Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-22T05:36:03.617Z Has data issue: false hasContentIssue false

Diffraction by a gap between two breakwaters: solution for long waves by matched asymptotic expansions

Published online by Cambridge University Press:  21 April 2006

J. V. Smallman
Affiliation:
Hydraulics Research, Wallingford, Oxon, OX10 8BA, UK

Abstract

A mathematical model is constructed to represent the diffraction of plane harmonic waves through a gap between two semi-infinite breakwaters in water of constant depth. The boundary-value problem corresponding to this model is formulated and then specialized to the case of waves that are long relative to the gap width. A solution to the long-wave problem is found using the method of matched asymptotic expansions. A selection of results are presented and, where possible, comparisons are made with previous work.

Type
Research Article
Copyright
© 1991 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

Abramowitz, H. & Stegun I. A.1965 Handbook of Mathematical Functions. Dover.
Gilbert, G. & Brampton A. H.1985 The solution of two wave diffraction problems using integral equations. Hydraulics Res. Rep. IT 299.Google Scholar
Kober H.1957 Dictionary of Conformal Representations. Dover.
Memos C. D.1980 Energy transmitted by surface waves through an opening. J. Fluid Mech. 97, 557568.Google Scholar
Smallman J. V.1983 Wave diffraction by breakwaters. Ph.D. thesis, Reading University.
Smallman J. V., & Porter, D. 1985 Wave diffraction by two inclined semi-infinite breakwaters. Intl Conf. on Numerical and Hydraulic modelling of Ports and Harbours. Birmingham, England, pp. 269278. BHRA.Google Scholar
Southgate H. N.1985 A ray model of wave action in harbours. Intl Conf. on Numerical and Hydraulic modelling of Ports and Harbours. Birmingham, England, pp. 309316. BHRA.Google Scholar
Tuck E. O.1975 Matching problems involving flow through small holes. Adv. Appl. Mech. 15, 89158.Google Scholar
Wehausen, J. V. & Laitone E.1960 Surface waves. Handbuch der Physik, ix/iii (ed. S. Flugge). Springer.