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Nonlinear wave loads on a slender vertical cylinder

Published online by Cambridge University Press:  26 April 2006

O. M. Faltinsen ,
J. N. Newman  and
T. Vinje
O. M. Faltinsen
Affiliation:
Marine Hydrodynamics Division, Norwegian Institute of Technology, N-7043 Trondheim, Norway
J. N. Newman
Affiliation:
Department of Ocean Engineering, MIT, Cambridge, MA 02139, USA
T. Vinje
Affiliation:
Norwegian Contractors a.s., N-1320 Stabekk, Norway
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Abstract

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 179 - 198
Copyright
© 1995 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office and Dover.
Acton, F. S. 1970 Numerical Methods that Work. Harper & Row.
Chau, F. P. & Eatock Taylor, R. 1992 Second-order wave diffraction by a vertical cylinder. J. Fluid Mech. 242, 571–599.Google Scholar
Eatock Taylor, R., Rainey, R. C. T. & Dai, D. N. 1992 Non-linear hydrodynamic analysis of TLP's in waves: slender body and diffraction theories compared. Proc. 8th Intl Conf on the Behaviour of Offshore Structures, London (ed. M. H. Patel & R. Gibbins), pp. 569–583. BPP Technical Services Ltd.
Emmerhoff, O. J. & Sclavounos, P. D. 1992 The slow-drift motion of arrays of vertical cylinders. J. Fluid Mech. 242, 31–50.Google Scholar
Faltinsen, O. M. 1990 Sea Loads on Ships and Offshore Structures. Cambridge University Press.
Grue, J., Bjørshol, G. & Strand, Ø. 1994 Nonlinear wave loads which may generate ringing responses of offshore structures. 9th Intl Workshop on Water Waves and Floating Bodies, Kyushu, Japan. Research Institute for Applied Mechanics, Kyushu University.
Jefferys, E. R. & Rainey, R. C. T. 1994 Slender body models of TLP and GBS ringing. Proc. 7th Intl Conf on the Behaviour of Offshore Structures, MIT Cambridge, MA (ed. C. Chryssostomidis). Pergamon.
Jefferys, R. 1993 A slender body model of ringing. 8th Intl Workshop on Water Waves and Floating Bodies, St. John's, Newfoundland. Institute for Marine Dynamics, St. John's.
Lighthill, M. J. 1979 Waves and hydrodynamic loading. Proc. 2nd Intl Conf on the Behaviour of Offshore Structures, vol. 1, pp. 1–40. Cranfield: BHRA Fluid Engineering.
Lighthill, M. J. 1986 Fundamentals concerning wave loading on offshore structures. J. Fluid Mech. 173, 667–681.Google Scholar
Luke, Y. L. 1969 The Special Functions and Their Approximations. Academic.
Malenica, S. & Molin, B. 1994 Third order triple frequency wave forces on fixed vertical cylinders. 9th Intl Workshop on Water Waves and Floating Bodies, Kyushu, Japan. Institute for Applied Mechanics, Kyushu University.
Mei, C. C. 1983 The Applied Dynamics of Ocean Waves. Wiley.
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.
Rainey, R. C. T. 1989 A new equation for wave loads on offshore structures. J. Fluid Mech. 204. 295–324.Google Scholar
Watson, G. N. 1952 Theory of Bessel Functions. Cambridge University Press.