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Wave scattering by Pi-type breakwater floating in deep water

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Abstract

This article presents a study on surface gravity wave scattering by a rectangular (box-type) breakwater with thin side plates in the situation of oblique incident waves in deep water. Applying the continuity of fluid pressure and velocity to Havelock’s expansion of velocity potentials, the problem is converted to an integral equation of the Fredholm type, whose solution is the horizontal component of fluid velocity. The integral equation is solved by employing Galerkin’s approximation with polynomials as basis functions multiplied by suitable weight functions. The wave reflection and transmission coefficients are calculated numerically to find the breakwater’s performance on wave scattering. The accuracy of the results is verified through numerical convergence and checking of the energy balance equation. The rectangular breakwater reflects long waves to some extent in water of infinite depth, in contrast to a thin breakwater. The thin plates attached to the rectangular breakwater show a reduction in wave transmission. Furthermore, the attachment of thin plates leads to an increment in horizontal force and a reduction in vertical force.

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Acknowledgements

The authors thank the reviewers for their comments and suggestions to revise the paper in the present form. This work is carried out with the funding support of Science and Engineering Research Board, Government of India under MATRICS project with grant No. MTR/2022/000113.

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Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, 826004, India

    R. B. Kaligatla & S. Singh

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

    B. N. Mandal

Authors
  1. R. B. Kaligatla
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  2. S. Singh
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  3. B. N. Mandal
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Contributions

RBK: Problem formulation, Derivations, Investigation, Editing; SS: Derivations, Computations, Manuscript preparation; BNM: Method construction, Supervision; All authors reviewed the manuscript.

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Correspondence to R. B. Kaligatla.

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Kaligatla, R.B., Singh, S. & Mandal, B.N. Wave scattering by Pi-type breakwater floating in deep water. J Eng Math 143, 7 (2023). https://doi.org/10.1007/s10665-023-10301-7

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  • DOI: https://doi.org/10.1007/s10665-023-10301-7

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