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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.
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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

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