Skip to main content Accessibility help

Second-order wave diffraction by a submerged circular cylinder

  • M. Mciveri (a1) and P. Mciver (a2)


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.



Hide All
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.
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.
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.
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.
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.
Maruo, H.: 1960 The drift of a body floating in waves. J. Ship Res. 4, 110.
Molin, B.: 1979 Second-order diffraction loads upon three-dimensional bodies. Appl. Ocean Res. 1, 197202.
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.
Pinkster, J. A.: 1979 Mean and low frequency wave drifting forces on floating structures. Ocean Engng 6, 593615.
Thorne, R. C.: 1953 Multipole expansions in the theory of surface waves. Proc. Camb. Phil. Soc. 49, 707715.
Ursell, F.: 1950 Surface waves on deep water in the presence of a submerged cylinder I. Proc. Camb. Phil. Soc. 46, 141158.
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.
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).
MathJax is a JavaScript display engine for mathematics. For more information see

Second-order wave diffraction by a submerged circular cylinder

  • M. Mciveri (a1) and P. Mciver (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed