Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T17:41:13.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Edge waves along periodic coastlines. Part 2

Published online by Cambridge University Press:  26 April 2006

D. V. Evans  and
M. Fernyhough
D. V. Evans
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
M. Fernyhough
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical evidence of the existence of edge waves travelling along a periodic coastline consisting of a straight and vertical cliff face from which protrudes an infinite number of identical rectangular barriers, each extending throughout the water depth, is given based on a Galerkin approximation to an integral representation of the problem derived using the linear theory of water waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 307 - 325
Copyright
© 1995 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

Erdéalyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms. Bateman manuscript project, vol. 1. McGraw-Hill.
Evans, D. V. 1992 Trapped acoustic modes. IMA J. Appl. Maths 49, 45–60.Google Scholar
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 21–31.Google Scholar
Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225, 153–175.Google Scholar
Evans, D. V. & Linton, C. M. 1993 Edge waves along periodic coastlines. Q. J. Mech. Appl. Maths 46, 644–656 (referred to herein as Part 1).Google Scholar
Jones, D. S. 1953 The eigenvalues of $ + $ = 0 when the boundary conditions are given semi-infinite domains. Proc. Camb. Phil. Soc. 49, 668–684.Google Scholar
Jones, D. S. 1986 Acoustic and Electromagnetic Waves. Science Publications, Oxford.
Mittra, R. & Lee, S. W. 1971 Analytical Techniques in the Theory of Guided Waves. Macmillan.
Petit, R. 1980 Electromagnetic Theory of Gratings. Topics in Current Physics. Springer.
Porter, R. 1995 PhD thesi, University of Bristol, in preparation.
Porter, R. & Evans, D. V. 1995 Complementary approximations to wave scattering by vertical barriers. J. Fluid Mech. 294, 155–180.Google Scholar
Stokes, G. G. 1846 Report on recent researches in hydrodynamics. Brit. Assoc. Rep.
Twersky, V. 1962 On scattering of waves by the infinite grating of circular cylinders. IRE Trans. Antennas Propagation 10, 737–765.Google Scholar
Ursell, F. 1952 Edge waves over a sloping beach. Proc. R. Soc. Lond. A 214, 79–97.Google Scholar
Wilcox, C. H. 1984 Scattering Theory for Diffraction Gratings. Springer.