Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-08-05T05:35:20.732Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agnon, Y. & Mei, C. C. 1985 Slow-drift motion of a two-dimensional block in beam seas. J. Fluid Mech. 151, 279–294.Google Scholar
Chakrabarti, S. K. 1972 Nonlinear wave forces on vertical cylinder. J. Hydraulics Division, ASCE, 98, HY 11, 1895–1909.Google Scholar
Havelock, T. H. 1940 The pressure of water waves upon a fixed obstacle. Proc. R. Soc. Lond. A 963, 175–190.Google Scholar
Hunt, J. N. & Baddour, R. E. 1981 The diffraction of nonlinear progressive waves by a vertical cylinder. Q. J. Mech. Appl. Maths 24, 69–87.Google Scholar
Hunt, J. N. & Williams, A. N. 1982 Nonlinear diffraction of Stokes water waves by a circular cylinder for arbitrary uniform depth. J. Méc. 1 (3), 429–449.Google Scholar
Isaacson, M. DeSt. Q. 1977 Nonlinear wave forces on large offshore structures. J. of Waterway, Port, Coastal and Ocean Division, ASCE, 103, WW, 166–170.Google Scholar
MacCamy, R. C. & Fuchs, R. A. 1954 Wave forces on piles: a diffraction theory. Beach Erosion Board, Tech. Memo, no. 69, 17 pp.
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley.
Raman, H., Jothishanker, N. & Venkatanarasaiah, P. 1977 Nonlinear wave interaction with vertical cylinder of large diameter. J. Ship Research, 21 (2), 120–124.Google Scholar