Wave Attenuation due to Stratified Porous Structure with Stepped Seabed

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.

Keywords

Stratified porous structure / Surface-piercing / Porous block / Stepped seabed / Eigenfunction expansion method / Wave force

References

[1] Ashok R, Manam SR. Oblique wave scattering problems involving vertical porous membranes. Journal of Marine Science and Application, 2022, 21: 51-66

[2] Behera H, Ghosh S. Oblique wave trapping by a surface-piercing flexible porous barrier in the presence of step-type bottoms. Journal of Marine Science and Application, 2019, 18: 433-443

[3] Dalrymple RA, Losada MA, Martin PA. Reflection and transmission from porous structures under oblique wave attack. Journal of Fluid Mechanics, 1991, 224: 625-644

[4] Dattatri J, Raman H, Shankar NJ (1978) Performance characteristics of submerged breakwaters. In Coastal Engineering Proceedings, Hamburg, 2153–2171. https://doi.org/10.9753/icce.v16.130

[5] Das S, Bora SN. Reflection of oblique ocean water waves by a vertical rectangular porous structure placed on an elevated horizontal bottom. Ocean Engineering, 2014, 82: 135-143

[6] Hu J, Zhao Y, Liu PLF. A model for obliquely incident wave interacting with a multi-layered object. Applied Ocean Research, 2019, 87: 211-222

[7] Karmakar D, Guedes Soares C. Wave transformation due to multiple bottom-standing porous barriers. Ocean Engineering, 2014, 80: 50-63

[8] Koley S, Behera H, Sahoo T. Oblique wave trapping by porous structures near a wall. Journal of Engineering Mechanics, 2015, 141(3): 04014122

[9] Koley S, Sahoo T. Oblique wave trapping by vertical permeable membrane barriers located near a wall. Journal of Marine Science and Application, 2017, 16: 490-501

[10] Kondo H, Toma S. Reflection and transmission for a porous structure. Coastal Engineering Proceedings, 1972, 1(13): 1847-1866

[11] Liu Y, Li H. Wave reflection and transmission by porous breakwaters: A new analytical solution. Coastal Engineering, 2013, 78: 46-52

[12] Liu Y, Li Y, Teng B. Wave interaction with a new type perforated breakwater. Acta Mech Sin, 2007, 23(4): 351-358

[13] Madsen PA. Wave reflection from a vertical permeable wave absorber. Coastal Engineering, 1983, 7(4): 381-396

[14] Mallayachari V, Sundar V. Reflection characteristics of permeable seawalls. Coastal Engineering, 1994, 23(1–2): 135-150

[15] Mendez FJ, Losada IJ. A perturbation method to solve dispersion equations for water waves over dissipative media. Coastal Engineering, 2004, 51(1): 81-89

[16] Sahoo T, Lee MM, Chwang AT. Trapping and generation of waves by vertical porous structures. Journal of Engineering Mechanics, 2000, 126: 1074-1082

[17] Sollitt CK, Cross RH (1972) Wave transmission through permeable breakwaters. In Coastal Engineering, 1827–1846. https://doi.org/10.9753/icce.v13.99

[18] Somervell LT, Thampi SG, Shashikala AP. A novel approach for the optimal design of a vertical cellular breakwater based on multi-objective optimization. Coastal Engineering Journal, 2017, 59(4): 1750019

[19] Sulisz W. Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coastal Engineering, 1985, 9(4): 371-386

[20] Tabssum S, Kaligatla RB, Sahoo T. Gravity wave interaction with a porous breakwater in a two-layer ocean of varying depth. Ocean Engineering, 2020, 196: 106816

[21] Twu SW, Chieu CC. A highly wave dissipation offshore breakwater. Ocean Engineering, 2000, 27(3): 315-330

[22] Twu SW, Lin DT (1990) Wave reflection by a number of thin porous plates fixed in a semi-infinitely long flume. In Coastal Engineering Proceedings, Delft, 1046–1059. https://doi.org/10.1061/9780872627765.081

[23] Twu SW, Liu CC, Twu CW. Wave damping characteristics of vertically stratified porous structures under oblique wave action. Ocean Engineering, 2002, 29(11): 1295-1311

[24] Venkateswarlu V, Praveen KM, Karmakar D. Surface gravity wave scattering by multiple energy absorbing structures of variable horizontal porosity. Coastal Engineering Journal, 2020, 62(4): 504-526

[25] Venkateswarlu V, Karmakar D. Significance of seabed characteristics on wave transformation in the presence of stratified porous block. Coastal Engineering Journal, 2020, 62(1): 1-22

[26] Venkateswarlu V, Karmakar D. Wave motion over stratified porous absorber combined with seaward vertical barrier. Proceedings of the Institution of Mechanical Engineers, Part M. Journal of Engineering for the Maritime Environment, 2020, 234(4): 830-845

[27] Yu X, Chwang AT. Wave motion through porous structures. Journal of Engineering Mechanics, 1994, 120(5): 989-1008

[28] Zhu S, Chwang AT. Analytical study of porous wave absorber. Journal of Engineering Mechanics, 2001, 127(4): 326-332