Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-28T10:33:03.763Z Has data issue: false hasContentIssue false

Second-order wave diffraction by a submerged circular cylinder

Published online by Cambridge University Press:  26 April 2006

M. Mciveri
Affiliation:
School of Mathematical Sciences, University of Bath, Claverton Down. Bath, BA2 7AY, UK
P. Mciver
Affiliation:
Department of Mathematics and Statistics, Brunel University, Uxbridge. Middlesex, UBU 3PH, UK

Abstract

Expressions are derived for the amplitudes of the second-harmonic waves generated when a uniform wave train is normally incident upon a two-dimensional body, submerged in water of infinite depth. These amplitudes are given in terms of integrals over the free surface of products of first-order quantities. For a submerged, circular cylinder, it is shown analytically that there is no second-order reflected wave at any frequency. This extends the classical result that there is no reflection at first-order for this body.

Type
Research Article
Copyright
© 1990 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

Abramowitz, M. & Stegun, I. A., 1965 Handbook of Mathematical Functions. Dover.
Chaplin, J. R.: 1984 Nonlinear forces on a horizontal cylinder beneath waves. J. Fluid Mech. 147, 449464.Google Scholar
Cointe, R.: 1989 Quelques aspects de la simulation numerique d'un canal a houle. Doctoral thesis, L'Ecole Nationale des Ponts et Chaussees, France.
Dean, W. R.: 1948 On the reflection of surface waves by a submerged, circular cylinder. Proc. Camb. Phil. Soc. 44, 483491.Google Scholar
Dommermuth, D. G.: 1987 Numerical methods for solving nonlinear waterwave problems in the time domain. Ph.D. dissertation, MIT.
Evans, D. V.: 1984 A note on the transparency of a submerged, circular cylinder to the waves radiated by a pulsating line source. IMA J. Appl. Math. 33, 105107.Google Scholar
Evans, D. V., Jeffrey, D. C., Salter, S. H. & Taylor, J. R. M. 1979 Submerged cylinder wave energy device: theory and experiment. Appl. Ocean Res. 1, 312.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M., 1980 Table of Integrals, Series and Products. Academic.
Kellogg, O. D.: 1953 Foundations of Potential Theory. Dover.
Longuet-Higgins, M. S.: 1977 The mean forces exerted by waves on floating or submerged bodies with applications to sand bars and wave power machines. Proc. R. Soc. Lond. A 352, 463480.Google Scholar
Maruo, H.: 1960 The drift of a body floating in waves. J. Ship Res. 4, 110.Google Scholar
Molin, B.: 1979 Second-order diffraction loads upon three-dimensional bodies. Appl. Ocean Res. 1, 197202.Google Scholar
Newman, J. N.: 1974 Second-order, slowly varying forces on vessels in irregular waves. Proc. Intl Symp. on the Dynamics of Marine Vehicles and Structures in Waves, University College, London, pp. 182186.Google Scholar
Pinkster, J. A.: 1979 Mean and low frequency wave drifting forces on floating structures. Ocean Engng 6, 593615.Google Scholar
Thorne, R. C.: 1953 Multipole expansions in the theory of surface waves. Proc. Camb. Phil. Soc. 49, 707715.Google Scholar
Ursell, F.: 1950 Surface waves on deep water in the presence of a submerged cylinder I. Proc. Camb. Phil. Soc. 46, 141158.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, 2337.Google Scholar
Whittaker, E. T. & Watson, G. N., 1935 A Course of Modern Analysis. Cambridge University Press.
Wu, G. W.: 1990 On the second order wave reflection and transmission by a horizontal cylinder. Appl. Ocean Res. (to appear).Google Scholar