Oblique wave scattering by a rectangular submarine trench

Rumpa Chakraborty, B. N. Mandal

Abstract


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.


doi: 10.1017/S1446181115000024

Keywords


water wave scattering; rectangular submarine trench; oblique incident wave; multi-term Galerkin approximation; reflection and transmission coefficients



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.7922



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.