Hostname: page-component-76d6cb85b7-6jg5l Total loading time: 0 Render date: 2026-07-26T06:38:34.653Z Has data issue: false hasContentIssue false
  • English
  • Français

On surface-wave diffraction by a trench

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, San Diego
Get access Rights & Permissions [Opens in a new window]

Abstract

The two-dimensional diffraction of a long surface wave by a deformation of the bottom is calculated through a conformal-mapping algorithm (Kreisel 1949). The result is applied to obtain the complex reflection coefficient for a rectangular trench. The corresponding reflection coefficient for oblique incidence is obtained through a variational formulation.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 315 - 325
Copyright
© 1982 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.)

Article purchase

Temporarily unavailable

References

Byrd, P. F. & Friedman, M. D. 1954 Handbook of Elliptic Integrals for Engineers and Physicists. Springer.
Carter, F. W. 1926 The electric field of the dynamo-electric machine. Proc. I. E. E. 64, 1115–1138.Google Scholar
Flagg, C. N. & Newman, J. N. 1971 Sway added-mass coefficients for rectangular profiles in shallow water. J. Ship Res. 15, 257–265.Google Scholar
Kreisel, G. 1949 Surface waves. Quart. Appl. Math. 7, 21–44.Google Scholar
Lamb, H. 1898 On the diffraction in transmission of electric waves by a metallic grating. Proc. Lond. Math. Soc. 29, 523–544.Google Scholar
Lassiter, J. B. 1972 The propagation of water waves over sediment pockets. Doctoral dissertation, M.I.T.
Lee, J. J. & Ayer, R. M. 1981 Wave propagation over a rectangular trench. J. Fluid Mech. 110, 335–347.Google Scholar
Mei, C. C. & Black, J. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Pólya, G. & Szegö, G. 1951 Isoperimetric Inequalities in Mathematical Physics. Princeton University Press.
Rayleigh, Lord 1897 On the passage of waves through apertures in plane screens, and allied problems. Phil. Mag. 43, 259–272 (Scientific Papers, vol. 4, pp. 283–296. Cambridge University Press).Google Scholar
Schwinger, J. & Saxon, D. S. 1968 Discontinuities in Waveguides. Gordon & Breach.
Tuck, E. O. 1976 Some classical water-wave problems in varying depth. In Waves on Water of Varying Depth (ed. D. G. Provis & R. Radok). Springer.