NadhiraKarimaaIkhaMagdalenaabIndrianaMarcelaaMohammadFaridbaFaculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 40132, IndonesiabCenter for Coastal and Marine Development, Bandung Institute of Technology, Indonesia
Highlights
•A new three-layer model for n-block submerged porous breakwaters is developed.
•New analytical approach in finding the wave transmission coefficient is presented.
•A finite volume method successfully simulates the wave attenuation process.
•Porous media blocks characteristics and configuration can optimize wave reduction.
Abstract
높은 파도 진폭은 해안선에 위험한 영향을 미치고 해안 복원력을 약화시킬 수 있습니다. 그러나 다중 다공성 매체는 해양 생태계의 환경 친화적인 해안 보호 역할을 할 수 있습니다.
이 논문에서 우리는 n개의 잠긴 다공성 미디어 블록이 있는 영역에서 파동 진폭 감소를 계산하기 위해 3층 깊이 통합 방정식을 사용합니다. 수학적 모델은 파동 전달 계수를 얻기 위해 여러 행렬 방정식을 포함하는 변수 분리 방법을 사용하여 해석적으로 해결됩니다.
이 계수는 진폭 감소의 크기에 대한 정보를 제공합니다. 또한 모델을 수치적으로 풀기 위해 지그재그 유한 체적 방법이 적용됩니다.
수치 시뮬레이션을 통해 다공성 매질 블록의 구성과 특성이 투과파 진폭을 줄이는 데 중요하다는 결론을 내렸습니다.
High wave amplitudes may cause dangerous effects on the shoreline and weaken coastal resilience. However, multiple porous media can act as environmental friendly coastal protectors of the marine ecosystem. In this paper, we use three-layer depth-integrated equations to calculate wave amplitude reduction in a domain with n submerged porous media blocks. The mathematical model is solved analytically using the separation of variables method involving several matrix equations to obtain the wave transmission coefficient. This coefficient provides information about the magnitude of amplitude reduction. Additionally, a staggered finite volume method is applied to solve the model numerically. By conducting numerical simulations, we conclude that porous media blocks’ configuration and characteristics are crucial in reducing transmitted wave amplitude.
Keywords
Three-layer equations, Submerged porous media, Wave transmission coefficient, Finite volume method
References
[1]M. Beck, G. Lange, Managing Coasts with Natural Solutions: Guidelines for Measuring and Valuing the Coastal Protection Services of Mangroves and Coral Reefs.
Y. Zhao, Y. Liu, H. Li, A. Chang
Oblique wave motion over multiple submerged porous bars near a vertical wall
J. Ocean Univ. China, 16 (2017), pp. 568-574, 10.1007/s11802-017-3333-5 View PDF
View Record in ScopusGoogle Scholar[3]C. K. Sollitt, R. H. Cross, Wave transmission through permeable breakwaters, Coast. Eng..
Google Scholar[4]J.-F. Lee, L.-F. Tu, C.-C. Liu, Nonlinear wave evolution above rectangular submerged structures, J. Mar. Sci. Technol. 22. doi:10.6119/JMST-013-0503-3.
Y.T. Wu, C.L. Yeh, S.-C. Hsiao
Three-dimensional numerical simulation on the interaction of solitary waves and porous breakwaters
Coast. Eng., 85 (2014), pp. 12-29
ArticleDownload PDFView Record in ScopusGoogle Scholar[6]
Y. feng Xu, X. he Xia, J. hua Wang, J. jian Chen
Numerical analysis on cnoidal wave induced response of porous seabed with definite thickness
J. Shanghai Jiao Tong Univ. (Sci.), 18 (2013), pp. 650-654, 10.1007/s12204-013-1446-6 View PDF
D.M. Pérez-Romero, M. Ortega-Sánchez, A. Moñino, M.A. Losada
Characteristic friction coefficient and scale effects in oscillatory porous flow
Coast. Eng., 56 (9) (2009), pp. 931-939, 10.1016/j.coastaleng.2009.05.002
ArticleDownload PDFView Record in ScopusGoogle Scholar[8]
A. Torres-Freyermuth, M. Brocchini, S. Corvaro, J.C. Pintado-Patiño
Wave attenuation over porous seabeds: a numerical study
Ocean Model., 117 (2017), pp. 28-40, 10.1016/j.ocemod.2017.07.004
ArticleDownload PDFView Record in ScopusGoogle Scholar[9]F. Hajivalie, S. M. Mahmoudof, Experimental study of energy dissipation at rectangular submerged breakwater, Proceedings of the 8th International Conference on Fluid Mechanics.
