Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T18:51:37.272Z Has data issue: false hasContentIssue false
  • English
  • Français

Scattering of water waves by a submerged thin vertical wall with a gap

Published online by Cambridge University Press:  17 February 2009

Sudeshna Banerjea  and
B. N. Mandal
Sudeshna Banerjea
Affiliation:
Department of Mathematics, Jadavpur University, Calcutta 700 032, India
B. N. Mandal
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Calcutta 700 035, India
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A train of surface water waves normally incident on a thin vertical wall completely submerged in deep water and having a gap, experiences reflection by the wall and transmission through the gaps above and in the wall. Using Havelock's expansion of water wave potential, two different integral equation formulations of the problem are presented. While the first formulation involves multiple integral equations which are solved here by reducing them to a singular integral equation with Cauchy kernel in a double interval, the second formulation involves a first-kind singular integral equation in a double interval with a combination of logarithmic and Cauchy kernel, the solution of which is obtained by utilizing the solution of a singular integral equation with Cauchy kernel in (0, ∞) and also in a double interval. The reflection coefficient is evaluated by both the methods.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 3 , January 1998 , pp. 318 - 331
Copyright
Copyright © Australian Mathematical Society 1998

References

[1] Banerjea, Sudeshna and Mandal, B. N., “Solution of a singular integral equation in a double interval arising in the theory of water waves”, Appl. Math. Lett. 6 (1993) 81–84.CrossRefGoogle Scholar
[2] Chakrabarti, A. and Vijayabharati, L., “Transmission of water waves through a gap in a submerged vertical barrier”, Indian J. Pure Appl. Math. 22 (1991) 491–512.Google Scholar
[3] Dean, W. R., “On the reflection of surface waves by a submerged plane barrier”, Proc. Camb. Phil. Soc. 41 (1945) 231–238.CrossRefGoogle Scholar
[4] Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–451.CrossRefGoogle Scholar
[5] Muskhelishvili, N. I., Singular integral equations (Noordhoff, Groningen, 1963).Google Scholar
[6] Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411–422.CrossRefGoogle Scholar
[7] Ursell, F., “The effect of a fixed vertical barrier on surface waves in deep water”, Proc. Camb. Phil. Soc. 43 (1947) 374–382.CrossRefGoogle Scholar