Bragg Scattering of Surface Gravity Waves by an Array of Surface-Piercing Variable Porosity Barriers
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 148, Issue 6
Abstract
The scattering of gravity waves by vertically staggered multiple porous barriers having variable porosity is analyzed within the framework of linearized water wave theory in two dimensions. The barriers are assumed to follow quadratic pressure boundary conditions to account for energy dissipation with the changes in the wave height, which is often neglected in the case of Darcy’s law. A generalized code based on the dual boundary element method (DBEM) is developed for solving the boundary value problem. Three different wave barrier configurations are considered with the same volume of materials required for its construction to identify the best-performing barriers. The hydrodynamic performance of the barriers with progressively decreasing porosity is found to be better than the barriers with gradually increasing porosity or barriers with constant porosity. The scattering coefficients attain optimal at integer multiples of half the wavelength. It is appropriate to select relative spacing in the range of 0.2–0.3 for better hydrodynamic performance for any field design condition. For deeper water depths (k0h > π), increasing the relative submergence depth beyond 0.2 is insignificant to the change in hydrodynamic performance. For the practical field range of k0h and for a threshold wave transmission coefficient of 0.2, the appropriate relative submergence depth is 0.6. The results of this study would help in the hydrodynamic design of a progressive wave absorber.
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Acknowledgments
C. S. Nishad and K. G. Vijay thank Professor Jeng Tzong Chen of National Taiwan Ocean University, Taiwan, for quality discussions on the methodology in the DBEM code development. T. Sahoo acknowledges the financial support of the Department of Science and Technology, Government of India via award No. DST/CCP/CoE/79/2017(G). S. Neelamani thanks the Kuwait Institute for Scientific Research (KISR) facilities for carrying out this research work.
Notation
The following symbols are used in this paper:
- C
- blockage (inertia) coefficient of the quadratic porous boundary condition;
- g
- acceleration due to gravity;
- H
- incident wave height;
- h
- water depth;
- h1
- submergence depth of the porous barriers;
- KL
- energy loss coefficient;
- KR
- reflection coefficient;
- KT
- transmission coefficient;
- k0
- wave number;
- L
- clearance distance from the breakwater extreme edge (L ≥ 5h);
- Lij, Mij
- kernels of the hyper-singular boundary integral equation;
- MR
- moment coefficient about the reference (0, −h);
- S
- spacing between the barriers;
- Uij, Tij
- kernels of the singular boundary integral equation;
- X
- horizontal force coefficient;
- α
- discharge coefficient of the quadratic porous boundary condition;
- Γ
- boundary of the computational domain;
- δ
- barrier thickness;
- κ
- constant of proportionality;
- λ
- wavelength of the incident wave;
- μj
- porosity of the barriers from seaside to lee side, where j ∈ [1, 4];
- ν
- panel (discrete element) size;
- Ω
- computational domain; and
- ω
- angular frequency.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 148 • Issue 6 • November 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jun 10, 2021
Accepted: Jul 21, 2022
Published online: Sep 9, 2022
Published in print: Nov 1, 2022
Discussion open until: Feb 9, 2023
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