Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T06:28:38.857Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface-wave scattering matrix for a shelf

Published online by Cambridge University Press:  28 March 2006

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

Abstract

The diffraction of gravity waves at a discontinuity in depth is described by a scattering matrix that relates the asymptotic, plane-wave fields (each of which may contain waves travelling towards and away from the discontinuity) on the two sides of the discontinuity. Plane-wave and variational approximations for the elements of this scattering matrix are developed. These approximate results are tested by comparison with the more accurate results obtained by Newman for an infinite step. The plane-wave approximation to the magnitude of the transmission coefficient is within 5% of Newman's result for all wavelengths, but the corresponding approximation to the reflexion coefficient is satisfactory only for rather long wavelengths. The variational approximations to the complex transmission and reflexion coefficients agree with Newman's results, within the accuracy with which his graphs can be read, for all wavelengths. The variational approximations also are used to determine the effects of trapped modes on the resonant width of a shelf that terminates at a vertical cliff.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 4 , 22 June 1967 , pp. 755 - 767
Copyright
© 1967 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

Bartholomeusz, E. F. 1958 The reflexion of long waves at a step Proc. Camb. Phil. Soc. 54, 106–18.Google Scholar
Keller, J. B. 1952 Scattering of water waves treated by the variational method (abstract only). Gravity Waves. Washington: National Bureau of Standards.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Marcuvitz, N. 1951 Waveguide Handbook. New York: New York.
Miles, J. W. 1946 The analysis of plane discontinuities in cylindrical tubes. Parts I and II. J. Acoust. Soc. Am. 17, 259–71, 272–84.Google Scholar
Miles, J. W. & Munk, W. H. 1961 Harbor paradox J. WatWays Harb. Div., Am. Soc. Civ. Engrs 87, 111–30.Google Scholar
Newman, J. N. 1965a Propagation of water waves over an infinite step J. Fluid Mech. 23, 399–415.Google Scholar
Newman, J. N. 1965b Propagation of water waves past long two-dimensional obstacles J. Fluid Mech. 23, 23–30.Google Scholar
Rayleigh, Lord 1945 Theory of Sound, $264, 301. New York: Dover.
Schwinger, J. 1944 Unpublished reports at M.I.T. Radiation Laboratory. (See Marcuvitz 1951.)
Sretenskii, L. N. 1950 Refraction and reflexion of plane waves in liquids at a transition from one depth to another (in Russian). Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, p. 1601. (Cited by Newman 1965a).Google Scholar