本文以潰壩湧潮 (dam-break bore) 研究海嘯波抵達近岸時之海嘯湧潮行為，以及其與近岸結構物之交互作用。在上溯期間，海嘯湧潮在近岸地區之行為與潰壩湧潮相似。為了研究湧潮的特性，使用數值和實驗室試驗產生一個潰壩湧潮，於壩體下游5.26m處設置一垂直方柱12*12cm。本研究求解不可壓縮流之三維 Navier-Stokes 方程式及大渦模擬 (Large-eddy Simulation, LES) 紊流模式，以體積分率法 (Volume of Fluid, VOF) 描述自由液面之運動，以有限體積法來離散網格，並以移動固體法 (Moving Solid Method, MSM) 模擬潰壩實驗時擋板抽取之運動。潰壩湧潮於長達14.72m之渠道內前進，以模擬海嘯波抵達近岸地區後所造成之類均勻 (Quasi-uniform) 海嘯湧潮。討論在潰壩湧潮產生時之初始波形、撞擊於結構物之力、波形、速度場、以及壓力場。結果顯示在潰壩湧潮所施於結構物之力主要與壩後水深 (impoundment)以及結構物面積有關，並敏感於壩前薄水墊厚度 (waterbed thickness) 以及壩體閘門之抽取速度。分析結果得知，要取得良好之數值模擬結果，閘門抽取速度以及薄水墊厚度需要精確描述。本研究發現，壩前薄水墊扮演潤滑之角色，有薄水墊之湧潮將產生較大之初期撞擊力。本研究亦發現潰壩湧潮撞擊至結構物時，將於結構物前方產生上下兩個方向相反之漩渦，其尺度與湧潮深度相仿。其飛濺之碎波高度亦相仿於湧潮深度。構物受力最大之區域並非落於結構物底端，而是位於二分之ㄧ平均湧潮高度，證實初期主破壞力為水體之動壓力，而非靜壓力。

When a tsunami wave propagates to the near-shore region, it transforms from a long wave to a tsunami bore and dissipates the energy in the coastal region. This is the most destructive period during the whole tsunami life. In order to have better understanding on the tsunami bore, this paper investigates the physical processes of a dam-break bore which has similar behavior as the tsunami bore. The bore-structure interaction is studied by placing a square cylinder at the downstream region. The numerical approach is adopted. We solve the 3D incompressible Navier-Stokes (NS) equations with large-eddy simulation (LES) turbulence model. The free-surface kinematics and wave breaking are tracked by the volume-of-fluid (VOF) method. The domain is discretized by the finite volume method (FVM) with an irregular mesh domain. The broken dam is modeled by the moving-solid algorithm (MSM) to detailed describe the lifting motion of the gate. The dam-break bore is marching in a channel with a length of 14.72 m to mimic the quasi-uniform tsunami bore. The numerical results are validated with the laboratory experiments in terms of the wave force acting on the square structure. We focuses the discussions on the effect of the impoundment height, waterbed lubrication, gate motion, free-surface profiles around the broken-dam and square cylinder, pressure profile around the cylinder. The results show that the impinging force on the cylinder is mainly determined by the impoundment, width of the channel, and the projected area of the structure. However, it also sensitive to the thickness of the waterbed and the lifting speed of the gate. When the bore is impinging with the cylinder structure, two eddies with inversed rotation direction will be generated right in front of the structure. Their length scales are similar to each other and close to the thickness of the incoming bore. The largest wave fore acting on the cylinder is not located at the bottom but at half of the incoming bore height. This indicates that the maximum impinging force is dominated by the hydrodynamic pressure. The waterbed plays a lubrication role which accelerates the bore speed and increases the wave force.

中文摘要i
ABSTRACTiii
致謝v
目錄vi
圖目錄ix
表目錄xii
符號說明xiii
第一章 緒 論1
1-1 前言1
1-2 研究方法2
1-3 本文目的5
1-4 本文架構5
第二章 文 獻 回 顧7
2-1潰壩湧潮特性之實驗與理論回顧8
2-2湧潮對結構物衝擊之實驗與理論回顧11
2-3數值解運用11
第三章 數值方法18
3-1模式簡介18
3-2紊流模式18
3-3有限體積法21
3-4流體體積法22
3-5自由液面之建立24
3-6二步法24
3-7無滑動之穩定邊壁邊界條件26
3-8滑動邊界條件27
3-9移動固體法27
3-10數值穩定度31
3-11小結32
第四章 數值模擬設定與流程33
4-1實驗架設33
4-2數值設置42
4-3網格建構42
4-4邊界條件47
4-5初始條件47
4-6影響流場因子之探討47
4-6-1柱體與底床間距(Cl)之影響48
4-6-2閘門速度(GS)之影響50
4-6-3薄水墊(WT)之影響52
4-6-4LES紊流模式(LES)之影響52
4-6-5閘後水深(Ip)之影響52
4-6-6渠道寬度(CW)之影響52
4-6-7柱體尺寸(SW)之影響53
第五章 結果與討論54
5-1次影響因子之分析54
5-1-1柱體與底床間距(Cl)之影響54
5-1-2閘門速度（GS）之影響56
5-1-3薄水墊(WT)之影響59
5-1-4紊流模式LES之影響66
5-1-5閘後水深(Ip)之影響68
5-1-6渠寬(CW)之影響70
5-1-7柱體尺寸(SW)之影響70
5-2湧潮特性之分析73
5-2-1湧潮初形成之流場73
5-2-2湧潮行進之流場83
5-2-3湧潮撞擊柱體之流場87
5-2-4湧潮撞擊柱體之自由液面94
5-2-5各個時間之自由液面99
第六章 結論101
6-1影響因子之分析101
6-2湧潮特性之分析102
6-3 未來發展與展望103
參考文獻104
附錄A114
附錄B118
附錄C119
附錄D122
附錄E132

[1]A. Colagrossi and M. Landrini, “Numerical simulation of interfacial flows by smoothed particle hydrodynamics”, Journal of Computational Physics, 191, pp. 448-475.
[2]A. Ferrari, M. Dumbser, E. F. Toro and A. Armanini, “A new 3D parallel SPH scheme for free surface flows”, Computers & Fluids, 38, pp. 1203-1217, 2009.
[3]A. G. Abul-Azm, “Diffraction through wide submerged breakwaters under oblique waves”, Oc. Engng, Vol. 21, pp. 683-706, 1994.
[4]A. J. Chorin, “Numerical solution of the Navier-Stokes equations” Math. Comp., Vol. 22, pp.745-762, 1968.
[5]A. J. Chorin, “On the convergence of discrete approximations of the Navier-Stokes equations”, Math. Comp., Vol. 23, pp.341-353, 1969.
[6]A. J. C. Crespo, M. Gómez-Gesteira and R. A. Dalrymple, “Modeling Dam Break Behavior over a Wet Bed by a SPH Technique”, Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, pp. 313-320, 2008.
[7]A. L. Moore, “Combined use of clast-size measurements Combined use of clast-size measurements and wave-tank experiments to estimate Pleistocene tsunami size at Molokai”, Hawaii, Ph.D. dissertation, University of Washington, 1999.
[8]A. N. Kolmogorov, “A refinement of previous hypothesis concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number”, J. Fluid Mech, pp. 13-82, 1962.
[9]A. Ritter, “Die Fortpflanzung der Wasserwellen”, Zeitschrift des Vereines Deutscher Ingenieure, Vol. 36, NO. 24, pp.947–954, 1892.
[10]A. T. Ippen and G., “The shoaling and breaking of the solitary wave”, Proc., 5th Int. Conf. on Coastal Engineering, ASCE, New York, N.Y., pp. 24-47, 1954.
[11]A. Valian, V. Caleffi and A. Zanni, ”Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method”, Journal of Hydraulic Engineering, ASCE, Vol. 128, No. 5, pp. 460-472, 2002.
[12]B. Ataie-Ashtiani, G. Shobeyri and L. Farhadi, “Modified incompressible SPH method for simulating free surface problems”, Fluid Dynamics Research, 40, pp. 637-661, 2008.
[13]C. Giuseppina, L. Maurizio and J. R. Chaplin, “Level-set computations of free surface rotational flows”, Journal of Fluids Engineering, 127, 6, pp. 1111-1121, 2005.
[14]C. J. Huang and C. M. Dong, “Wave deformation and vortex generation in water waves propagating over a submerged dike”, Coast. Engng, Vol. 37, pp. 123-148, 1999.
[15]C. J. Tang and J. H. Chang, “Flow separation during solitary wavepassing over submerged obstacle”, J. Hydr. Engng, pp. 742-749, 1998.
