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Scattering of water waves by a vertical wall with gaps

Published online by Cambridge University Press:  17 February 2009

Sudeshna Banerjea
Sudeshna Banerjea
Affiliation:
Department of Mathematics, Jadavpur University, Calcutta - 700 032, India.
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Abstract

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This paper is concerned with a reinvestigation of the problem of water wave scattering by a wall with multiple gaps by using the solution of a singular integral equation with a combination of logarithmic and power (Cauchy-type) kernels in disjoint multiple intervals. Use of Havelock's expansion of water wave potential reduces the problem to such an integral equation in the horizontal velocity across the gaps. The solution of the integral equation is obtained by utilizing the solutions of Cauchy-type integral equations in (0,∞) and also in multiple disjoint intervals. An explicit expression for the reflection coefficient is obtained for a wall with n gaps and supplemented by numerical results for up to three gaps.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 512 - 529
Copyright
Copyright © Australian Mathematical Society 1996

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 (3) (1993) 81–84.CrossRefGoogle Scholar
[2]Dean, W. R., “On the reflexion of surface waves by a submerged vertical plate”, Proc. Camb. Phil. Soc. 41 (1945) 231–238.CrossRefGoogle Scholar
[3]Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–451.CrossRefGoogle Scholar
[4]Havelock, T. H., “Forced surface-waves on water”, Philos. Mag. 8 (1929) 569–576.CrossRefGoogle Scholar
[5]Lewin, M., “The effect of vertical barriers on progressing waves”, J. Math. Phys. 42 (1963) 287–300.Google Scholar
[6]Macaskill, C., “Reflexion of water waves by a permeable barrier”, J. Fluid Mech. 95 (1979) 141–157.CrossRefGoogle Scholar
[7]Mei, C. C., “Radiation and scattering of transient gravity waves by vertical plates”, Quart. J. Mech. Appl. Math. 19 (1966) 417–440.CrossRefGoogle Scholar
[8]Muskhelishvili, N. I., Singular integral equations (Noordhoff, Groningen, 1963).Google Scholar
[9]Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411–421.CrossRefGoogle Scholar
[10]Porter, D., “The radiation and scattering of surface waves by vertical barriers”, J. Fluid Mech. 63 (1974) 625–634.CrossRefGoogle Scholar
[11]Tuck, E. O., “Transmission of water waves through small apertures”, J. Fluid Mech. 49 (1971) 65–74.CrossRefGoogle Scholar
[12]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