https://orcid.org/0000-0002-7287-4693
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ABSTRACT
The oblique wave scattering by fully-extended two-layered, three-layered and submerged two-layered porous structures occupying finite width is reported using an analytical model based on the eigenfunction expansion method. The fully extended two-layered structure is composed of two porosities and friction factors in the surface porous layer and the bottom porous layer. In addition, the three-layered energy-absorbing structure is composed of two-porous layers along with the bottom rigid layer to replace the natural seabed variation. Further, the study is extended for multiple energy-absorbing structures to report the impact of free spacing available between the two subsequent structures on fluid resonance. The two-layered porous structure dispersion relation is derived and solved using step approach and Newton-Raphson method. The derived analytical results are validated with the published results of notable authors. The effect of the surface and bottom layers porosity, friction factor, free spacing, structural width, number of structures, and angle of contact on the wave scattering is reported. Finally, the comparative study between the single and multiple energy absorbing structures of multiple horizontal layers is discussed. Further, the significance of the critical angle of contact and fluid resonance for better wave blocking is presented precisely, which is essential for the coastal engineers to design offshore structures.
Nomenclature
| aj | = | depth of each porous and rigid layers |
| bN | = | positions of the energy absorbing structure |
| Cf | = | turbulent resistant coefficient |
| dj | = | width of each energy absorbing structure |
| d | = | cumulative structural width |
| fj | = | linearized friction factor in each of the porous layers |
| fjn | = | vertical eigenfunction in each of the regions |
| g | = | acceleration due to gravity |
| hj | = | water depth in each region |
| i | = | imaginary number |
| Kd | = | energy dissipation |
| Kip | = | intrinsic permeability |
| Kr | = | reflection coefficient |
| Kt | = | transmission coefficient |
| kjn | = | wave number in the x-direction |
| l | = | wave number in z-direction |
| M | = | truncated number |
| N | = | number of energy absorbing structures |
| = | instantaneous Eulerian velocity vector | |
| R10 | = | complex amplitude of the reflected wave |
| sj | = | inertial force in each of the porous layer |
| T30 | = | complex amplitude of the transmitted wave |
| t | = | time |
| ζj | = | free surface wave elevation |
| ρ | = | density of water |
| ω | = | wave frequency |
| λ | = | wavelength |
| ϕ | = | velocity potential |
| δmn | = | Kronecker delta |
| θ | = | angle of contact |
| γjn | = | wave number in y-direction |
| εj | = | porosity in each of the porous layer |
| = | kinematic viscosity |
Acknowledgments
The authors are grateful to the Ministry of Human Resources Development (MHRD) Government of India and the National Institute of Technology Karnataka Surathkal for providing necessary facilities for pursuing the research work. DK acknowledges Science and Engineering Research Board (SERB), India through research grant CRG/2018/004184.
Disclosure statement
No potential conflict of interest was reported by the authors.