. J. Fluid Mech. (to appear).
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley-Interscience.
Newman, J. N. 1967 The drift force and moment on ships in waves. J. Ship Res. 11, 5159.
Newman, J. N. 1975 Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems. J. Fluid Mech. 71, 273282.
Newman, J. N. 1976 The interaction of stationary vessels with regular waves. Proc. 11th Symp. on Naval Hydrodynamics, London.
Newman, J. N. 1977 Marine Hydrodynamics MIT Press.
Simon, M. & Ursell, F. 1984 Uniqueness in linearized two-dimensional water-wave problems. J. Fluid Mech. 148, 137154.
Ursell, F. 1947 The effect of a fixed, vertical barrier on surface waves in deep water. Proc. Camb. Philo. Soc. 43, 374382.
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged cylinder II. Proc. Camb. Philo. Soc. 46, 153158.
Wang, S. & Wahab, R. 1971 Heaving oscillations of twin cylinders in a free surface. J. Ship Res. 15, 3348.
Wu, G. X. & Eatock Taylor, R. 1989 Second order diffraction forces on horizontal cylinders J. Hydrodyn. 2, 5565.
Yeung, R. W. 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395442.
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Global relationships between two-dimensional water wave potentials

  • M. McIver (a1)


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