跳到主要內容

簡易檢索 / 詳目顯示

研究生: 張明南
Nhat-Minh Truong
論文名稱: 近岸地區受風作用下之捲浪破碎機制研究
An investigation of plunging breakers in the nearshore area under the influence of wind
指導教授: 吳祚任
Tso-Ren Wu
口試委員:
學位類別: 碩士
Master
系所名稱: 地球科學學院 - 水文與海洋科學研究所
Graduate Instittue of Hydrological and Oceanic Sciences
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 187
中文關鍵詞: 卷浪碎波風效應LESVOF
外文關鍵詞: plunging waves, breaking waves, wind effects, LES, VOF
相關次數: 點閱:23下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本研究旨在了解風效應對近岸地區卷浪發展之作用,尤其是衝浪波。這項研究有三種不同風的類型:陸風、海風和無風。本文利用結合大渦模擬 (LES) 之 Navier-Stokes 方程進行流場模擬與分析。流體體積函數 (VOF) 被用於追蹤水與空氣之界面。數值模擬採用內源造波器以生成目標波浪,在邊界上則採用海綿層法吸收反射波。驗證案例為存在和不存在陸風之情況下波浪淺化過程。比對結果可以看出數值模式與實驗波高計時序紀錄有良好之一致性。完成驗證後,進行實驗室尺度和野外尺度之波浪淺化過程模擬,並討論陸風和海風對卷浪發展過程之影響。為了解風力對於波浪上溯中碎波對於底床之影響,本研究添加數值染料以追蹤碎波帶水體運動過程。數值結果顯示,在海風情況下,卷浪破碎點發生較晚,其對海床之衝擊較海風或無風條件下之卷浪碎波機制更強。對於現場尺度模擬部分,本文探討吹程(Fetch)、風速大小和斜坡坡度效應對卷浪破碎過程之影響。數值結果顯示,隨著風速的增加,較長之吹程會影響卷浪破碎點位置以及卷浪波傳播速度。此外,較強之陸風會導致波碎點較早出現,而較強之海風會導致破碎點較晚出現。底床坡度對卷浪點位置有很大影響。陡峭的斜坡使卷浪破碎點位置更靠近海岸線。在上下文中提供詳細之分析和討論。


    This study aims to understand the role of wind effects on the development of plunging waves in the nearshore region especially surfing waves. There are three different types of wind for this study: onshore, offshore, and no wind. In this study, the Navier-Stokes Equation associated with Large Eddy Simulation (LES) is used to simulate and analyze the flow field. The Volume-of-Fluid function (VOF) has been adopted to track the air and water interface. The numerical experiments are deployed and validated with laboratory experiments. The numerical simulations used the internal-source wavemaker and sponge-layer methods to generate the incident waves and absorb the reflected waves on the boundary. The validation cases are the shoaling processes in the absence and presence of onshore wind. The comparison results show that numerical model is good agreement with experimental altimeter time series records. After the verification is completed, the simulation of the wave shallowing process at the laboratory scale and the field scale is carried out, and the influence of the offshore and onshore wind on the wave development is discussed. In order to understand the effect of wind on the near-bed of breaking waves in the up-going wave, numerical dyes were added in this study to track the water movement process in the breaking wave zone. The numerical results show that the breaking points occurred later in the case of offshore wind, and its impact on the seabed is stronger than the breaking wave mechanism of the breaking waves under the sea breeze or no wind conditions. As for the field-scale simulations, this paper discusses the influence of blowing distance (Fetch), wind speed and slope effect on the wave-breaking process. The numerical results show that with the increase of wind speed, the longer blowing distance will affect the position of the breaking point and the propagation speed of the wave. In addition, the stronger onshore wind will cause earlier breaking points, while stronger offshore wind will cause later breaking points. The slope of the bed has a great influence on the position of the breaking point. The steep slope brings the breaking point of the wave closer to the shoreline. A steeper slope made the location of the breaking point closer to the shoreline. Detailed analysis and discussions are presented in the context.

