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Oblique wave interaction with an infinite trench in presence of a bottom-standing thick rectangular barrier

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Abstract

The present field of study is to analyse the interaction of water waves with an infinite trench and a bottom-standing thick rectangular barrier by assuming linear theory. Motivational theme behind this study is that wave scattering by an infinite trench along with thick structure is quite a new representation of breakwater model in the history of water wave theory. Applying eigenfunction expansion method, the problem is reduced to solve the four weakly singular integral equations involving horizontal component of velocity across the gaps above the edges of the thick barrier and the infinite trench. Those integral equations are solved by employing multi-term Galerkin approximation involving expansions in terms of ultra-spherical Gegenbauer polynomials multiplied by appropriate weight functions having one-third singularity. The accuracy of the present model is corroborated by generating some previous available results in the literature of water waves for limiting cases. Numerical estimates for reflection and transmission coefficients are depicted graphically against the wavenumber for different non-dimensional parameters.

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Acknowledgements

The authors thank the reviewers for their comments and suggestions to improve the article in the present form. This work is partially supported by a SERB, DST(TAR/2022/000107).

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Authors and Affiliations

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

    Swagata Ray & Soumen De

  2. Department of Mathematics, Swami Vivekananda University, Barrackpore, Kolkata, 700121, India

    Biman Sarkar

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  1. Swagata Ray
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  2. Biman Sarkar
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  3. Soumen De
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Contributions

SR: Methodology, Numerical computations, Investigation. BS: Investigation, Writing. SD: Conceptualization, Investigation, Supervision, Writing and editing.

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Correspondence to Soumen De.

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Ray, S., Sarkar, B. & De, S. Oblique wave interaction with an infinite trench in presence of a bottom-standing thick rectangular barrier. J Eng Math 141, 1 (2023). https://doi.org/10.1007/s10665-023-10273-8

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