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Water wave scattering by two submerged nearly vertical barriers

Published online by Cambridge University Press:  17 February 2009

B. N. Mandal  and
Soumen De
B. N. Mandal
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India; e-mail: [email protected].
Soumen De
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India; e-mail: [email protected].
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Abstract

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The problem of surface water wave scattering by two thin nearly vertical barriers submerged in deep water from the same depth below the mean free surface and extending infinitely downwards is investigated here assuming linear theory, where configurations of the two barriers are described by the same shape function. By employing a simplified perturbational analysis together with appropriate applications of Green's integral theorem, first-order corrections to the reflection and transmission coefficients are obtained. As in the case of a single nearly vertical barrier, the first-order correction to the transmission coefficient is found to vanish identically, while the correction for the reflection coefficient is obtained in terms of a number of definite integrals involving the shape function describing the two barriers. The result for a single barrier is recovered when two barriers are merged into a single barrier.

Keywords

water wave scatteringlinear theoryperturbation analysisnearly vertical barriersreflection and transmission coefficients.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 107 - 117
Copyright
Copyright © Australian Mathematical Society 2006

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