Abstract
The present study investigates the wave-damping characteristics due to the combination of bottom-standing porous structure, submerged porous plate, and fully-extended porous structure of finite width using the small amplitude wave theory. The hydrodynamic characteristics such as reflection, transmission, and dissipation coefficients are determined to analyse the wave energy dissipation by the composite breakwater using the matched eigenfunction expansion method and orthogonal mode-coupling relation. Darcy’s law is incorporated to the flow through porous media. The composite breakwater system is investigated experimentally to validate and compare the numerical results with the physical model study. The complex porous effect parameter for the submerged plate is incorporated in the numerical analysis, which represents the reactance and resistance of the porous structure. The wave forces on the submerged plate and porous structure for the composite breakwater are investigated by considering the effects of changing parameters such as structural porosity, plate submergence, angle of incidence, width of the submerged porous structure and distance between the structures. The study illustrates that the increasing width of the fully-extended porous structure improves the performance of the breakwater system. The proposed study on the composite breakwater yields an useful information for wave energy attenuation, which can be designed and implemented in coastal and harbour areas to achieve wave tranquillity.
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Abbreviations
- b :
-
Distance between the porous structure
- f :
-
Linearized friction factor
- g :
-
Accelaration due to gravity
- h :
-
Water depth
- h 1 :
-
Submergence depth of plate and bottom-standing porous structure
- i:
-
Imaginary number
- k jn :
-
Wave number in x-direction
- K r :
-
Reflection coefficient
- K t :
-
Transmission coefficient
- K d :
-
Dissipation coefficient
- \(K_{{\rm{f}}{{\rm{s}}_1}}^1\) :
-
Wave force on the front of the bottom-standing porous structure
- \(K_{{\rm{f}}{{\rm{s}}_2}}^1\) :
-
Wave force on the back of the bottom-standing porous structure
- K fp :
-
Wave force on submerged porous pate
- \(K_{{\rm{f}}{{\rm{s}}_1}}^2\) :
-
Wave force on the front of the fully-extended porous structure
- \(K_{{\rm{f}}{{\rm{s}}_2}}^2\) :
-
Wave force on the back of the fully-extended porous structure
- l :
-
Wave number in z-direction
- L :
-
Distance between the plate and porous structures
- s :
-
Inertial effect of the porous medium
- w 1 :
-
Width of the bottom-standing porous structure
- w 2 :
-
Width of the fully-extended porous structure
- γ jn :
-
Wave number in γ-direction
- ε j :
-
The porosity of each layer
- θ :
-
Angle of incidence
- η j :
-
Free surface wave elevation
- ρ :
-
Density of water
- ω :
-
Wave frequency
- φ :
-
Velocity potential
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Acknowledgement
The authors acknowledge Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India for supporting financially under the research Grant No. CRG/2018/004184 and Ministry of Ports, Shipping and Waterways, Government of India through the research Grant No. DW/01013(13)/2/2021.
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Competing interest D. Karmakar is an editorial board member for the Journal of Marine Science and Application and was not involved in the editorial review, or the decision to publish this article. All authors declare that there are no other competing interests.
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Article Highlights
• The hydrodynamic performance of composite breakwater consisting of porous structure and submerged plate is analysed analytically and validated using the experimental investigation.
• The effect of structural and geometrical parameters are analysed for the compsite breakwater system.
• The influence of the wave attenuation charecteristics along with wave force experience on the composite breakwater sustem is analysed.
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Athul Krishna, K.R., Abdulla, K. & Karmakar, D. Wave Energy Damping due to Coupled Porous Structure and Submerged Porous Plate. J. Marine. Sci. Appl. 22, 456–474 (2023). https://doi.org/10.1007/s11804-023-00346-6
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DOI: https://doi.org/10.1007/s11804-023-00346-6