Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T14:18:16.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction of gravity waves by a barrier reef

Published online by Cambridge University Press:  20 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla, California 92093
Get access Rights & Permissions [Opens in a new window]

Abstract

The gravity-wave scattering matrix for a barrier reef that separates two different depths of water is calculated by an extension of a variational analysis of diffraction by a discontinuity in depth (Miles 1967). The resulting transmission coefficient for equal depths differs from that obtained by Johnson, Fuchs & Morison (1951), which appears to be incorrect. The results are applied to the calculation of resonant amplification of incoming swell or tsunamis by a shallow lagoon that is bounded by the reef and a vertical inner boundary. The results for this last problem agree closely (exactly for equal depths) with those obtained by Tuck (1980) through a rather different approach.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 115 - 123
Copyright
© 1981 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. 1964 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Allison, H. & Grassia, A. 1979 Sporadic sea-level oscillations along the Western Australian coastline. Aust. J. Mar. Freshwater Res. 30, 723–30.Google Scholar
Johnson, J. W., Fuchs, R. A. & Morison, J. A. 1951 The damping action of submerged breakwaters. Trans. Amer. Geophys. Union 32, 704–718.Google Scholar
Miles, J. W. 1946 The analysis of plane discontinuities in cylindrical tubes. Part II. J. Acoust. Soc. Am. 17, 272–284.Google Scholar
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Miles, J. W. & Munk, W. H. 1961 Harbour paradox. Proc. A.S.C.E., J. Waterways and Harbors Div. 87, 111–130.Google Scholar
Tuck, E. O. 1980 The effect of a submerged barrier on the natural frequencies and radiation damping of a shallow basin connected to open water. J. Aust. Math. Soc. B 22, 104–128.Google Scholar
Tuck, E. O., Allison, H., Field, S. R. & Smith, J. W. 1980 The effect of a submerged reef chain on periods of sea-level oscillations in Western Australia. Aust. J. Mar. Freshwater Res. 31, 719–728.Google Scholar
Kreisel, C. 1949 Surface waves. Quart. Appl. Math. 7, 21–44.Google Scholar