    Table of Contents CHINESE ABSTRACT v ABSTRACT vi ACKNOWLEDGMENTS vii TABLE OF CONTENTS viii LIST OF FIGURES xi LIST OF TABLES xvii CHAPTER 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 LITERATURE REVIEW OF WIND WAVES 4 1.2.1 THEORETICAL ANALYSES OF WIND-WAVES INTERACTION 5 1.2.2 BREAKING WAVES UNDER WIND ACTION 6 1.3 BREAKING WAVES MECHANISMS 10 1.3.1 GEOMETRICAL BREAKING CRITERIA 11 1.3.2 EXPERIMENTAL STUDIES 13 1.3.3 NUMERICAL STUDIES 16 CHAPTER 2 EQUATION AND ALGORITHM 22 2.1 NAVIER-STOKES EQUATION 22 2.2 TURBULENCE MODELLING 23 2.3 LARGE-EDDY SIMULATION (LES) 25 2.3.1 SPATIAL-FILTERING OPERATION 25 2.3.2 LES GOVERNING EQUATION 26 2.4 VOLUME-OF-FLUID METHOD FOR MULTI-PHASE FLOW 28 2.5 VOLUME-TRACKING ALGORITHM 30 2.6 PROJECTION METHOD 32 2.7 PARTIAL-CELL TREATMENT 33 2.8 COMPUTATIONAL CYCLE 33 2.9 BOUNDARY CONDITIONS 34 2.9.1 FREE-SLIP WALL BOUNDARY CONDITION 34 2.9.2 NO-SLIP WALL BOUNDARY CONDITION 35 2.9.3 DIRICHLET BOUNDARY CONDITION 35 2.10 NUMERICAL STABILITY 35 2.11 INTERNAL-SOURCE WAVEMAKER 36 2.12 SPONGE LAYER 37 CHAPTER 3 MODEL VALIDATION 39 3.1 MODEL VALIDATION 1 39 3.1.1 NUMERICAL SETUP 39 3.1.2 RESULTS 42 3.2 MODEL VALIDATION 2 46 3.2.1 EXPERIMENTAL SETUP 46 3.2.2 NUMERICAL SETUP 49 3.2.3 MODEL QUALITY ASSESSMENT 52 3.2.4 RESULTS 53 3.3 SHORT SUMMARY 59 CHAPTER 4 RESULTS AND DISCUSSION 60 4.1 LABORATORY-SCALE SIMULATION 60 4.1.1 PURPOSE OF NUMERICAL EXPERIMENT 60 4.1.2 NUMERICAL SETUP 60 4.1.3 RESULTS 62 4.1.4 MODELLING FOR NEAR-BED FLOWS UNDER WIND EFFECTS 110 4.1.5 RESULTS 111 4.2 FILED-SCALE SIMULATION 120 4.2.1 WIND-SPEED EFFECTS 120 4.2.2 SLOPING BEACH EFFECTS 133 CHAPTER 5 CONCLUSION AND FUTURE WORK 140 5.1 CONCLUDING REMARK 140 5.2 SUGGESTING FUTURE WORK 142 APPENDIX A-RECORD OF ORAL DEFENSE AND RESPONSE TO REVIEW COMMENTS 144 BIBLIOGRAPHY 155

    Al-Zanaidi, M.A., Hui, W.H., 1984. Turbulent airflow over water waves-a numerical study. J. Fluid Mech. 148, 225–246. https://doi.org/10.1017/S0022112084002329
    Banner, M.L., 1990. The influence of wave breaking on the surface pressure distribution in wind-wave interactions. J. Fluid Mech. 211, 463–495. https://doi.org/10.1017/S0022112090001653
    Banner, M.L., Melville, W.K., 1976. On the separation of airflow over water waves. J. Fluid Mech. 77, 825–842. https://doi.org/10.1017/S0022112076002905
    Banner, M.L., Peirson, W.L., 2007. Wave breaking onset and strength for two-dimensional deep-water wave groups. J. Fluid Mech. 585, 93–115. https://doi.org/10.1017/S0022112007006568
    Banner, M.L., Peirson, W.L., 1998. Tangential stress beneath wind-driven air-water interfaces. J. Fluid Mech. 364, 115–145. https://doi.org/10.1017/S0022112098001128
    Banner, M.L., Peregrine, D.H., 1993. Wave breaking in deep water. Annu. Rev. Fluid Mech. 25, 373–397. https://doi.org/10.1146/annurev.fluid.25.1.373
    Banner, M.L., Phillips, M., 1974. On the incipient breaking of small scale waves, Journal of Fluid Mechanics.
    Barranco, I., Liu, P.L.F., 2021. Run-up and inundation generated by non-decaying dam-break bores on a planar beach. J. Fluid Mech. 915, 1–29. https://doi.org/10.1017/jfm.2021.98
    Battjes, J.A., 1988. Surf-zone dynamics. Annu. Rev. Fluid Mech. 20, 257–93. https://doi.org/10.1007/978-3-642-84847-6_4
    Battjes, J.A., 1974. Surf similarity, in: Coastal Engineering Proceedings. pp. 466–479. https://doi.org/10.9753/icce.v14.26
    Belcher, S.E., Hunt, J.C.R., 1993. Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109–148. https://doi.org/10.1017/S0022112093003350
    Blenkinsopp, C.E., Chaplin, J.R., 2007. Void fraction measurements in breaking waves. Proc. R. Soc. A Math. Phys. Eng. Sci. 463, 3151–3170. https://doi.org/10.1098/rspa.2007.1901
    Boussinesq, J., 1872. Théorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. J. Mathématiques Pures Appliquées 2e série 17, 55–108.
    Burgers, G., Makin, V.K., 1993. Boundary-layer model results for wind-sea growth. J. Phys. Oceanogr. 23, 372–385.
