Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-13T19:35:16.938Z Has data issue: false hasContentIssue false
  • English
  • Français

Second-order wave diffraction by a vertical cylinder

Published online by Cambridge University Press:  26 April 2006

F. P. Chau and
R. Eatock Taylor
F. P. Chau
Affiliation:
Department of Naval Architecture and Offshore Engineering, University of California, Berkeley, CA 94720, USA
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Get accessRights & Permissions [Opens in a new window]

Abstract

The main difficulty in second-order diffraction analysis stems from the contribution of the second-order potential, which obeys an inhomogeneous free-surface boundary condition. In some applications it is sufficient to know the second-order hydro-dynamic force, which can be calculated without explicitly evaluating this second-order potential. This technique cannot however be used for calculating other quantities such as the hydrodynamic pressure at any point, the sectional force and bending moment in the cylinder or the free-surface elevation due to the second-order effects. This paper provides a detailed analysis of the second-order diffraction problem of a uniform vertical circular cylinder in regular waves. This furnishes results not only on the cylinder surface, but also on the free surface, and in principle in the fluid domain surrounding the body. The analysis may help to throw some light on the physical interpretation of the second-order theory and its mathematical description. Moreover, this information is intended to complement the development of general numerical methods for arbitrary bodies.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992, pp. 571 - 599
Copyright
© 1992 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.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
Chau, F. P. 1989 The second order velocity potential for diffraction of waves by fixed offshore structures. Ph.D. thesis, University of London. (Department of Mechanical Engineering, University College London, Rep. OEG/89/1).
Chau, F. P. & Eatock Taylor, R. 1988 Second order velocity potential for arbitrary bodies in waves. 3rd Intl Workshop on Water Waves and Floating Bodies, Woods Hole (ed. F. T. Korsmeyer). Massachusetts Institute of Technology.
Chen, M. C. & Hudspeth, R. T. 1982 Nonlinear diffraction by eigenfunction expansions. J. Waterway, Port, Coastal, Ocean Div. ASCE 108, 306–325.Google Scholar
Eatock Taylor, R. & Hung, S. M. 1987 Second order diffraction forces on a vertical cylinder in regular waves. Appl. Ocean Res. 9, 19–30.Google Scholar
Eatock Taylor, R., Hung, S. M. & Chau, F. P. 1989 On the distribution of second order pressure on a vertical circular cylinder. Appl. Ocean Res. 11, 183–193.Google Scholar
Fenton, J. D. 1978 Wave forces on vertical bodies of revolution. J. Fluid Mech. 85, 241–255.Google Scholar
Friedman, B. 1956 Principles and Techniques of Applied Mathematics. John Wiley and Sons.
Garrison, C. J. 1984 Nonlinear wave loads on large structures. Proc. 3rd Intl Offshore Mechanics and Arctic Engineering Symp., vol. 1, pp. 128–135, American Society of Mechanical Engineers.
Jolley, L. B. W. 1961 Summation of Series. Dover.
Kim, M. H. & Yue, D. K. P. 1989 The complete second-order diffraction waves around an axisymmetric body. Part 1. monochromatic waves. J. Fluid Mech. 200, 235–262.Google Scholar
Lighthill, J. 1979 Waves and hydrodynamic loading. Proc. 2nd Intl Conf. on Behaviour of Offshore Structures, vol. 1. pp. 1–40. BHRA Fluid Engineering, Cranfield, Bedford.
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. John Wiley and Sons.
Molin, B. 1979 Second order diffraction loads upon three-dimensional bodies. Appl. Ocean Res. 1, 197–202.Google Scholar
Newman, J. N. 1990 Second harmonic wave diffraction at large depth. J. Fluid Mech. 213, 59–70.Google Scholar
Telles, J. C. F. 1987 A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Intl J. Numer. Meth. Engng 24, 959–973.Google Scholar