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Second-order low-frequency wave forces on a vertical circular cylinder

Published online by Cambridge University Press:  21 April 2006

Chinpu Zhou  and
Philip L.-F. Liu
Chinpu Zhou
Affiliation:
Joseph H. DeFree Hydraulies Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Permanent address: Department of Mechanics, Zhongshan University, People's Republic of China.
Philip L.-F. Liu
Affiliation:
Joseph H. DeFree Hydraulies Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

Using the multiple-scale perturbation method, the diffraction of a nonlinear nearly periodic wavetrain by a vertical circular cylinder is investigated. The envelope of the incident wavetrain is assumed to modulate slowly in the direction of wave propagation. The relationship between the envelopes of incident and scattered waves is derived. It is shown that second-order scattered set-down waves propagate only at the long-wave velocity (gh)½. The formula for low-frequency wave forces acting on the cylinder is presented. The low-frequency wave forces, which are second-order quantities, are caused by set-down waves beneath the wavetrain and the results of the self-interactions of the leading-order first harmonic wave components. Numerical solutions are presented for the case where the wave envelope varies sinusoidally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 143 - 155
Copyright
© 1987 Cambridge University Press

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