    Carter, D.J.T., 1982. Prediction of wave height and period for a constant wind velocity using the JONSWAP results. Ocean Eng. 9, 17–33. https://doi.org/10.1016/0029-8018(82)90042-7
    Chang, K.A., Liu, P.L.F., 1998. Velocity, acceleration and vorticity under a breaking wave. Phys. Fluids 10, 327–329. https://doi.org/10.1063/1.869544
    Chen, G., Belcher, S.E., 2000. Effects of long waves on wind-generated waves. J. Phys. Oceanogr. 30, 2246–2256. https://doi.org/10.1175/1520-0485(2000)030<2246:EOLWOW>2.0.CO;2
    Cho, Y.S., Liu, P.L.F., 1999. Crest-length effects in nearshore tsunami run-up around islands. J. Geophys. Res. Ocean. 104, 7907–7913. https://doi.org/10.1029/1999jc900012
    Chorin, A.J., 1969. On the convergence of discrete approximations to the Navier-Stokes Equations. Math. Comput. 23, 341. https://doi.org/10.2307/2004428
    Chorin, A.J., 1968. Numerical solution of the Navier-Stokes. Math. Comput. 22, 745–762. https://doi.org/10.2307/2004575
    Chu, C.-R., Chung, C.-H., Wu, T.-R., Wang, C.-Y., 2016. Numerical Analysis of Free Surface Flow over a Submerged Rectangular Bridge Deck. J. Hydraul. Eng. 142, 1–11. https://doi.org/10.1061/(asce)hy.1943-7900.0001177
    Chu, C.R., Lin, Y.A., Wu, T.R., Wang, C.Y., 2018a. Hydrodynamic force of a circular cylinder close to the water surface. Comput. Fluids 171, 154–165. https://doi.org/10.1016/j.compfluid.2018.05.032
    Chu, C.R., Tran, T.T.T., Wu, T.R., 2021. Numerical analysis of free-surface flows over rubber dams. Water (Switzerland) 13. https://doi.org/10.3390/w13091271
    Chu, C.R., Wu, Y.R., Wu, T.R., Wang, C.Y., 2018b. Slosh-induced hydrodynamic force in a water tank with multiple baffles. Ocean Eng. 167, 282–292. https://doi.org/10.1016/j.oceaneng.2018.08.049
    Ciurana, A.B., Aguilar, E., 2020. Expected distribution of surfing days in the Iberian peninsula. J. Mar. Sci. Eng. 8. https://doi.org/10.3390/JMSE8080599
    Cox, D.T., Shin, S., 2003. Laboratory measurements of void fraction and turbulence in the bore region of surf zone waves. ASCE 129, 1197–1205. https://doi.org/10.1061/ASCE0733-93992003129:101197
    Davis, R.E., 1972. On the turbulent flow over a wavy boundary. J. Fluid Mech. 52, 287–306. https://doi.org/10.1017/S002211207000157X
    Dean, R.G., Dalrymple, R.A., 1991. Water wave mechanics for engineers and scientists, World Scientific Publishing Co. Pte. Ltd.
    Deane, G.B., Stokes, M.D., 2002. Scale dependence of bubble creation mechanisms in breaking waves. Nature 418, 839–844. https://doi.org/10.1038/nature00967
    Deng, B., Wang, M., Yao, W., Tang, H., Jiang, C., 2021. Laboratory and numerical investigations on characteristics of air bubbles in plunging breakers on beach. Ocean Eng. 224. https://doi.org/10.1016/j.oceaneng.2021.108728
    Dommermuth, D.G., Yue, D.K.P., Lin, W.M., Rapp, R.J., Chan, E.S., Melville, W.K., 1988. Deep-water plunging breakers: A comparison between potential theory and experiments. J. Fluid Mech. 189, 423–442. https://doi.org/10.1017/S0022112088001089
    Douglass, S.L., 1990. Influence of wind on breaking waves. J. Waterw. Port, Coastal, Ocean Eng. 116, 651–663. https://doi.org/10.1061/(asce)0733-950x(1990)116:6(651)
    Drazen, D.A., Melville, W.K., 2009. Turbulence and mixing in unsteady breaking surface waves. J. Fluid Mech. 628, 85–119. https://doi.org/10.1017/S0022112009006120
    Feddersen, F., Veron, F., 2005. Wind effects on shoaling wave shape. J. Phys. Oceanogr. 35, 1223–1228. https://doi.org/10.1175/JPO2753.1
    Fulgosi, M., Lakehal, D., Banerjee, S., De Angelis, V., 2003. Direct numerical simulation of turbulence in a sheared air-water flow with a deformable interface. J. Fluid Mech. 482, 319–345. https://doi.org/10.1017/S0022112003004154
    Galloway, J.S., Collins, M.B., Moran, A.D., 1989. Onshore/offshore wind influence on breaking waves: An empirical study. Coast. Eng. 13, 305–323. https://doi.org/10.1016/0378-3839(89)90039-2
    Galvin, C.J., 1972. Wave breaking in shallow water, Waves on Beaches and Resulting Sediment Transport. https://doi.org/10.1016/b978-0-12-493250-0.50015-1
    Gent, P.R., Taylor, P.A., 1977. A note on “separation” over short wind waves. Boundary-Layer Meteorol. 11, 65–87. https://doi.org/10.1007/BF00221825
    Gent, P.R., Taylor, P.A., 1976. A numerical model of the air flow above water waves. J. Fluid Mech. 77, 105–128. https://doi.org/10.1017/S0022112077000706
    Grilli, S.T., Svendsen, I.A., Subramanya, R., 1997. Breaking criterion and characteristics for solitary waves on slopes. J. Waterw. Port, Coastal, Ocean Eng. 123, 102–112. https://doi.org/10.1061/(asce)0733-950x(1997)123:3(102)
    Harlow, F.H., Welch, J.E., 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189. https://doi.org/10.1063/1.1761178
    Henriquez, M., 2004. Artificial Surf Reefs. Delft University of Technology.
