Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-17T17:42:49.488Z Has data issue: false hasContentIssue false

Mechanisms for the generation of edge waves over a sloping beach

Published online by Cambridge University Press:  21 April 2006

D. V. Evans
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK

Abstract

Two mechanisms for the generation of standing edge waves over a sloping beach are described using classical linear water-wave theory. The first is an extension of the result of Yih (1984) to a class of localized bottom protrusions on a sloping beach in the presence of a longshore current. The second is a class of longshore surface-pressure distributions over a beach. In both cases it is shown that Ursell-type standing edge-wave modes can be generated in an appropriate frame of reference. Typical curves of the mode shapes are presented and it is shown how in certain circumstances the dominant mode is not the lowest.

Type
Research Article
Copyright
© 1988 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 on water of variable depth. Lecture notes, Wave Rep. 100, Ref. S1–12. Scripps Institution of Oceanography.
Greenspan, H. P. 1956 The generation of edge waves by moving pressure distributions. J. Fluid Mech. 1, 574590.Google Scholar
Greenspan, H. P. 1970 A note on edge waves in a stratified fluid. Stud. Appl. Maths 44, 381388.Google Scholar
Holman, R. A. & Bowen, A. J. 1984 Longshore structure of infragravity wave motions. J. Geophys. Res. 89, 64466452.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Munk, W., Snodgrass, F. & Carrier, G. 1956 Edge waves on the continental shelf. Science 123, 127132.Google Scholar
Peters, A. S. 1952 Water waves over sloping beaches and the solution of a mixed boundary value problem for Δ2ϕ−k2ϕ = 0 in a sector. Commun. Pure Appl. Maths 5, 87108.Google Scholar
Roseau, M. 1958 Short waves parallel to the shore over a sloping beach. Commun. Pure Appl. Maths 6, 433493.Google Scholar
Stoker, J. J. 1957 Water Waves. Interscience.
Stokes, G. G. 1846 Report on recent researches in hydrodynamics. Brit. Assoc. Rep.Google Scholar
Ursell, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 7997.Google Scholar
Yih, C.-S. 1984 Edge waves created by a long-shore current over a ridge in the sea-bed. Proc. 15th Symp. Naval Hydrodynamics, Hamburg, pp. 367371.