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OBLIQUE WAVE SCATTERING BY A RECTANGULAR SUBMARINE TRENCH

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  16 March 2015

RUMPA CHAKRABORTY  and
B. N. MANDAL
RUMPA CHAKRABORTY*
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute 203, B. T. Road, Kolkata 700108, India email chak.rumpa@gmail.com, birenisical@gmail.com
B. N. MANDAL
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute 203, B. T. Road, Kolkata 700108, India email chak.rumpa@gmail.com, birenisical@gmail.com
*
✉chak.rumpa@gmail.com
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Abstract

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The problem of oblique wave scattering by a rectangular submarine trench is investigated assuming a linearized theory of water waves. Due to the geometrical symmetry of the rectangular trench about the central line $x=0$, the boundary value problem is split into two separate problems involving the symmetric and antisymmetric potential functions. A multi-term Galerkin approximation involving ultra-spherical Gegenbauer polynomials is employed to solve the first-kind integral equations arising in the mathematical analysis of the problem. The reflection and transmission coefficients are computed numerically for various values of different parameters and different angles of incidence of the wave train. The coefficients are depicted graphically against the wave number for different situations. Some curves for these coefficients available in the literature and obtained by different methods are recovered.

Keywords

water wave scatteringrectangular submarine trenchoblique incident wavemulti-term Galerkin approximationreflection and transmission coefficients

MSC classification

Primary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 3 , January 2015 , pp. 286 - 298
Copyright
© 2015 Australian Mathematical Society 

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