隨著暴潮和降雨強度的增加，在人口稠密的沿海地區面臨災害的風險增加。潛沒式防波堤是一種消散波浪能量並反射入射波的海岸防護方法，在環境保護與經濟成本之間有較好的平衡。隨著氣候變遷及大眾對於生態環境的重視，傳統剛性結構物的防護方法逐漸改變。

因此，本研究旨在瞭解潛沒式彈性平板對長波的影響。首先進行了二維實驗，考慮三種不同材質與兩種不同厚度的平板。使用質點影像測速儀測量自由液面、平板運動、速度場和紊流場，受力的時序列由荷重元量測。由重複相同條件實驗數次以得到平均場及紊流的擾動場。由波高計電壓訊號觸發高速攝影機以及與荷重元同步收錄，得到時間序列的比較。不同材料之間，探討不同勁度的材質在核心區的速度與紊流差異，並分析渦流形狀與渦流中心位置受平板運動影響。實驗上，最大受力時刻早於最大波高通過平板的時刻，最後為平板最大位移的時刻。由實驗亦可見，最大受力隨波浪尖銳度的改變呈線性分布。

此外，本研究亦使用OpenFOAM模擬以了解更詳細的流場，流固耦合求解器為solids4Foam，並搭配stabilized k-ω SST紊流模式求解雷諾應力及幾何流體體積法(isoAdvector)建立自由液面。將實驗與數值驗證，確認模式的適用性，進一步延伸探討不同板高、板寬、楊氏模量與波浪條件的影響。由數值模擬與樑的理論探討各變量對位移的影響。加長板高、減小板寬或減小楊氏模量導致位移增加，其中又以增加長度的影響最大。以樑的理論估計值的75%可與模擬結果相符。

Densely-populated coastal areas are exposed to higher flood risk more than ever before due to increasing storm surge and rainfall intensity. Submerged breakwater is the coastal protection method to dissipate wave energy and reflect the incident waves, which achieves a good balance between environmental protection and economic cost. Traditional methods of rigidly fixed structural protection have evolved in response to climate change and public awareness of the environment.

Therefore, this study aimed to understand the effect of flexibility of a submerged vertical plate on the propagation of long waves. For this purpose, two-dimensional experiments were carried out varying plates with three different elasticity and two different thickness. Free surface elevation, elastic plate motion, velocity field, and turbulence field were measured using the particle image velocimetry (PIV) technique. The wave load on the plate was measured by load cells. The averaged field and fluctuating field were obtained by repeating the same experiment several times. The high-speed camera was triggered by the wave gauge voltage signal, which was recorded synchronously with the load cells. As a result, time series comparisons could be obtained. We first illustrated the evolution of the flow fields. Furthermore, a comparison of different materials was performed, revealing differences in velocity magnitude and turbulence intensity for plates of different stiffnesses. In addition, the shape of the vortex and the position of the vortex center affected by plate motion were investigated. By comparing the time histories of surface elevation, the x direction displacement at the upper-left corner of the plate, and the acting force on the plate, it was found that the maximum force occurred first, and the maximum deformation of the plate occurred last. It was also seen that the force varied linearly with the wave nonlinearity for different elastic plates.

In order to understand the flow field in more detail, the FSI solver in OpenFOAM, solids4Foam was used with stabilized k-ω SST turbulence model to solve for Reynolds stresses and a geometric volume of fluid method (isoAdvector) to reconstruct the free surface. After the validation by the experimental data, the effect of different plate heights, plate thicknesses and Young’s Modulus were be investigated by numerical simulations. The displacement was also estimated by Euler-Bernoulli beam theory. Referring to the theory, lengthening the plate height, reducing the plate thicknesses, or reducing Young’s modulus resulted in an increase in displacement. Among them, lengthening the plate height has the greatest impact. According to the results, the simulated results correspond to 75% of the theoretically estimated displacement of the plate.

Antoci, C., Gallati, M., Sibilla, S., 2007. Numerical simulation of fluid–structure interaction by sph. Computers & structures, 85(11-14): 879-890.
Aristodemo, F., Tripepi, G., Ferraro, D.A., Veltri, P., 2020. An experimental and numerical study on solitary wave loads at cylinders near the bed. Ocean Engineering, 195: 106747.
Aristodemo, F., Tripepi, G., Gurnari, L., Filianoti, P., 2021. Determination of force coefficients for a submerged rigid breakwater under the action of solitary waves. Water, 13(3): 315.
Aristodemo, F., Tripepi, G., Meringolo, D.D., Veltri, P., 2017. Solitary wave-induced forces on horizontal circular cylinders: Laboratory experiments and sph simulations. Coastal Engineering, 129: 17-35.
Bi, C., Wu, M.S., Law, A.W.-K., 2022. Surface wave interaction with a vertical viscoelastic barrier. Applied Ocean Research, 120: 103073.
Boussinesq, J., 1871. Theory of the liquid intumescence, called a solitary wave or a wave of translation, propagated in a channel of rectangular cross section. CR Acad. Sci., Paris, 72: 755-759.
Brown, S., Xie, N., Hann, M., Greaves, D., 2022. Investigation of wave-driven hydroelastic interactions using numerical and physical modelling approaches. Applied Ocean Research, 129: 103363.
Cáceres-Euse, A., Orfila, A., Hernández-Carrasco, I., Wyssmann, M.A., Osorio, A.F., Toro-Botero, F., 2022. Backwards wave breaking by flow separation vortices under solitary waves. Journal of Fluids and Structures, 115: 103779.
Cardiff, P., Karač, A., De Jaeger, P., Jasak, H., Nagy, J., Ivanković, A., Tuković, Ž., 2018. An open-source finite volume toolbox for solid mechanics and fluid-solid interaction simulations. arXiv preprint arXiv:1808.10736.
Chang, C.-H., Lin, C., Wang, K.-H., Jaf, J.M., 2018. Numerical simulations and experimental visualizations of the vortex characteristics for a solitary wave interacting with a bottom-mounted vertical plate. Journal of Hydro-environment Research, 19: 88-102.
Chang, C.W., Mori, N., Tsuruta, N., Suzuki, K., Yanagisawa, H., 2022. An experimental study of mangrove‐induced resistance on water waves considering the impacts of typical rhizophora roots. Journal of Geophysical Research: Oceans: e2022JC018653.
Chang, K.-A., Hsu, T.-J., Liu, P.L.-F., 2001. Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part i. Solitary waves. Coastal Engineering, 44(1): 13-36.
Chang, K.-A., Liu, P.L.-F., 1999. Experimental investigation of turbulence generated by breaking waves in water of intermediate depth. Physics of Fluids, 11(11): 3390-3400.
Chuang, W.-L., Chang, K.-A., Kaihatu, J., Cienfuegos, R., Mokrani, C., 2020. Experimental study of force, pressure, and fluid velocity on a simplified coastal building under tsunami bore impact. Natural Hazards, 103(1): 1093-1120.
Cooker, M., Peregrine, D., Vidal, C., Dold, J., 1990. The interaction between a solitary wave and a submerged semicircular cylinder. Journal of Fluid Mechanics, 215: 1-22.
Devolder, B., Rauwoens, P., Troch, P., 2017. Application of a buoyancy-modified k-ω sst turbulence model to simulate wave run-up around a monopile subjected to regular waves using openfoam®. Coastal Engineering, 125: 81-94.
Diamantoulaki, I., Angelides, D.C., Manolis, G.D., 2008. Performance of pile-restrained flexible floating breakwaters. Applied Ocean Research, 30(4): 243-255.
Durbin, P., 2009. Limiters and wall treatments in applied turbulence modeling. Fluid Dynamics Research, 41(1): 012203.
Elhanafi, A., Fleming, A., Macfarlane, G., Leong, Z., 2016. Numerical energy balance analysis for an onshore oscillating water column–wave energy converter. Energy, 116: 539-557.
ESIGroup, 2007. Guidelines for specification of turbulence at inflow boundaries. ESI Group CFD Customer Portal.
Fenton, J., 1972. A ninth-order solution for the solitary wave. Journal of fluid mechanics, 53(2): 257-271.
Gautam, P., Eldho, T., Mazumder, B., Behera, M., 2019. Experimental study of flow and turbulence characteristics around simple and complex piers using piv. Experimental Thermal and Fluid Science, 100: 193-206.
Goring, D.G., 1978. Tsunamis--the propagation of long waves onto a shelf.
Griggs, G., 2021. Rising seas in california—an update on sea-level rise science, World scientific encyclopedia of climate change: Case studies of climate risk, action, and opportunity volume 3. World Scientific, pp. 105-111.
Habchi, C., Russeil, S., Bougeard, D., Harion, J.-L., Lemenand, T., Ghanem, A., Della Valle, D., Peerhossaini, H., 2013. Partitioned solver for strongly coupled fluid–structure interaction. Computers & Fluids, 71: 306-319.
Higuera, P., Lara, J.L., Losada, I.J., 2013. Realistic wave generation and active wave absorption for navier–stokes models: Application to openfoam®. Coastal Engineering, 71: 102-118.
Hou, G., Wang, J., Layton, A., 2012. Numerical methods for fluid-structure interaction—a review. Communications in Computational Physics, 12(2): 337-377.
Hsiao, S.-C., Chiang, W.-S., Jang, J.-H., Wu, H.-L., Lu, W.-S., Chen, W.-B., Wu, Y.-T., 2021. Flood risk influenced by the compound effect of storm surge and rainfall under climate change for low-lying coastal areas. Science of the total environment, 764: 144439.
Hsiao, Y., Hsiao, S.-C., 2022. Experimental study on the interaction of solitary wave with elastic submerged plate. Ocean Engineering, 261: 112106.
Hsiao, Y., Tsai, C.-L., Chen, Y.-L., Wu, H.-L., Hsiao, S.-C., 2020. Simulation of wave-current interaction with a sinusoidal bottom using openfoam. Applied Ocean Research, 94: 101998.
Hu, Z., Huang, L., Li, Y., 2022. Fully-coupled hydroelastic modelling of a deformable wall in waves. Coastal Engineering: 104245.
Hu, Z., Suzuki, T., Zitman, T., Uittewaal, W., Stive, M., 2014. Laboratory study on wave dissipation by vegetation in combined current–wave flow. Coastal Engineering, 88: 131-142.
Huang, L., Li, Y., Benites-Munoz, D., Windt, C.W., Feichtner, A., Tavakoli, S., Davidson, J., Paredes, R., Quintuna, T., Ransley, E., 2022. A review on the modelling of wave-structure interactions based on openfoam. OpenFOAM® Journal, 2: 116-142.
Huang, L., Ren, K., Li, M., Tuković, Ž., Cardiff, P., Thomas, G., 2019. Fluid-structure interaction of a large ice sheet in waves. Ocean Engineering, 182: 102-111.
Huang, Z.-C., Hsiao, S.-C., Hwung, H.-H., Chang, K.-A., 2009. Turbulence and energy dissipations of surf-zone spilling breakers. Coastal Engineering, 56(7): 733-746.
Idelsohn, S., Marti, J., Souto-Iglesias, A., Oñate, E., 2008. Interaction between an elastic structure and free-surface flows: Experimental versus numerical comparisons using the pfem. Computational Mechanics, 43(1): 125-132.
Jasak, H., Weller, H., 2000. Application of the finite volume method and unstructured meshes to linear elasticity. International journal for numerical methods in engineering, 48(2): 267-287.
Kalitzin, G., Medic, G., Iaccarino, G., Durbin, P., 2005. Near-wall behavior of rans turbulence models and implications for wall functions. Journal of Computational Physics, 204(1): 265-291.
Kim, H., Park, S., 2021. Coupled level-set and volume of fluid (clsvof) solver for air lubrication method of a flat plate. Journal of Marine Science and Engineering, 9(02): 231.
Kirwan, M.L., Megonigal, J.P., 2013. Tidal wetland stability in the face of human impacts and sea-level rise. Nature, 504(7478): 53-60.
Larsen, B.E., Fuhrman, D.R., 2018. On the over-production of turbulence beneath surface waves in reynolds-averaged navier–stokes models. Journal of Fluid Mechanics, 853: 419-460.
Launder, B.E., Sharma, B.I., 1974. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in heat and mass transfer, 1(2): 131-137.
Lee, J.-F., Chen, C.-J., 1990. Wave interaction with hinged flexible breakwater. Journal of Hydraulic Research, 28(3): 283-297.
Liao, K., Hu, C., Sueyoshi, M., 2015. Free surface flow impacting on an elastic structure: Experiment versus numerical simulation. Applied Ocean Research, 50: 192-208.
Lin, C., Kao, M.-J., Yang, J., Raikar, R.V., Yuan, J.-M., Hsieh, S.-C., 2020. Particle acceleration and pressure gradient in a solitary wave traveling over a horizontal bed. AIP Advances, 10(11): 115210.
Lin, C., Yeh, P.-H., Kao, M.-J., Yu, M.-H., Hsieh, S.-C., Chang, S.-C., Wu, T.-R., Tsai, C.-P., 2015. Velocity fields in near-bottom and boundary layer flows in prebreaking zone of a solitary wave propagating over a 1: 10 slope. Journal of Waterway, Port, Coastal, and Ocean Engineering, 141(3): 04014038.
Lin, P., 2004. A numerical study of solitary wave interaction with rectangular obstacles. Coastal Engineering, 51(1): 35-51.
Lin, P., Liu, P.L.-F., 1998. A numerical study of breaking waves in the surf zone. Journal of fluid mechanics, 359: 239-264.
Liu, P.-F., Simarro, G., Vandever, J., Orfila, A., 2006. Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank. Coastal Engineering, 53(2-3): 181-190.
Liu, P.L.-F., Al-Banaa, K., 2004. Solitary wave runup and force on a vertical barrier. Journal of Fluid Mechanics, 505: 225-233.
Liu, P.L., Abbaspour, M., 1982. Wave scattering by a rigid thin barrier. Journal of the Waterway, Port, Coastal and Ocean Division, 108(4): 479-491.
Maza, M., Lara, J.L., Losada, I.J., 2015. Tsunami wave interaction with mangrove forests: A 3-d numerical approach. Coastal Engineering, 98: 33-54.
Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA journal, 32(8): 1598-1605.
Mori, N., Chang, K.-A., 2003. Introduction to mpiv. user reference manual, 14.
Ng, K., Alexiadis, A., Chen, H., Sheu, T., 2020. A coupled smoothed particle hydrodynamics-volume compensated particle method (sph-vcpm) for fluid structure interaction (fsi) modelling. Ocean Engineering, 218: 107923.
Persoons, T., O’Donovan, T.S., 2011. High dynamic velocity range particle image velocimetry using multiple pulse separation imaging. Sensors, 11(1): 1-18.
Piña, J.S., Godino, D., Corzo, S., Ramajo, D., 2022. Air injection in vertical water column: Experimental test and numerical simulation using volume of fluid and two-fluid methods. Chemical Engineering Science, 255: 117665.
Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T., Kompenhans, J., 2018. Particle image velocimetry: A practical guide. Springer.
Roenby, J., Bredmose, H., Jasak, H., 2016. A computational method for sharp interface advection. Royal Society open science, 3(11): 160405.
Rusche, H., 2003. Computational fluid dynamics of dispersed two-phase flows at high phase fractions, Imperial College London (University of London).
Sarno, L., Tai, Y.-C., Carravetta, A., Martino, R., Papa, M.N., Kuo, C.-Y., 2019. Challenges and improvements in applying a particle image velocimetry (piv) approach to granular flows. Journal of Physics: Conference Series, p.^pp. 012011.
Seiffert, B., Hayatdavoodi, M., Ertekin, R.C., 2014. Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part i: Flat plate. Coastal Engineering, 88: 194-209.
Sigren, J.M., Figlus, J., Highfield, W., Feagin, R.A., Armitage, A.R., 2018. The effects of coastal dune volume and vegetation on storm-induced property damage: Analysis from hurricane ike. Journal of Coastal Research, 34(1): 164-173.
Spalding, D., 1961. A single formula for the law of the wall. Journal of Applied Mechanics, 28(3): 455-458.
Sree, D.K., Mandal, S., Law, A.W.-K., 2021. Surface wave interactions with submerged horizontal viscoelastic sheets. Applied Ocean Research, 107: 102483.
Strusinska-Correia, A., Oumeraci, H., 2012. Nonlinear behaviour of tsunami-like solitary wave over submerged impermeable structures of finite width. Coastal engineering proceedings(33): 6-6.
Thielicke, W., Stamhuis, E., 2014. Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. Journal of open research software, 2(1).
Tomasicchio, U., 1996. Submerged breakwaters for the defence of the shoreline at ostia field experiences, comparison, Coastal engineering 1996, pp. 2404-2417.
Tripepi, G., Aristodemo, F., Meringolo, D.D., Gurnari, L., Filianoti, P., 2020. Hydrodynamic forces induced by a solitary wave interacting with a submerged square barrier: Physical tests and δ-les-sph simulations. Coastal Engineering, 158: 103690.
Tukovic, Z., Cardiff, P., Karac, A., Jasak, H., Ivankovic, A., 2014. Openfoam library for fluid structure interaction. 9th openfoam workshop, p.^pp.
Ursell, F., 1947. The effect of a fixed vertical barrier on surface waves in deep water. Mathematical Proceedings of the Cambridge Philosophical Society, p.^pp. 374-382.
van Veelen, T.J., Fairchild, T.P., Reeve, D.E., Karunarathna, H., 2020. Experimental study on vegetation flexibility as control parameter for wave damping and velocity structure. Coastal Engineering, 157: 103648.
Wang, J., He, G., You, R., Liu, P., 2018. Numerical study on interaction of a solitary wave with the submerged obstacle. Ocean engineering, 158: 1-14.
Wang, Y., Liu, P.L.-F., 2022. On finite amplitude solitary waves—a review and new experimental data. Physics of Fluids, 34(10): 101304.
Wiegel, R.L., 1960. Transmission of waves past a rigid vertical thin barrier. Journal of the Waterways and harbors division, 86(1): 1-12.
Wilcox, D.C., 1988. Reassessment of the scale-determining equation for advanced turbulence models. AIAA journal, 26(11): 1299-1310.
Wu, N.-J., Hsiao, S.-C., Chen, H.-H., Yang, R.-Y., 2016. The study on solitary waves generated by a piston-type wave maker. Ocean Engineering, 117: 114-129.
Wu, Y.-T., Hsiao, S.-C., Huang, Z.-C., Hwang, K.-S., 2012. Propagation of solitary waves over a bottom-mounted barrier. Coastal Engineering, 62: 31-47.
Wüthrich, D., Pfister, M., Nistor, I., Schleiss, A.J., 2018. Experimental study on the hydrodynamic impact of tsunami-like waves against impervious free-standing buildings. Coastal Engineering Journal, 60(2): 180-199.
Yilmaz, A., Kocaman, S., Demirci, M., 2021. Numerical modeling of the dam-break wave impact on elastic sluice gate: A new benchmark case for hydroelasticity problems. Ocean Engineering, 231: 108870.
Zeng, Q., Cai, J., Yin, H., Yang, X., Watanabe, T., 2015. Numerical simulation of single bubble condensation in subcooled flow using openfoam. Progress in Nuclear Energy, 83: 336-346.
Zhu, D., Dong, Y., 2020. Experimental and 3d numerical investigation of solitary wave forces on coastal bridges. Ocean Engineering, 209: 107499.