Google Scholar[10]G. T. Klonaris, A. S. Metallinos, C. D. Memos, K. A. Galani, Experimental and numerical investigation of bed morphology in the lee of porous submerged breakwaters, Coast. Eng. 155.
A. Kubowicz-Grajewska
Experimental investigation into wave interaction with a rubble-mound submerged breakwater (case study)
J. Mar. Sci. Technol., 22 (2) (2017), pp. 313-326 View PDF
CrossRefView Record in ScopusGoogle Scholar[12]
S.M. Mahmoudof, F. Hajivalie
Experimental study of hydraulic response of smooth submerged breakwaters to irregular waves
Oceanologia, 63 (4) (2021), pp. 448-462
ArticleDownload PDFView Record in ScopusGoogle Scholar[13]
C. Tsai, H. Chen, F. Lee
Wave transformation over submerged permeable breakwater on porous bottom
Ocean Eng., 33 (2006), pp. 1623-1643, 10.1016/j.oceaneng.2005.09.006
ArticleDownload PDFView Record in ScopusGoogle Scholar[14]
S. Rojanakamthorn, M. Isobe, A. Watanabe
A mathematical model of wave transformation over a submerged breakwater
Coastal Engineering in Japan, 31 (1989), pp. 209-234, 10.1080/05785634.1989.11924515 View PDF
View Record in ScopusGoogle Scholar[15]
Q. Lin, Q.r. Meng, D.q. Lu
Waves propagating over a two-layer porous barrier on a seabed
J. Hydrodyn., 30 (3) (2018), pp. 453-462 View PDF
CrossRefView Record in ScopusGoogle Scholar[16]X. Yu, A. T. Chwang, Wave motion through porous structures, J. Eng. Mech. 120. doi:10.1061/(ASCE)0733-9399(1994)120:5(989).
K.G. Vijay, V. Venkateswarlu, D. Karmakar
Scattering of gravity waves by multiple submerged rubble-mound breakwaters
Arabian J. Sci. Eng., 45 (10) (2020), pp. 8529-8550 View PDF
CrossRefView Record in ScopusGoogle Scholar[18]
I. Magdalena, G. Jonathan
Water waves resonance and its interaction with submerged breakwater
Results in Engineering, 13 (2022), Article 100343, 10.1016/j.rineng.2022.100343
ArticleDownload PDFView Record in ScopusGoogle Scholar[19]
I. Magdalena, K. Firdaus, D. Jayadi
Analytical and numerical studies for wave generated by submarine landslide
Alex. Eng. J., 61 (9) (2022), pp. 7303-7313, 10.1016/j.aej.2021.12.069
ArticleDownload PDFView Record in ScopusGoogle Scholar[20]
L. Arpaia, M. Ricchiuto, A.G. Filippini, R. Pedreros
An efficient covariant frame for the spherical shallow water equations: well balanced dg approximation and application to tsunami and storm surge
Ocean Model., 169 (2022), Article 101915, 10.1016/j.ocemod.2021.101915
ArticleDownload PDFView Record in ScopusGoogle Scholar[21]
M. Briani, G. Puppo, M. Ribot
Angle dependence in coupling conditions for shallow water equations at channel junctions
Comput. Math. Appl., 108 (2022), pp. 49-65, 10.1016/j.camwa.2021.12.021
ArticleDownload PDFView Record in ScopusGoogle Scholar[22]
I. Magdalena, G.R. Andadari, D.E. Reeve
An integrated study of wave attenuation by vegetation
Wave Motion, 110 (2022), Article 102878, 10.1016/j.wavemoti.2021.102878
ArticleDownload PDFView Record in ScopusGoogle Scholar[23]
I. Magdalena, R. La’lang, R. Mendoza
Quantification of wave attenuation in mangroves in manila bay using nonlinear shallow water equations
Results in Applied Mathematics, 12 (2021), Article 100191, 10.1016/j.rinam.2021.100191
ArticleDownload PDFView Record in ScopusGoogle Scholar[24]
K.T. Mandli
A numerical method for the two layer shallow water equations with dry states
Ocean Model., 72 (2013), pp. 80-91, 10.1016/j.ocemod.2013.08.001
ArticleDownload PDFView Record in ScopusGoogle Scholar[25]
M. Farhan, Z. Omar, F. Mebarek-Oudina, J. Raza, Z. Shah, R.V. Choudhari, O.D. Makinde
Implementation of the one-step one-hybrid block method on the nonlinear equation of a circular sector oscillator
Comput. Math. Model., 31 (2020), pp. 116-132, 10.1007/s10598-020-09480-0 View PDF
View Record in ScopusGoogle Scholar[26]
R. Djebali, F. Mebarek-Oudina, C. Rajashekhar
Similarity solution analysis of dynamic and thermal boundary layers: further formulation along a vertical flat plate
Phys. Scripta, 96 (8) (2021), Article 085206, 10.1088/1402-4896/abfe31 View PDF
View Record in ScopusGoogle Scholar[27]
M. Alkasassbeh, O. Zurni, F. Mebarek-Oudina, J. Raza
Heat transfer study of convective fin with temperature,Äêdependent internal heat generation by hybrid block method
Heat Tran. Asian Res., 48 (2019), pp. 1225-1244, 10.1002/htj.21428 View PDF
View Record in ScopusGoogle Scholar[28]
I. Magdalena, M.F. Eka Pebriansyah
Numerical treatment of finite difference method for solving dam break model on a wet-dry bed with an obstacle
Results in Engineering, 14 (2022), Article 100382, 10.1016/j.rineng.2022.100382
ArticleDownload PDFView Record in ScopusGoogle Scholar[29]
M. Uddin, S. Rasel, J.K. Adewole, K.S. Al Kalbani
Finite element simulation on the convective double diffusive water-based copper oxide nanofluid flow in a square cavity having vertical wavy surfaces in presence of hydro-magnetic field
Results in Engineering, 13 (2022), Article 100364, 10.1016/j.rineng.2022.100364
ArticleDownload PDFView Record in ScopusGoogle Scholar[30]
E.H.H. Al-Qadami, A.S. Abdurrasheed, Z. Mustaffa, K.W. Yusof, M. Malek, A.A. Ghani
Numerical modelling of flow characteristics over sharp crested triangular hump
Results in Engineering, 4 (2019), Article 100052, 10.1016/j.rineng.2019.100052
ArticleDownload PDFView Record in ScopusGoogle Scholar[31]
I. Magdalena, V. Kusnowo, M.I. Azis
Widowati, 1d-2d numerical model for wave attenuation by mangroves as a porous structure
Computation, 9 (6) (2021), pp. 1-21
I. Magdalena, M.F. Atras, L. Sembiring, M.A. Nugroho, R.S.B. Labay, M.P. Roque
Wave transmission by rectangular submerged breakwaters
Computation, 8 (2) (2020), pp. 1-18 View PDF
View Record in ScopusGoogle Scholar[33]
I. Magdalena, S.R. Pudjaprasetya
Numerical modeling for gravity waves over submerged porous media
Australian Journal of Basic and Applied Sciences, 9 (28) (2015), pp. 124-130
View Record in ScopusGoogle Scholar[34]
I. Magdalena, A. Hariz, M. Farid, M.S.B. Kusuma
Numerical studies using staggered finite volume for dam break flow with an obstacle through different geometries
Results in Applied Mathematics, 12 (2021), Article 100193, 10.1016/j.rinam.2021.100193
ArticleDownload PDFView Record in ScopusGoogle Scholar[35]
R. Walters, E. Hanert, J. Pietrzak, D. Le Roux
Comparison of unstructured, staggered grid methods for the shallow water equations
Ocean Model., 28 (1) (2009), pp. 106-117, 10.1016/j.ocemod.2008.12.004
the Sixth International Workshop on Unstructured Mesh Numerical Modelling of Coastal, Shelf and Ocean Flows
ArticleDownload PDFView Record in ScopusGoogle Scholar[36]
F. Mebarek-Oudina
Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths, Engineering Science and Technology
Int. J., 20 (4) (2017), pp. 1324-1333, 10.1016/j.jestch.2017.08.003
ArticleDownload PDFView Record in ScopusGoogle Scholar[37]
S. Pudjaprasetya, I. Magdalena
Numerical modeling for gravity waves over submerged porous media
Australian Journal of Basic and Applied Sciences, 9 (2015), pp. 124-130