The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- The Journal of the Australian Mathematical Society. Series B. Applied Mathematics / Volume 37 / Issue 04 / April 1996, pp 512-529
- Copyright © Australian Mathematical Society 1996
- DOI: http://dx.doi.org/10.1017/S0334270000010845 (About DOI), Published online: 17 February 2009
Research Article
Scattering of water waves by a vertical wall with gaps
Sudeshna Banerjeaa1
a1 Department of Mathematics, Jadavpur University, Calcutta - 700 032, India.
Abstract
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.
(Received October 15 1993)
(Revised August 23 1994)
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