Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T14:13:36.291Z Has data issue: false hasContentIssue false
  • English
  • Français

The transmission of surface waves through a gap in a vertical barrier

Published online by Cambridge University Press:  24 October 2008

D. Porter
D. Porter
Affiliation:
Department of Mathematics, University of Beading
Get access Rights & Permissions [Opens in a new window]

Abstract

The two-dimensional configuration is considered of a fixed, semi-infinite, vertical barrier extending downwards from a fluid surface and having, at some depth, a gap of arbitrary width. A train of surface waves, incident on the barrier, is partly transmitted and partly reflected. The velocity potential of the resulting fluid motion is determined by a reduction procedure and also by an integral equation formulation. It is shown that the two methods lead to the same Riemann–Hilbert problem. Transmission and reflexion coefficients are calculated for several values of the ratio gap width/mean gap depth.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 411 - 421
Copyright
Copyright © Cambridge Philosophical Society 1972

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

REFERENCES

(1)Dean, W. R.Proc. Cambridge Philos. Soc. 41 (1945), 231–238.CrossRefGoogle Scholar
(2)Evans, D. V. J.Fluid Mech. 40 (1970), 433–451.CrossRefGoogle Scholar
(3)Haskind, M. D.Inz. Sb. 4 (1948), 147–160.Google Scholar
(4)John, F.Comm. Pure Appl. Math. 1 (1948), 149–200.CrossRefGoogle Scholar
(5)Levine, H. and Rodemich, E.Tech. Rep. No. 78, Appl. Maths, and Stats. Lab, Stanford Univ. (1958).Google Scholar
(6)Lewin, M. J.Math. and Phys. 42 (1963), 287–300.CrossRefGoogle Scholar
(7)Muskhelishvili, N. I.Singular integral equations (Noordhoff, 1963).Google Scholar
(8)Smith, S. H. J.Inst. Math. Appl. 5 (1969), 217–229.CrossRefGoogle Scholar
(9)Ursell, F.Proc. Cambridge Philos. Soc. 43 (1947), 374–382.CrossRefGoogle Scholar
(10)Wehausen, J. V. and Laitone, E. V.Handbuch der Physik IX (Springer-Verlag, 1960).Google Scholar