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Dissipation of incident wave energy by two floating horizontal porous plates over a trench-type bottom

PUBLISHED July 03, 2023 (DOI: https://doi.org/10.54985/peeref.2307p2018211)

5th Place Peeref Competition


Sunita Choudhary1 , Subash Chandra Martha1
  1. Department of Mathematics, Indian Institute of Technology Ropar

Conference / event

Cynasore 2023, December 2022 (Rupnagar, India)

Poster summary

A mathematical model for wave interaction with a pair of plates over a trench-type bottom topography is developed. This problem is modelled based on Darcy's law for flow past a porous structure. Havelock's expansions of water wave potentials, suitable matching conditions, and the algebraic least-square method handle the boundary value problem. The role of the horizontal porous plates is studied by analysing the scattering coefficients, energy loss, hydrodynamic wave force and free surface elevation through graphs which show a periodic oscillatory pattern as a function of gap length. The study reveals that if the porous effect parameter of plates or the length of plates is increased, more energy is dissipated, and the plates experience less wave force. The free surface elevation on the lee side is decreased. The findings from the present model are likely to help understand the role of breakwaters in engineering applications.


Eigenfunction expansion method, Algebraic least-square method, System of equation

Research areas

Mathematics, Mechanical Engineering


  1. Linton, C.M., 2001. The finite dock problem. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 52(4), pp.640-656.
  2. Cho, I.H. and Kim, M.H., 2013. Transmission of oblique incident waves by a submerged horizontal porous plate. Ocean Engineering, 61, pp.56-65.
  3. Chakraborty, R. and Mandal, B.N., 2015. Oblique wave scattering by a rectangular submarine trench. The ANZIAM Journal, 56(3), pp.286-298.


  1. University Grants Commission (UGC), Govt. of India (No. Ref. No. JUNE18-419784)

Supplemental files

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Additional information

Competing interests
No competing interests were disclosed.
Data availability statement
The datasets generated during and / or analyzed during the current study are available from the corresponding author on reasonable request.
Creative Commons license
Copyright © 2023 Choudhary et al. This is an open access work distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Choudhary, S., Martha, S. Dissipation of incident wave energy by two floating horizontal porous plates over a trench-type bottom [not peer reviewed]. Peeref 2023 (poster).
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