Effects of flexible bed on oblique wave interaction with multiple surface-piercing porous barriers

Abstract

Within the framework of linearised theory of water waves, a model of oblique wave scattering by obstacles in the form of thin multiple surface-piercing porous barriers having non-uniform porosity is analysed. Herein, we consider a flexible base in an ocean of uniform finite depth. The flexible base surface is modelled as a thin elastic plate under the acceptance of Euler–Bernoulli beam equation. With the aid of eigenfunction expansion method along with mode-coupling relations, four Fredholm-type integral equations are obtained from the boundary value problem. The multi-term Galerkin approximations in terms of Chebychev polynomials multiplied by suitable weight functions are used for solving those integral equations. Analytic solutions for different hydrodynamic quantities (viz. reflection coefficients, transmission coefficients, dissipated wave energy and non-dimensional wave force) are determined, and those quantities are displayed graphically for various values of the dimensionless parameters. It is observed from the graphical representations that the permeability of the barriers and thickness of the bottom surface play a crucial role in modelling of efficient breakwaters.

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Acknowledgements

The authors are very much indebted to the reviewer for his/her valuable suggestions which enabled the authors to carry out the desired revision of the manuscript. This work is completely supported by Higher Education, Science and Technology and Bio-Technology, Government of West Bengal, Memo No: 14(Sanc.)/ST/P/S&T/16G-38/2017.

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Correspondence to Soumen De.

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Sarkar, B., Paul, S. & De, S. Effects of flexible bed on oblique wave interaction with multiple surface-piercing porous barriers. Z. Angew. Math. Phys. 72, 83 (2021). https://doi.org/10.1007/s00033-021-01518-6

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Keywords

  • Flexible bottom surface
  • Surface-piercing barriers
  • Non-uniform porosity
  • Mode-coupling relations
  • Multi-term Galerkin approximation
  • Hydrodynamic coefficients and forces

Mathematics Subject Classification

  • 76B15