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Oblique scattering by thin vertical barriers in deep water : solution by multi-term Galerkin technique using simple polynomials as basis

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Abstract

This paper is concerned with scattering of obliquely incident surface waves by a thin vertical barrier which may be either partially immersed or completely submerged extending infinitely downwards in deep water. Instead of one-term Galerkin approximation involving the known solution of the integral equation arising in the normal incidence problem, two-term Galerkin approximation involving simple polynomials as basis multiplied by appropriate weight function is used to solve the integral equations arising in the mathematical analysis of the oblique scattering problem. Very accurate numerical estimates for the reflection coefficient for each configuration of the barrier are obtained. The reflection coefficient is depicted graphically against the wavenumber and the incident angle for each configuration.

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Acknowledgements

The authors thank the reviewers for their comments and suggestions to improve the paper, and providing the reference [15]. B C Das acknowledges the financial support from UGC, New Delhi. This work is also supported by SERB through the research Project No. EMR/2016/005315, dated 23.05.2017

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Authors and Affiliations

  1. Department of Applied Mathematics, Calcutta University, 92, A.P.C.Road, Kolkata, 700009, India

    B. C. Das & Soumen De

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T.Road, Kolkata, 700108, India

    B. N. Mandal

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  1. B. C. Das
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  2. Soumen De
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  3. B. N. Mandal
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Correspondence to B. N. Mandal.

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Das, B.C., De, S. & Mandal, B.N. Oblique scattering by thin vertical barriers in deep water : solution by multi-term Galerkin technique using simple polynomials as basis. J Mar Sci Technol 23, 915–925 (2018). https://doi.org/10.1007/s00773-017-0520-4

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  • DOI: https://doi.org/10.1007/s00773-017-0520-4

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