Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T06:03:57.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Global relationships between two-dimensional water wave potentials

Published online by Cambridge University Press:  26 April 2006

M. McIver
M. McIver
Affiliation:
Department of Mathematical Sciences, Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 299 - 309
Copyright
© 1996 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Davis, A. M. J. 1976 A relation between the radiation and scattering of surface waves by axisymmetric bodies. J. Fluid Mech. 76, 85–88.Google Scholar
Evans, D. V. 1970 Diffraction of water waves by a submerged vertical plate. J. Fluid Mech. 40, 433–451.Google Scholar
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, 353–370.Google Scholar
Haskind, M. D. 1957 The exciting forces and wetting of ships in waves, (In Russian). Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, 7, 65–79. 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, 210–222.Google Scholar
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, 165–174.Google Scholar
John, F. 1948 Waves in the presence of an inclined barrier. Commun. Pure Appl. Maths 1, 149–200.Google Scholar
John, F. 1950 On the motion of floating bodies II. Commun. Pure Appl. Maths 3, 45–101.Google Scholar
Linton, C. M. 1991 Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Engng 18, 61–74.Google Scholar
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, 13–23.Google Scholar
Maruo, H. 1960 The drift of a body floating in waves. J. Ship Res. 4, 1–10.Google Scholar
Maz'ja, V. G. 1978 Solvability of the problem on the oscillations of a fluid containing a submerged body. J. Soviet Maths 10 86–89 (In English).Google Scholar
McIver, M. 1992 Second-order oscillatory forces on a body in waves. Appl. Ocean Res. 14, 325–332.Google Scholar
McIver, M. 1996 An example of non-uniqueness in the two-dimensional linear water wave problem. J. Fluid Mech. (to appear).Google Scholar
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, 51–59.Google Scholar
Newman, J. N. 1975 Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems. J. Fluid Mech. 71, 273–282.Google Scholar
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, 137–154.Google Scholar
Ursell, F. 1947 The effect of a fixed, vertical barrier on surface waves in deep water. Proc. Camb. Philo. Soc. 43, 374–382.Google Scholar
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged cylinder II. Proc. Camb. Philo. Soc. 46, 153–158.Google Scholar
Wang, S. & Wahab, R. 1971 Heaving oscillations of twin cylinders in a free surface. J. Ship Res. 15, 33–48.Google Scholar
Wu, G. X. & Eatock Taylor, R. 1989 Second order diffraction forces on horizontal cylinders J. Hydrodyn. 2, 55–65.
Yeung, R. W. 1982 Numerical methods in free-surface flows. Ann. Rev. Fluid Mech. 14, 395–442.Google Scholar