Abstract
The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory. The study is performed to analyse the effectiveness of partial porous structure in increasing the wave attenuation in the nearshore regions consisting of stratified porous structures of different configurations using the eigenfunction expansion method and orthogonal mode-coupling relation. The hydrodynamic characteristics such as wave reflection coefficient, transmission coefficient, dissipation coefficient, wave force impact and surface elevation are investigated due to the presence of both horizontally and vertically stratified porous structures. The effect of varying porosity, structural width, angle of incidence, wavelength and length between the porous block and stratified structure is examined. The numerical results are validated with the results available in the literature. The present study illustrates that the presence of the stratified structure decreases wave transmission and efficient wave attenuation can also be easily achieved. The wave force acting on stratified structure can be decreased if the structure is combined with wider surface-piercing porous blocks. Further, the presence of stratified porous structure combined with porous block helps in creating a tranquil zone in the leeside of the structure. The combination of vertical and horizontal stratified porous structure with surface-piercing porous block is intended to be an effective solution for the protection of coastal facilities.
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Abbreviations
- C m :
-
Added mass coefficient
- C f :
-
Turbulent resistant coefficient
- ε 2 :
-
Porosity of the surface piercing porous block
- ε 5 :
-
Porosity of the surface or seaward porous layer
- ε 6 :
-
Porosity of the bottom or leeward porous layer
- f 2 :
-
Frictional coefficient of surface piercing porous block
- f 5 :
-
Frictional coefficient of surface or seaward porous layer
- f 6 :
-
Frictional coefficient of bottom or leeward porous layer
- g :
-
Acceleration due to gravity
- I 10 :
-
Complex amplitude of incident wave energy
- i:
-
Imaginary number
- K d :
-
Energy dissipation coefficient
- K fb1 :
-
Wave force coefficient on front face of porous block
- K fs1 :
-
Wave force coefficient on front face of stratified porous structure
- k jn :
-
Wave number in x–direction
- K r :
-
Reflection coefficient
- K t :
-
Transmission coefficient
- L :
-
Gap between the porous block and stratified porous structure
- l :
-
Wave number in z–direction
- M :
-
Number of evanescent wave modes
- q :
-
Instantaneous Eularian velocity vector
- R 10 :
-
Complex amplitude of reflected wave energy
- S 2 :
-
Reactance coefficient of surface piercing porous block
- S 5 :
-
Reactance coefficient of surface or seaward porous layer
- S 6 :
-
Reactance coefficient of bottom or leeward porous layer
- t :
-
Time
- T :
-
Wave period
- T 90 :
-
Complex amplitude of transmitted wave energy
- V :
-
Volume
- w 1 :
-
Width of the porous block
- w 2 :
-
Width of the stratified porous structure
- ω :
-
Wave frequency
- x :
-
Horizontal distance along x–direction
- y :
-
Vertical distance along y–direction
- γ jn :
-
Wave number in y–direction
- θ :
-
Incident wave angle
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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 stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed using small amplitude wave theory.
• The effect of structural and geometrical parameters due to stepped bottom configuration are analysed for the compsite breakwater system.
• The wave attenuation charecteristics along with wave force experience on the stratified breakwater and porous block due to stepped sea-bed is analysed.
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Varghese, A., Athul Krishna, K.R. & Karmakar, D. Wave Attenuation due to Stratified Porous Structure with Stepped Seabed. J. Marine. Sci. Appl. (2024). https://doi.org/10.1007/s11804-024-00407-4
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DOI: https://doi.org/10.1007/s11804-024-00407-4