    Hieu, P.D., Katsutoshi, T., Ca, V.T., 2004. Numerical simulation of breaking waves using a two-phase flow model. Appl. Math. Model. 28, 983–1005. https://doi.org/10.1016/j.apm.2004.03.003
    Hieu, P.D., Vinh, P.N., Van Toan, D., Son, N.T., 2014. Study of wave-wind interaction at a seawall using a numerical wave channel. Appl. Math. Model. 38, 5149–5159. https://doi.org/10.1016/j.apm.2014.04.038
    Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225. https://doi.org/10.1007/s40998-018-0069-1
    Hoque, A., Aoki, S.I., 2005. Distributions of void fraction under breaking waves in the surf zone. Ocean Eng. 32, 1829–1840. https://doi.org/10.1016/j.oceaneng.2004.11.013
    Hu, K.C., Hsiao, S.C., Hwung, H.H., Wu, T.R., 2012. Three-dimensional numerical modeling of the interaction of dam-break waves and porous media. Adv. Water Resour. 47, 14–30. https://doi.org/10.1016/j.advwatres.2012.06.007
    Hubbard, M.E., Dodd, N., 2002. A 2D numerical model of wave run-up and overtopping. Coast. Eng. 47, 1–26. https://doi.org/10.1016/S0378-3839(02)00094-7
    Hwang, P.A., 2006. Duration- and fetch-limited growth functions of wind-generated waves parameterized with three different scaling wind velocities. J. Geophys. Res. Ocean. 111. https://doi.org/10.1029/2005JC003180
    Iafrati, A., 2009. Numerical study of the effects of the breaking intensity on wave breaking flows. J. Fluid Mech. 622, 371–411. https://doi.org/10.1017/S0022112008005302
    Iribarren, C.R., Nogales, C.M., 1949. Protection des ports, in: 17th Int. Navigation Congress. pp. 180–193.
    Israeli, M., Orszag, S.A., 1981. Approximation of radiation boundary conditions. J. Comput. Phys. 41, 115–135. https://doi.org/10.1016/0021-9991(81)90082-6
    Iwata, K., Kawasaki, K., Kim, D.S., 1996. Breaking limit, breaking, and post-breaking wave deformation due to submerged structures. Proc. 25th Int. Conf. Coast. Eng. https://doi.org/10.1061/9780784402429.181
    Jeffreys, H., 1925. On the formation of water waves by wind. Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character 107, 189–206. https://doi.org/10.1098/rspa.1925.0015
    Jiang, C., Yang, Y., Deng, B., 2020. Study on the nearshore evolution of regular waves under steady wind. Water 12, 686. https://doi.org/10.3390/w12030686
    Karambas, T. V., Koutitas, C., 1992. A breaking wave propagation model based on the Boussinesq equations. Coast. Eng. 18, 1–19. https://doi.org/10.1016/0378-3839(92)90002-C
    Kawai, S., 1982. Structure of air flow separation over wind wave crests. Boundary-Layer Meteorol. 23, 503–521. https://doi.org/10.1007/BF00116275
    Kawai, S., 1981. Visualization of airflow separation over wind-wave crests under moderate wind. Boundary-Layer Meteorol 21, 93–104.
    Kharif, C., Giovanangeli, J.P., Touboul, J., Grare, L., Pelinovsky, E., 2008. Influence of wind on extreme wave events: Experimental and numerical approaches. J. Fluid Mech. 594, 209–247. https://doi.org/10.1017/S0022112007009019
    Kim, J., Moin, P., Moser, R., 1987. Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech. 177, 133–166. https://doi.org/10.1017/S0022112087000892
    Kubo, H., Sunamura, T., 2001. Large-scale turbulence to facilitate sediment motion under spilling breakers, in: Coastal Dynamics. pp. 212–221.
    Lakehal, D., Meier, M., Fulgosi, M., 2002. Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows. Int. J. Heat Fluid Flow 23, 242–257. https://doi.org/10.1016/S0142-727X(02)00172-8
    Lamarre, Melville, W.K., 1991. Air entrainment and dissipation in breaking waves. Nature 351, 469–471.
