Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-19T10:57:25.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Edge waves over a shelf: full linear theory

Published online by Cambridge University Press:  20 April 2006

D. V. Evans  and
P. Mciver
D. V. Evans
Affiliation:
Department of Mathematics, University of Bristol
P. Mciver
Affiliation:
Department of Mathematics, University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

Edge-wave solutions to the linearized shallow-water equations for water waves are well known for a variety of bottom topographies. The only explicit solution using the full linearized theory describes edge waves over a uniformly sloping beach, although the existence of such waves has been established for a wide class of bottom geometries. In this paper the full linearized theory is used to derive the properties of edge waves over a shelf. In particular, curves are presented showing the variation of frequency with wavenumber along the shelf, together with some mode shapes for a particular shelf geometry.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 142 , May 1984 , pp. 79 - 95
Copyright
© 1984 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

Eckart, C. 1951 Surface waves in water of variable depth. Marine Phys. Lab. Scripps Inst. Oceanogr. Wave Rep. 100–99.Google Scholar
Grimshaw, R. 1974 Edge waves: a long wave theory for oceans of finite depth. J. Fluid Mech. 62, 775–791.Google Scholar
Guza, R. T. & Davis, R. E. 1974 Excitation of edge waves by waves incident on a beach. J. Geophys. Res. 79, 1285–1291.Google Scholar
Huntley, D. A. & Bowen, A. J. 1973 Field observations of edge waves. Nature 243, 160–162.Google Scholar
Jones, D. S. 1953 The eigenvalues of Δ2u + Λu = 0 when the boundary conditions are given on semi-infinite domains. Proc. Camb. Phil. Soc. 49, 668–684.Google Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.Google Scholar
Miles, J. W. 1967 Surface-wave scattering for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Newman, J. N., Sortland, B. & Vinje, T. 1983 The added mass and damping of rectangular bodies close to the free surface. Private communication.
Roseau, M. 1958 Short waves parallel to the shore over a sloping beach. Commun. Pure Appl. Maths 11, 433–493.Google Scholar
Snodgrass, F. E., Munk, W. H. & Miller, G. R. 1962 Long period waves over California's Continental Borderland. Part I: Background Spectra. J. Mar. Res. 20, 3–30.Google Scholar
Stokes, G. G. 1846 Report on recent researches in hydrodynamics. Brit. Assn Rep.Google Scholar
Summerfield, W. 1972 Circular islands as resonators of long-wave energy. Phil. Trans. R. Soc. Lond. A 272, 361–402.Google Scholar
Tuck, E. O. 1976 Some classical water-wave problems in varying depth. In Proc. IUTAM Symp. Waves on Water of Varying Depth, Canberra.
Tuck, E. O. 1980 The effect of a submerged barrier on the natural frequencies and radiation damping of a shallow basin connected to open water. J. Austral. Math. Soc. (Series B) 22 104–128.Google Scholar
Ursell, F. 1951 Trapping modes in the theory of surface waves. Proc. Camb. Phil. Soc. 47, 347–358.Google Scholar
Ursell, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 79–97.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik (ed. W. Flügge), vol. 9, pp. 446–778. Springer.