Abstract
Assuming linear theory, the two-dimensional problem of water wave scattering by a rectangular submarine trench is reinvestigated here employing the multiterm Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving the integral equations arising in the mathematical analysis. Because of the geometrical symmetry of the rectangular trench about the \(y\)-axis, the problem is split into two separate problems involving symmetric and antisymmetric potential functions. Very accurate numerical estimates for the reflection and transmission coefficients for various values of different parameters are obtained, and these are seen to satisfy the energy identity. These coefficients are computed numerically and depicted graphically against the wave number in a number of figures. Some figures available in the literature drawn using different mathematical methods and laboratory experiments are also recovered following the present analysis, thereby confirming the correctness of the results presented here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the trench.
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Acknowledgments
The authors thank the reviewers and Professor A. A. Korobkin for their comments and suggestions for improving the paper in the present form. This work is supported by a NASI Senior Scientist Fellowship and a DST research project (Sr/S4/MS:521/08).
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Chakraborty, R., Mandal, B.N. Water wave scattering by a rectangular trench. J Eng Math 89, 101–112 (2014). https://doi.org/10.1007/s10665-014-9705-6
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DOI: https://doi.org/10.1007/s10665-014-9705-6