Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T07:11:49.228Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-analytical solution for second-order wave diffraction by a truncated circular cylinder in monochromatic waves

Published online by Cambridge University Press:  26 April 2006

J. B. Huang  and
R. Eatock Taylor
J. B. Huang
Affiliation:
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, OX1 3PJ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A complete semi-analytical solution is given for second-order diffraction of monochromatic waves by a truncated vertical circular cylinder in water of uniform finite depth. The methodology presented in detail elsewhere (Eatock Taylor & Huang 1996) is adopted to find a particular solution which exactly satisfies the governing equation, the inhomogeneous free-surface condition and the seabed condition. In order to satisfy the boundary condition on the cylinder bottom, the fluid domain around the cylinder is divided into two regions. First- and second-order velocity potentials are described separately in the two regions and matched on the interface by the pressure and normal-velocity continuity conditions. Based on the formulation, the second-order wave field in the vicinity of the cylinder and the corresponding wave forces and overturning moments on the cylinder are studied in detail. Numerical results for the double frequency forces obtained by using the present semi-analytical approach are compared with those computed with a higher-order boundary element method (Eatock Taylor & Chau 1992). As well as the exact solution, an approximate solution is also given for the second-order potential and the corresponding forces. Numerical results show that the approximate solution possesses excellent accuracy for the total second-order heave force over a wide range of conditions. When kb > 1.2 (where k, b are the incident wavenumber and the draught of the cylinder respectively), the accuracy for total second-order surge force and pitch moment is also satisfactory. These results could lead to the development of very efficient solutions and corresponding algorithms for the analysis of second-order wave diffraction by more complicated structures such as tension leg platforms. Numerical results based on the present solution show that in many cases, both the first- and the second-order-free surface elevation in the vicinity of a truncated cylinder is very close to that of a bottom-seated cylinder. For waves with larger amplitudes, the maximum free-surface elevation around a vertical cylinder predicted with the second-order theory can significantly exceed that given by linear theory. There is also a considerable difference in the location of the maximum elevation predicted by the linear and nonlinear theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 319 , 25 July 1996 , pp. 171 - 196
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

Abul-Azm, A. G. & Williams, A. N. 1988 Second-order diffraction loads on truncated cylinders. J. Waterway, Port, Coastal Ocean Div. ASCE 114, 436–454.Google Scholar
Abul-Azm, A. G. & Williams, A. N. 1989a Approximation of second-order diffraction loads on arrays of vertical circular cylinders. J. Fluids Struct. 3, 17–36.Google Scholar
Abul-Azm, A. G. & Williams, A. N. 1989b Second-order diffraction loads on arrays of semi-immersed circular cylinder. J. Fluids Struct. 3, 365–388.Google Scholar
Chau, F. P. 1989 The second-order velocity potential for diffraction of waves by fixed offshore structures. PhD thesis, University College London, London University.
Chau, F. P. & Eatock Taylor, R. 1992 Second-order wave diffraction by a vertical cylinder. J. Fluid Mech. 240, 571–599.Google Scholar
Chen, X. & Molin, B. 1991 Calcul des efforts de deuxieme ordre a tres haute frequence sur des plates-forms a lignes tendues. Proc. Troisieme Journees de l'Hydrodynamique, pp. 133–146.Google Scholar
Eatock Taylor, R. & Chau, F. P. 1992 Wave diffraction theory, some developments in linear and nonlinear theory. J. Offshore Mech. Arctic Engng 114, 185–194.Google Scholar
Eatock Taylor, R. & Huang, J. B. 1996 Application of second-order diffraction analysis to TLP design. Final Report on Project A4, Managed Programme on Uncertainties in Loads on Offshore Structures. University of Oxford.
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
Garrett, C. J. R. 1971 Wave forces on a circular dock J. Fluid Mech. 46, 129–139.Google Scholar
Ghalayini, S. A. & Williams, A. N. 1991 Nonlinear wave forces on vertical cylinder arrays. J. Fluids Struct. 5, 1–32.Google Scholar
Kagemoto, H. & Yue, D. K. P. 1986 Interaction among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.Google Scholar
Kim, M. H. 1993 Second-harmonic vertical wave loads on arrays of deep draught circular cylinders in monchromatic uni- and multi-directional waves. Appl. Ocean Res. 15, 245–262.Google Scholar
Kim, M. H. & Yue, D. K. P. 1989 The complete second-order diffraction solution for an axisymmetric body, Part 1, monochromatic waves. J. Fluid Mech. 200, 235–264.Google Scholar
Kim, M. H. & Yue, D. K. P. 1990 The complete second-order diffraction solution for an axisymmetric body. Part 2. bichromatic incident waves and body motions. J. Fluid Mech. 211, 557–593.Google Scholar
Kriebel, D. L. 1990 Nonlinear wave interaction with a vertical circular cylinder, part 1: diffraction theory. Ocean Engng 17, 345–377.Google Scholar
Kriebel, D. L. 1992 Nonlinear wave interaction with a vertical circular cylinder, part 2: wave run-up. Ocean Engng 19, 75–99.Google Scholar
Lee, C.-H., Newman, J. N., Kim, M.-H. & Yue, D. K. P. 1991 The computation of second-order wave loads. Proc. 10th Int. Conf. on Offshore Mechanics and Arctic Engineering, I-A, pp. 113–123. ASME.
Lee, C.-H. & Sclavounos, P. D. 1989 Removing the irregular frequencies from integral equations in wave-body interactions. J. Fluid Mech. 207, 393–418.Google Scholar
Lighthill, M. J. 1979 Waves and hydrodynamic loading. Proc. 2nd Intl. Conf. Behaviour Offshore Structures, BOSS London, pp. 1–40.
Linton, C. M. & Evans, D. V. 1990 The interaction of waves with arrays of vertical circular cylinders. J. Fluid Mech. 215, 549–569.Google Scholar
Malenica, š & Molin, B. 1994 Third order triple frequency wave forces on fixed vertical cylinders. Proc. 9th Intl Workshop on Water Waves and Floating Bodies, Kyushu, Japan.Google Scholar
Mciver, P. & Evans, D. V. 1984 Approximation of wave forces on cylinder arrays. Appl. Ocean Res. 6, 101–107.Google Scholar
Molin, B. 1979 Second-order diffraction loads on three-dimensional bodies. Appl. Ocean Res. 1, 197–212.Google Scholar
Moubayed, W. I. & Williams, A. N. 1994 The second-order diffraction loads and associated motions of a freely floating cylindrical body in regular waves: an eigenfunction expansion approach. J. Fluids Struct. 8, 417–451.Google Scholar
Moubayed, W. I. & Williams, A. N. 1995 Second-order hydrodynamic interactions in an array of vertical cylinders in bichromatic waves. J. Fluids Struct. 9, 61–98.Google Scholar
Newman, J. N. 1990 Second harmonic wave diffraction at large depths. J. Fluid Mech. 213, 59–70.Google Scholar
Williams, A. N., Abul-Azm, A. G. & Ghalayini, S. A. 1990 A comparison of complete and approximate solutions for second order diffraction loads on arrays of vertical cylinders. Ocean Engng 17, 427–446.Google Scholar