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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
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K. P. Yue
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA


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.

Research Article
© 1989 Cambridge University Press

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