Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-13T13:30:39.437Z Has data issue: false hasContentIssue false
  • English
  • Français

Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method

Published online by Cambridge University Press:  21 April 2006

Hiroshi Kagemoto  and
Dick K. P. Yue
Hiroshi Kagemoto
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts Present address: Ship Research Institute, Tokyo, Japan.
Dick K. P. Yue
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider three-dimensional water-wave diffraction and radiation by a structure consisting of a number of separate (vertically) non-overlapping members in the context of linearized potential flow. An interaction theory is developed which solves the complete problem, predicting wave exciting forces, hydrodynamic coefficients and second-order drift forces, but is based algebraically on the diffraction characteristics of single members only. This method, which includes also the diffraction interaction of evanescent waves, is in principle exact (within the context of linearized theory) for otherwise arbitrary configurations and spacings. This is confirmed by a number of numerical examples and comparisons involving two or four axisymmetric legs, where full three-dimensional diffraction calculations for the entire structures are also performed using a hybrid element method. To demonstrate the efficacy of the interaction theory, we apply it finally to an array of 33 (3 by 11) composite cylindrical legs, where experimental data are available. The comparison with measurements shows reasonable agreement.

The present method is valid for a large class of arrays of arbitrary individual geometries, number and configuration of bodies with non-intersecting vertical projections. Its application should make it unnecessary to perform full diffraction computations for many multiple-member structures and arrays.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 166 , May 1986 , pp. 189 - 209
Copyright
© 1986 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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Government Printing Office, Washington.
Ando, S., Okawa, Y. & Ueno, I. 1983 Feasibility study of a floating offshore airport. Rep. Ship Res. Inst. Suppl. 4, Tokyo (in Japanese).
Budal, K. 1977 Theory for absorption of wave power by a system of interacting bodies. J. Ship Res. 21, 241–253.Google Scholar
Duncan, J. H. & Brown, C. E. 1982 Development of a numerical method for the calculation of power absorption by arrays of similar arbitrarily shaped bodies in a seaway. J. Ship Res. 26, 38–44.Google Scholar
Greenhow, M. J. L. 1980 The hydrodynamic interactions of spherical wave-power devices in surface waves. In Power from Sea Waves (ed. B. M. Count), pp. 287–343. Academic.
Havelock, T. H. 1940 The pressure of water waves upon a fixed obstacle. Proc. R. Soc. Lond. A 175, 409–421.Google Scholar
Heaviside, O. 1950 Electromagnetic Theory, 182. Dover.
Kagemoto, H. 1982 The drift force on offshore structures. Internal Rep. Ship Res. Inst. Tokyo (in Japanese).
Kyllingstad, A. 1984 A low-scattering approximation for the hydrodynamic interactions of small wave-power devices. Appl. Ocean Res. 6, 132–139.Google Scholar
Lebreton, J. C. & Cormault, P. 1969 Wave action on slightly immersed structures, some theoretical and experimental considerations. In Proc. Symp. Wave Action. 9, Paper 12A.
Mciver, P. 1984 Wave forces on arrays of floating bodies. J. Engng. Maths 18, 273–285.Google Scholar
Mciver, P. & Evans, D. V. 1984 Approximation of wave forces on cylinder arrays. Appl. Ocean Res. 6, 101–107.Google Scholar
Martin, P. A. 1984 Multiple scattering of surface water waves and the null-field method. In Proc. 15th Symp. Naval Hydrodynamics, pp. 119–132.
Matsui, T. & Kato, K. 1983 Computation of wave drift forces on floating axisymmetric bodies in regular waves. Mem. Fac. Engng. Nagoya Univ. 35, 117–130.Google Scholar
Mei, C. C. 1978 Numerical methods in water-wave diffraction and radiation. Ann. Rev. Fluid Mech. 10, 393–416.Google Scholar
Newman, J. N. 1967 The drift force and moment on ships in waves. J. Ship Res. 11, 51–60.Google Scholar
Ohkusu, M. 1974 Hydrodynamic forces on multiple cylinders in waves. In Proc. Intl. Symp. on Dynamics of Marine Vehicles and Structures in Waves, London, Paper 12, pp. 107–112.
Simon, M. J. 1982 Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane-wave approximation. J. Fluid Mech. 120, 1–25.Google Scholar
Spring, B. H. & Monkmeyer, P. L. 1974 Interaction of plane waves with vertical cylinders. In Proc. 14th Intl. Conf. on Coastal Engineering, Chap. 107, pp. 1828–1845.
Srokosz, M. A. & Evans, D. V. 1979 A theory for wave-power absorption by two independently oscillating bodies. J. Fluid Mech. 90, 337–362.Google Scholar
Twersky, V. 1952 Multiple scattering of radiation by an arbitrary configuration of parallel cylinders. J. Acoust. Soc. Am. 24, 42–46.Google Scholar
Wang, S. & Wahab, R. 1970 Heaving oscillations of twin cylinders in a free surface. J. Ship Res. 15, 33–48.Google Scholar
Yue, D. K. P., Chen, H. S. & Mei, C. C. 1978 A hybrid element method for diffraction of water waves by three-dimensional bodies. Intl. J. Numer. Meth. Engng. 12, 245–266.Google Scholar