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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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