    Lamb, K.G., 2014. Internal wave breaking and dissipation mechanisms on the continental slope/shelf. Annu. Rev. Fluid Mech. 46, 231–254. https://doi.org/10.1146/annurev-fluid-011212-140701
    Larsen, J., Dancy, H., 1983. Open boundaries in short wave simulations - A new approach. Coast. Eng. 7, 285–297. https://doi.org/10.1016/0378-3839(83)90022-4
    Leonard, A., 1975. Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248. https://doi.org/10.1016/S0065-2687(08)60464-1
    Lim, H.J., Chang, K.A., Huang, Z.C., Na, B., 2015. Experimental study on plunging breaking waves in deep water. J. Geophys. Res. C Ocean. 120, 2007–2049. https://doi.org/10.1002/2014JC010269
    Lin, C., Hwung, H., 1992. External and internal flow fields of plunging breakers. Exp. Fluids 12, 229–237. https://doi.org/10.1007/bf00187300
    Lin, P., Li, C.W., 2003. Wave-current interaction with a vertical square cylinder. Ocean Eng. 30, 855–876. https://doi.org/10.1016/S0029-8018(02)00068-9
    Lin, P., Liu, P.L.F., 1999. Internal wave-maker for Navier-Stokes equations models. J. Waterw. Port, Coastal, Ocean Eng. 124, 207–215.
    Lin, P., Liu, P.L.F., 1998. Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone. J. Geophys. Res. Solid Earth 103, 15677–15694. https://doi.org/10.1029/98jc01360
    Liu, D., Lin, P., 2008. A numerical study of three-dimensional liquid sloshing in tanks. J. Comput. Phys. 227, 3921–3939. https://doi.org/10.1016/j.jcp.2007.12.006
    Liu, P.L.F., 1995. Model equations for wave propagations from deep to shallow water 125–157. https://doi.org/10.1142/9789812797582_0003
    Liu, Philip L. F., Cho, Y.S., Briggs, M.J., Synolakis, C.E., Kanoglu, U., 1995. Run-up of solitary waves on a circular island. J. Fluid Mech. 302, 259–285.
    Liu, P. L. F., Cho, Y.S., Yoon, S.B., Seo, S.N., 1995. Numerical Simulations of the 1960 Chilean Tsunami Propagation and Inundation at Hilo, Hawaii 99–115. https://doi.org/10.1007/978-94-015-8565-1_7
    Liu, P.L.F., Wu, T.R., Raichlen, F., Synolakis, C.E., Borrero, J.C., 2005. Runup and rundown generated by three-dimensional sliding masses. J. Fluid Mech. 536, 107–144. https://doi.org/10.1017/S0022112005004799
    Liu, Z.B., Fang, K.Z., Cheng, Y.Z., 2018. A new multi-layer irrotational Boussinesq-type model for highly nonlinear and dispersive surface waves over a mildly sloping seabed. J. Fluid Mech. 842, 323–353. https://doi.org/10.1017/jfm.2018.99
    Lo, H.Y., Park, Y.S., Liu, P.L.F., 2013. On the run-up and back-wash processes of single and double solitary waves - An experimental study. Coast. Eng. 80, 1–14. https://doi.org/10.1016/j.coastaleng.2013.05.001
    Longo, S., Petti, M., Losada, I.J., 2002. Turbulence in the swash and surf zones: A review. Coast. Eng. 45, 129–147. https://doi.org/10.1016/S0378-3839(02)00031-5
    Longuet-Higgins, M.S., Cartwright, D. E., Smith, N.D., 1963. Observations of the directional spectrum of sea waves using the motions of a floating buoy. Ocean Wave Spectra, Prentice Hall 111–132. https://doi.org/10.1016/s0011-7471(76)80012-5
    Longuet-Higgins, M.S., 1969. On Wave Breaking and the Equilibrium Spectrum of Wind-Generated Waves, in: Proceedings of the Royal Society of London. pp. 151–159. https://doi.org/10.1098/rspa.1969.0069
    Longuet-Higgins, M.S., Cokelet, E.D., 1976. The deformation of steep surface waves on water - I. A numerical method of computation. Proc. R. Soc. London. A. Math. Phys. Sci. 350, 1–26. https://doi.org/10.1098/rspa.1976.0092
    Lubin, P., Vincent, S., Abadie, S., Caltagirone, J.P., 2006. Three-dimensional Large Eddy Simulation of air entrainment under plunging breaking waves. Coast. Eng. 53, 631–655. https://doi.org/10.1016/j.coastaleng.2006.01.001
    Lynett, P., Liu, P.L.F., 2004a. Linear analysis of the multi-layer model. Coast. Eng. 51, 439–454. https://doi.org/10.1016/j.coastaleng.2004.05.004
    Lynett, P., Liu, P.L.F., 2004b. A two-layer approach to wave modelling. Proc. R. Soc. A Math. Phys. Eng. Sci. 460, 2637–2669. https://doi.org/10.1098/rspa.2004.1305
    Maiti, S., Sen, D., 1999. Computation of solitary waves during propagation and runup on a slope. Ocean Eng. 26, 1063–1083. https://doi.org/10.1016/S0029-8018(98)00060-2
    Melville, W.K., Matusov, P., 2002. Distribution of breaking waves at the ocean surface. Nature 417, 58–63.
