Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-19T01:05:46.466Z Has data issue: false hasContentIssue false

Nonlinear forces on a horizontal cylinder beneath waves

Published online by Cambridge University Press:  20 April 2006

John R. Chaplin
Affiliation:
Department of Civil Engineering, University of Liverpool

Abstract

Measurements of forces experienced by a submerged horizontal cylinder with its axis parallel to the crests in deep-water waves reveal nonlinear components with frequencies up to three times the fundamental wave frequency. The dominant nonlinear contribution to the loading is at the third order in the wave amplitude, and, for Keulegan-Carpenter numbers approaching 2, its magnitude was found to be as much as one-half that of the inertia force. It is suggested that the third-order force is associated with circulation generated by steady streaming in the oscillatory boundary layer on the cylinder. At higher Keulegan-Carpenter numbers, form drag becomes increasingly important, and velocity measurements close to the cylinder show the rapid development of the wake. Observations of nonlinear features of the transmitted waves are also discussed.

Type
Research Article
Copyright
© 1984 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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Chaplin, J. R. 1981 On the irrotational flow around a horizontal cylinder in waves. Trans. ASME E: J. Appl. Mech. 48, 689694.Google Scholar
Chaplin, J. R. 1984 Mass transport around a horizontal cylinder beneath waves. J. Fluid Mech. 140, 175187.Google Scholar
Dean, W. R. 1948 On the reflexion of surface waves by a submerged circular cylinder. Proc. Camb. Phil. Soc. 44, 483491.Google Scholar
Grue, J. & Palm, E. 1984 Reflection of surface waves by submerged cylinders. Appl. Ocean Res. 6, 5460.Google Scholar
Leppington, F. G. & Siew, P. F. 1980 Scattering of surface waves by submerged cylinders. Appl. Ocean Res. 2, 129137.Google Scholar
Longuet-Higgins, M. S. 1970 Steady currents induced by oscillations round islands. J. Fluid Mech. 42, 701720.Google Scholar
Mehlum, E. 1980 A circular cylinder in water waves. Appl. Ocean Res. 2, 171177.Google Scholar
Ogilvie, T. F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451472.Google Scholar
Riley, N. 1971 Stirring of a viscous fluid. Z. angew. Math. Phys. 22, 645653.Google Scholar
Riley, N. 1978 Circular oscillations of a cylinder in a viscous fluid. Z. angew. Math. Phys. 29, 439449.Google Scholar
Stansby, P. K. & Slaouti, A. 1984 On non-linear wave interaction with cylindrical bodies: a vortex sheet approach. Appl. Ocean Res. 6, 108115.Google Scholar
Ursell, F. 1950 Surface waves in the presence of a submerged circular cylinder. I and II. Proc. Camb. Phil. Soc. 46, 141158.Google Scholar