Hostname: page-component-84b7d79bbc-5lx2p Total loading time: 0 Render date: 2024-07-28T03:56:25.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly nonlinear interactions and wave trapping

Published online by Cambridge University Press:  20 April 2006

Yuriko Renardy
Yuriko Renardy
Affiliation:
University of Wisconsin–Madison, Mathematics Research Center, 610 Walnut Street, Madison, Wisconsin 53705
Get access Rights & Permissions [Opens in a new window]

Abstract

When the flow over a submerged, round, upright cylinder, situated in a large ocean, is forced by a train of plane waves, linear theory (Yamamuro 1981) shows that the response can be abnormally large for certain forcing frequencies. The aim of this paper is to present a weakly nonlinear theory, where wave interactions, arising from the quadratic terms in the free-surface boundary conditions, can yield abnormally large responses.

A specific interaction will be considered between a flow at a subharmonic frequency and a flow at the driving frequency. The reason for considering such an interaction derived from a consideration of some experimental results of Barnard, Pritchard & Provis (1981).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 27 - 39
Copyright
© 1983 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. 1972 Handbook of Mathematical Functions. Washington: Natl Bureau of Standards.
Barnard, B., Pritchard, W. G. & Provis, D. 1981 MRC Tech. Rep. 2412, Geophys. Astrophys. Fluid Dyn. (to be published).
Davis, A. M. & Hood, M. J. 1976 Surface waves normally incident on a submerged horizontal cylinder SIAM J. Appl. Maths 31, 28.Google Scholar
Guza, R. T. & Davis, R. E. 1974 Excitation of edge waves by waves incident on a beach J. Geophys. Res. 79, 1285–1291.Google Scholar
Havelock, T. H. 1929 Forced surface-waves on water Phil. Mag. 8, 569–576.Google Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy round islands J. Fluid Mech. 29, 781–821.Google Scholar
Mahony, J. J. & Smith, R. 1972 A model for spatial resonance phenomena J. Fluid Mech. 53, 193–207.Google Scholar
Mcewan, A. D. 1971 Degeneration of resonantly-excited standing internal gravity waves J. Fluid Mech. 50, 431–448.Google Scholar
Meyer, E. E. 1971 Resonance of unbounded water bodies. In Mathematical Problems in the Geophysical Sciences (ed. W. H. Reid). Lectures in Applied Mathematics, vol. 13, pp. 189–227. Am. Math. Soc., Providence, Rhode Island.
Meyer, R. E. 1979 Theory of water-wave refraction Adv. Appl. Mech. 19, 53–141.Google Scholar
Minzoni, A. A. & Whitham, G. B. 1977 On the excitation of edge waves on beaches J. Fluid Mech. 79, 273–287.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Pite, H. D. 1977 The excitation of damped waves diffracted over a submerged circular sill J. Fluid Mech. 82, 621–641.Google Scholar
Renardy, Y. 1983 Trapping of water waves above a round sill. J. Fluid Mech. (to be published).
Rockliff, N. 1978 Finite amplitude effects in free and forced edge waves Math. Proc. Camb. Phil. Soc. 83, 463.Google Scholar
Summerfield, W. C. 1969 On the trapping of wave energy by bottom topography. Horace Lamb Centre Ocean Res., Flinders Univ., Res. Paper no. 30.