    Melville, W.K., 1996. The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech. 28, 279–321. https://doi.org/10.1146/annurev.fl.28.010196.001431
    Melville, W.K., 1982. The instability and breaking of deep-water waves. J. Fluid Mech. 115, 165–185. https://doi.org/10.1017/S0022112082000706
    Melville, W.K., Veron, F., White, C.J., 2002. The velocity field under breaking waves: Coherent structures and turbulence. J. Fluid Mech. 454, 203–233. https://doi.org/10.1017/S0022112001007078
    Miles, J.W., 1960. On the generation of surface waves by turbulent shear flows. J. Fluid Mech. 7, 469–478.
    Miles, J.W., 1957. On the generation of surface waves by shear flow. J. Fluid Mech. 3, 185–204. https://doi.org/10.1017/S0022112062000828
    Mitsuyasu, H., 1985. A note on the momentum transfer from wind to waves. J. Geophys. Res. 90, 3343–3345. https://doi.org/10.1029/jc090ic02p03343
    Mitsuyasu, H., 1966. Interactions between water waves and wind (I), Research Institute for Applied Mechanics (RIAM).
    Mitsuyasu, H., Yoshida, Y., 2005. Air-sea interactions under the existence of opposing swell. J. Oceanogr. 61, 141–154. https://doi.org/10.1007/s10872-005-0027-1
    Miyata, H., Kanai, A., Kawamura, T., Park, J.C., 1996. Numerical simulation of three-dimensional breaking waves. J. Mar. Sci. Technol. 1, 183–197. https://doi.org/10.1007/BF02390795
    Mo, W., Jensen, A., Liu, P.L.F., 2013. Plunging solitary wave and its interaction with a slender cylinder on a sloping beach. Ocean Eng. 74, 48–60. https://doi.org/10.1016/j.oceaneng.2013.09.011
    Mori, N., Kakuno, S., 2008. Aeration and bubble measurements of coastal breaking waves. Fluid Dyn. Res. 40, 616–626. https://doi.org/10.1016/j.fluiddyn.2007.12.013
    Nadaoka, K., Hino, M., Koyano, Y., 1989. Structure of the turbulent flow field under breaking waves in the surf zone. J. Fluid Mech. 204, 359–387. https://doi.org/10.1017/S0022112089001783
    Orszag, S.A., Patterson, G.S., 1972. Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28, 76–79. https://doi.org/10.1103/PhysRevLett.28.76
    Otsuka, J., Saruwatari, A., Watanabe, Y., 2017. Vortex-induced suspension of sediment in the surf zone. Adv. Water Resour. 110, 59–76. https://doi.org/10.1016/j.advwatres.2017.08.021
    Perlin, M., Choi, W., Tian, Z., 2013. Breaking waves in deep and intermediate waters. Annu. Rev. Fluid Mech. 45, 115–145. https://doi.org/10.1146/annurev-fluid-011212-140721
    Perlin, M., He, J., Bernal, L.P., 1996. An experimental study of deep water plunging breakers. Phys. Fluids 8, 2365–2374. https://doi.org/10.1063/1.869021
    Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445. https://doi.org/10.1098/rsta.1980.0265
    Phillips, O.M., Banner, M.L., 1974. Wave breaking in the presence of wind drift and swell. J. Fluid Mech. 66, 625–640. https://doi.org/10.1017/S0022112074000413
    Rapp, R.J., Melville, W.K., 1990. Laboratory measurements of deep-water breaking waves. Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci. 331, 735–800. https://doi.org/10.1098/rsta.1990.0098
    Reul, N., Branger, H., Giovanangeli, J.P., 2008. Air flow structure over short-gravity breaking water waves. Boundary-Layer Meteorol. 126, 477–505. https://doi.org/10.1007/s10546-007-9240-3
    Rider, W.J., Kothe, D.B., 1998. Reconstructing Volume Tracking. J. Comput. Phys. 141, 41.
    Robertson, B., Hall, K., Zytner, R., Nistor, I., 2013. Breaking waves: review of characteristic relationship. Coast. Eng. J. 55, 40. https://doi.org/10.1142/S0578563413500022
    Ronmarin, P., 1989. Geometric properties of deep-water breaking waves. J. Fluid Mech. 209, 405–433. https://doi.org/10.1017/S0022112089003162
    Ryu, Y., Chang, K.A., Mercier, R., 2007. Runup and green water velocities due to breaking wave impinging and overtopping. Exp. Fluids 43, 555–567. https://doi.org/10.1007/s00348-007-0332-0
    Scarfe, B.E., Elwany, M.H.S., Mead, S.T., Black, K.P., 2003. The Science of surfing waves and surfing breaks - A review.
