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Nonlinear wave reflection from a submerged circular cylinder

Published online by Cambridge University Press:  26 April 2006

Enok Palm
Enok Palm
Affiliation:
Mechanics Division, Department of Mathematics, University of Oslo, Norway
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Abstract

The paper discusses analytically the nonlinear wave reflection caused by a circular cylinder, submerged under a free surface in water of infinite depth. For monochromatic incident waves it is shown that there is no reflection of order m and frequency mω (m integer). This means that the dominant part of the mode of frequency mω is not reflected. For bichromatic incident waves it is found that the second-order wave with ‘sum frequency’ has no reflection. It is shown that the x- and y-components of the oscillatory force of order m and frequency mω have identical amplitudes and a phase-difference ½π. A corresponding result is also true for bichromatic waves.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 49 - 63
Copyright
© 1991 Cambridge University Press

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References

Chaplin, J. R. 1984 Nonlinear forces on a horizontal cylinder beneath waves. J. Fluid Mech. 147, 449–464.Google Scholar
Dean, W. R. 1948 On the reflection of surface waves by a circular cylinder. Proc. Camb. Phil. Soc. 44, 483–491.Google Scholar
Friis, A. 1990 A second order diffraction forces on a submerged body by a second order Green function method. Fifth Intl Workshop on Water Waves and Floating Bodies, Manchester, UK (ed. P. A. Martin), pp. 73–74.
Friis, A., Grue, J. & Palm, E. 1991 Application of Fourier transform to the second order 2D wave diffraction problem. M. P. Tulin's Festschrift: Mathematical Approaches in Hydrodynamics (ed. T. Miloh), pp. 209–227. SIAM.
Grue, J. & Palm, E. 1985 Wave radiation and wave diffraction from a submerged body in a uniform current. J. Fluid Mech. 151, 257–278.Google Scholar
Mciver, M. & McIver, P. 1990 Second-order wave diffraction by a submerged circular cylinder. J. Fluid Mech. 219, 519–529.Google Scholar
Ogilvie, T. F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472.Google Scholar
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder. Proc. Camb. Phil. Soc. 46, 141–158.Google Scholar
Vada, T. 1987 A numerical solution of the second order wave diffraction problem for a submerged cylinder of arbitrary shape. J. Fluid Mech. 174, 23–37.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik, vol. 9 (ed. S. Flügge & C. Truesdell), pp. 446–814. Springer.
Wu, G. X. 1991 On the second order wave reflection and transmission by a horizontal cylinder. Appl. Ocean Res. 13, 58–62.Google Scholar