Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-27T03:11:34.590Z Has data issue: false hasContentIssue false
  • English
  • Français

The interaction of waves with arrays of vertical circular cylinders

Published online by Cambridge University Press:  26 April 2006

C. M. Linton  and
D. V. Evans
C. M. Linton
Affiliation:
Department of Mathematics, University of Bristol, BS8 1TW, UK
D. V. Evans
Affiliation:
Department of Mathematics, University of Bristol, BS8 1TW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 549 - 569
Copyright
© 1990 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

Eatock Taylor, R. & Hung, S. M. 1985 Wave drift enhancement effects in multi-column structures. Appl. Ocean Res. 7, 128–137.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Integrals, Series and Products. Academic.
Kagemoto, H. & Yue, D. K. P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.Google Scholar
Kim, M.-H. & Yue, D. K. P. 1989 The complete second-order diffraction solution for an axisymmetric body. Part 1. Monochromatic incident waves. J. Fluid Mech. 200, 235–264.Google Scholar
MacCamy, R. C. & Fuchs, R. A. 1954 Wave force on piles: A diffraction theory. US Army Coastal Engineering Research Center, Tech. Mem. 69.
Martin, P. A. 1985 Integral-equation methods for multiple scattering problems. I. Acoustics. Q. J. Mech. Appl. Maths 38, 105–118.Google Scholar
McIver, P. 1987 Mean drift forces on arrays of bodies due to incident long waves. J. Fluid Mech. 185, 469–482.Google Scholar
McIver, P. & Evans, D. V. 1984 Approximation of wave forces on cylinder arrays. Appl. Ocean Res. 6, 101–107.Google Scholar
Mingde, S. & Yu, P. 1987 Shallow water diffraction around multiple large cylinders. Appl. Ocean Res. 9, 31–36.Google Scholar
Molin, B. 1979 Second-order diffraction loads upon three-dimensional bodies. Appl. Ocean Res. 1, 197–202.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.
Twersky, V. 1952 Multiple scattering of radiation by an arbitrary configuration of parallel cylinders. J. Acoust. Soc. Am. 24, 42–46.Google Scholar
Záviška, F. 1913 Über die Beugung elektromagnetischer Wellen an parallelen, unendlich langen Kreiszylindern. Annln. Phys. 40, 1023–1056.Google Scholar