    Scarfe, B.E., Healy, T.R., Rennie, H.G., Mead, S.T., 2009. Sustainable management of surfing breaks: Case studies and recommendations. J. Coast. Res. 25, 684–703. https://doi.org/10.2112/08-0999.1
    Shemdin, O.H., Hsu, E.Y., 1967. The dynamics of wind in the vicinity of progressive water waves. Coast. Eng. Proc. 30, 403–416. https://doi.org/10.9753/icce.v10.24
    Sheng, W., Alcorn, R., Lewis, T., 2014. Physical modelling of wave energy converters. Ocean Eng. 84, 29–36. https://doi.org/10.1016/j.oceaneng.2014.03.019
    Smagorinsky, J., 1963. General circulation experiments with the primitive equation. Mon. Weather Rev. 91, 99–164. https://doi.org/10.1126/science.12.306.731-a
    Song, J.B., Banner, M.L., 2002. On determining the onset and strength of breaking for deep water waves. Part I: Unforced irrotational wave groups. J. Phys. Oceanogr. 32, 2541–2558. https://doi.org/10.1175/1520-0485-32.9.2541
    Soper, H.E., Young, A.W., Cave, B.M., Lee, A., Pearson, K., 1917. On the Distribution of the Correlation Coefficient in Small Samples. Appendix II to the Papers of “Student” and R. A. Fisher. Biometrika 11, 328. https://doi.org/10.2307/2331830
    Stanton, T., Marshall, D., Houghton, R., 1932. The growth of waves on water due to the action of the wind. Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character 137, 283–293. https://doi.org/10.1098/rspa.1932.0136
    Sverdrup, H.U., Munk, W.H., 1947. Wind, Sea, and Swell: Theory of relations for forecasting. U.S Navy Hydrogr. Off. 44.
    Tian, Z., Choi, W., 2013. Evolution of deep-water waves under wind forcing and wave breaking effects: Numerical simulations and experimental assessment. Eur. J. Mech. B/Fluids 41, 11–22. https://doi.org/10.1016/j.euromechflu.2013.04.001
    Tian, Z., Perlin, M., Choi, W., 2010. Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model. J. Fluid Mech. 655, 217–257. https://doi.org/10.1017/S0022112010000832
    Ting, F.C.K., Kirby, J.T., 1994. Observation of undertow and turbulence in a laboratory surf zone. Coast. Eng. 24, 51–80. https://doi.org/10.1016/0378-3839(94)90026-4
    Titov, V. V., Synolakis, C.E., 1998. Numerical modeling of tidal wave runup. J. Waterw. Port, Coastal, Ocean Eng. 124, 157–171. https://doi.org/10.1061/(asce)0733-950x(1998)124:4(157)
    Titov, V. V, Synolakis, C.E., 1995. Modeling of breaking and nonbreaking Long-Wave evolution and runup using VTCS-2. J. Waterw. Port, Coastal, Ocean Eng. 121, 308–316. https://doi.org/10.1061/(asce)0733-950x(1995)121:6(308)
    Troch, P., De Rouck, J., 1998. Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters, in: Coastal Engineering. pp. 1638–1649.
    Ursell, F., 1956. Wave generation by wind, in: Surveys in Mechanics (Ed. Batchelor, G.K.). Cambridge Univ. Press, Cambridge. pp. 216–249.
    Veeramony, J., Svendsen, I.A., 1998. Boussinesq model for breaking waves: comparisons with experiments. Proc. Coast. Eng. Conf. 1, 258–271. https://doi.org/10.1061/9780784404119.018
    Vollestad, P., Ayati, A.A., Jensen, A., 2019. Experimental investigation of intermittent airflow separation and microscale wave breaking in wavy two-phase pipe flow. J. Fluid Mech. 878, 796–819. https://doi.org/10.1017/jfm.2019.660
    Vollestad, P., Jensen, A., 2021. Modification of airflow structure due to wave breaking on a submerged topography. Boundary-Layer Meteorol. 180, 507–526. https://doi.org/10.1007/s10546-021-00631-3
    Voorde, M. ten, 2009. Contribution to the design of Multi-Functional Artificial Reefs.
    Vuong, T.H.N., Wu, T.R., Wang, C.Y., Chu, C.R., 2020. Modeling the slump-type landslide tsunamis part II: Numerical simulation of tsunamis with Bingham landslide model. Appl. Sci. 10, 1–23. https://doi.org/10.3390/app10196872
    WAMDI Group, 1988. The WAM model -A third generation ocean wave prediction model 18, 1775–1810.
    Ward, D.L., Wibner, C.G., Zhang, J., 1998. Runup on coastal revetments under the influence of onshore wind. J. Coast. Res. 14, 1325–1333.
