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The complete second-order diffraction solution for an axisymmetric body Part 1. Monochromatic incident waves

Published online by Cambridge University Press:  26 April 2006

Moo-Hyun Kim  and
Dick K. P. Yue
Moo-Hyun Kim
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K. P. Yue
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

We study the diffraction, to second order, of plane monochromatic incident gravity waves by a vertically axisymmetric body. The second-order double-frequency diffraction potential is obtained explicitly. A sequence of one-dimensional integral equations along the generator of the body involving free-surface ring sources of general order are formulated and solved for the circumferential components of the second-order potential. The solution is expedited by analytic integration in the entire local-wave-free outer field of a requisite free-surface integral. The method is validated by extensive convergence tests and comparisons to semi-analytic results for the second-order forces and moments on a uniform vertical circular cylinder. Complete second-order forces, moments, surface pressures and run-up on the vertical cylinder as well as a truncated vertical cone are presented. A summary of the important findings is given in §5.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 235 - 264
Copyright
© 1989 Cambridge University Press

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