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The diffraction of surface waves by plane vertical obstacles

Published online by Cambridge University Press:  11 April 2006

A. M. Ayad  and
F. G. Leppington
A. M. Ayad
Affiliation:
Department of Mathematics, Imperial College, London
F. G. Leppington
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

A short-wave asymptotic solution is derived for the problem of the diffraction of a surface wave train, in deep water, by a two-dimensional obstacle with plane vertical sides near its intersection with the free surface. Using matched asymptótic approximations, a detailed analysis is presented for the special case of a rectangular scatterer of depth a and width 2b, and the solution is then generalized to deal with a wider class of geometries. It is found that the transmission coefficient, at small wavelengths, has an exponentially small factor that depends on the depths of the plane sides, and an algebraically small factor that depends on the corner angles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 593 - 604
Copyright
© 1977 Cambridge University Press

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References

Alker, G. 1977 Ph.d. thesis, London University.
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Series, Products and Integrals, 8.11. Academic Press.
John, F. 1950 On the motion of floating bodies. II. Simple harmonic motions. Comm. Pure Appl. Math. 3, 45.Google Scholar
Leppington, F. G. 1973 On the radiation and scattering of short surface waves. Part 2. J. Fluid Mech. 59, 129.Google Scholar
Mei, C. C. & Black, J. L. 1969 Scattering of surface waves by rectangular obstacles in water of finite depth. J. Fluid Mech. 38, 499.Google Scholar
Ursell, F. 1947 The effect of a fixed vertical barrier on surface waves in deep water. Proc. Camb. Phil. Soc. 43, 374.Google Scholar