    Watanabe, Y., Saeki, H., 1999. Three-dimensional large eddy simulation of breaking waves. Coast. Eng. J. 41, 281–301. https://doi.org/10.1142/s0578563499000176
    Watanabe, Y., Saeki, H., Hosking, R.J., 2005. Three-dimensional vortex structures under breaking waves. J. Fluid Mech. 545, 291–328. https://doi.org/10.1017/S0022112005006774
    Willmott, C.J., Matsuura, K., 2005. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim. Res. 30, 79–82. https://doi.org/10.3354/cr030079
    Wu, C.H., Nepf, H.M., 2002. Breaking criteria and energy losses for three-dimensional wave breaking. J. Geophys. Res. Ocean. 107. https://doi.org/10.1029/2001jc001077
    Wu, T.-R., Lo, H.-Y., Tsai, Y.-L., Ko, L.-H., Chuang, M.-H., Liu, P.L.-F., 2021. Solitary Wave Interacting with a Submerged Circular Plate. J. Waterw. Port, Coastal, Ocean Eng. 147, 1–21. https://doi.org/10.1061/(asce)ww.1943-5460.0000605
    Wu, T.R., 2004. A numerical study of three-dimensional breaking waves and turbulence effects. Cornell Univ. 2004.
    Wu, T.R., Chu, C.R., Huang, C.J., Wang, C.Y., Chien, S.Y., Chen, M.Z., 2014. A two-way coupled simulation of moving solids in free-surface flows. Comput. Fluids 100, 347–355. https://doi.org/10.1016/j.compfluid.2014.05.010
    Wu, T.R., Ho, T.C., 2011. High resolution tsunami inversion for 2010 Chile earthquake. Nat. Hazards Earth Syst. Sci. 11, 3251–3261. https://doi.org/10.5194/nhess-11-3251-2011
    Wu, T.R., Huang, C.J., Chuang, M.H., Wang, C.Y., Chu, C.R., 2011. Dynamic coupling of multi-phase fluids with a moving obstacle. J. Mar. Sci. Technol. 19, 643–650. https://doi.org/10.51400/2709-6998.2206
    Wu, T.R., Huang, H.C., 2009. Modeling tsunami hazards from Manila trench to Taiwan. J. Asian Earth Sci. 36, 21–28. https://doi.org/10.1016/j.jseaes.2008.12.006
    Wu, T.R., Vuong, T.H.N., Lin, J.W., Chu, C.R., Wang, C.Y., 2018. Three-Dimensional Numerical Study on the Interaction between Dam-Break Wave and Cylinder Array. J. Earthq. Tsunami 12, 1–35. https://doi.org/10.1142/S1793431118400079
    Xie, Z., 2014. Numerical modelling of wind effects on breaking solitary waves. Eur. J. Mech. B/Fluids 43, 135–147. https://doi.org/10.1016/j.euromechflu.2013.08.001
    Yan, S., Ma, Q.W., 2010. Numerical simulation of interaction between wind and 2D freak waves. Eur. J. Mech. B/Fluids 29, 18–31. https://doi.org/10.1016/j.euromechflu.2009.08.001
    Yan, B., Luo, M., Bai, W., 2019. An experimental and numerical study of plunging wave impact on a box-shape structure. Mar. Struct. 66, 272–287. https://doi.org/10.1016/j.marstruc.2019.05.003
    Yang, Z., Deng, B.Q., Shen, L., 2018. Direct numerical simulation of wind turbulence over breaking waves. J. Fluid Mech. 850, 120–155. https://doi.org/10.1017/jfm.2018.466
    Yang, Z., Liu, P.L.F., 2022. Depth-integrated wave-current models. Part 2. Current with an arbitrary profile. J. Fluid Mech. 936. https://doi.org/10.1017/jfm.2022.42
    Yang, Z.T., Liu, P.L.F., 2019. Depth-integrated wave-current models. Part 1. Two-dimensional formulation and applications. J. Fluid Mech. 883. https://doi.org/10.1017/jfm.2019.831
    Yim, S.C., Yuk, D., Panizzo, A., Di Risio, M., Liu, P.L.-F., 2008. Numerical Simulations of Wave Generation by a Vertical Plunger Using RANS and SPH Models. J. Waterw. Port, Coastal, Ocean Eng. 134, 143–159. https://doi.org/10.1061/(asce)0733-950x(2008)134:3(143)
    Yoon, S.B., Liu, P.L.F., 1989. Interactions of currents and weakly nonlinear water waves in shallow water. J. Fluid Mech. 205, 397–419. https://doi.org/10.1017/S0022112089002089
    Zarruk, G.A., Cowen, E.A., Wu, T.R., Liu, P.L.F., 2015. Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure. J. Fluids Struct. 52, 181–198. https://doi.org/10.1016/j.jfluidstructs.2014.11.001
    Zhiyin, Y., 2015. Large-eddy simulation: Past, present and the future. Chinese J. Aeronaut. 28, 11–24. https://doi.org/10.1016/j.cja.2014.12.007
    Zou, Q., Chen, H., 2017. Wind and current effects on extreme wave formation and breaking. J. Phys. Oceanogr. 47, 1817–1841. https://doi.org/10.1175/JPO-D-16-0183.1

    QR CODE
    :::