[16]C. M. Lemos, “A simple numerical technique for turbulent flows with free surfaces”, International Journal of Numerical Methods in Fluids, Vol. 15, pp. 127– 146, 1992.
[17]C. Subarya, M. Chlieh, L. Prawirodirdjo, J. P. Avouac, Y. Bock, K. Sieh, A. J. Meltzner, D. H. Natawidjaja and R. McCaffrey, “Plate-boundary deformation associated with the great Sumatra – Andaman earthquake”, Nature, Vol. 440, pp. 46-51, 2006.
[18]C. V. Bellos, J. V. Soulis and J. G. Sakkas, ”Experimental Inverstigation of Two-Dimensional Dam-Break Induced Flows”, Advances in Water Resources, Vol. 14, No. 1, pp. 31-41, 1992.
[19]C. W. Hirt and B. D. Nichols, “Volume of Fluid (VOF) method for the dynamics of free surface boundaries.”, J. Comput. Phys., pp.201-225, 1981.
[20]D. Violeau and R. Issa, “Numerical modelling of complex turbulent free-surface flows with the SPH method : an overview”, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Int. J. Numer. Meth. Fluids, 53, pp. 277-304, 2007.
[21]E. Marchandise and J. F. Remacle, “A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows”, Journal of Computational Physics, 219, pp. 780-800, 2006.
[22]F. C. K. Ting and Y. K. Kim, “Vortex generation in water waves propagating over a submerged obstacle”, Coastal Engineering, Vol. 24, pp. 23–49, 1994.
[23]F. H. Harlow and J. E. Welch, “Numerical calculation of timedependent viscous incompressible flow of fluid with a free surface”, Phys. Fluids, Vol. 12, pp. 2182–2189, 1965.
[24]F. Zhuang and J. J. Lee, “A viscous rotational model for wave overtopping over marine structure”, Proc. 25th Int. Conf. Coastal Eng., ASCE, pp. 2178-2191, 1996.
[25]G. B. Whitham, “The effects of hydraulic resistance on the dam-break problem”, Proceedings of the Royal Society, series A 227, pp. 399–407, 1955.
[26]G. Chen, C. Kharif, S. Zaleski and J. Li, “Two-dimensional Navier-Stokes simulation of breaking waves”, Physics of Fluids, Vol. 11, NO. 1, pp. 121-133, 1999.
[27]G.. Colicchio, A. Colagrossi, , M. Greco and M. Landrini, “Free-surface flow after a dam Break: a comparative study”, Ship Technol, Res. 49(3), pp. 95–104, 2002.
[28]H. Árnason, “Interactions between an Incident Bore and a Free-Standing Coastal Structure”, University of Washington, Doctor of Philosophy, 2005.
[29]I. A. Svendsen and P. A. Madsen, “A turbulent bore on a beach”, Journal of Fluid Mechanics, pp. 73-96, 1984.
[30]I. J. Losada, R. Silva, and M. A. Losada, “3-D non-breaking regular wave interaction with submerged breakwaters”, Coast. Engng, Vol. 28, pp. 229-248,1996.
[31]J. A. Puleo, A. Farhadzadeh and N. Kobayashi, “Numerical simulation of swash zone fluid aWTelerations”, J Geophys Res, 112, 2007.
[32]J. D. Ramsden, “Tsunamis: Forces on a Vertical Wall Caused by Long Waves, Bores, and Surges on a Dry Bed”, Ph.D. dissertation, California Institute of Technology, 1993.
[33]J. D. Wang, and H. R. Ansari, “Dynamics of surge run-up on dry bed”, Internal report, Division of Applied Marine Physics, Rosentiel School of Marine and Atmospheric Science, University of Miami, 1986.
[34]J. J. Monaghan, “Simulating free surface flows with SPH”, J. Comput. Phys, 110, pp. 399–406, 1994.
[35]J. J. Monaghan and A. Kos, “Scott Russell’s wave generator”, Phys. Fluids, 12(3), pp. 622–630, 2000.
[36]J. J. Monaghan, A. Kos and N. Issa, “Fluid motion generated by impact”, J. Waterway Port Coastal Ocean Engng, 129(6), pp. 250–259, 2003.
[37]J. J. Monaghan, “Smoothed particle hydrodynamics”, Rep. Prog. Phys, 68, pp. 1703–1759, 2005.
[38]J. Smagorinsky, “General circulation experiments with the primitive equations”, I. The basic equations, Mon. Weather Rev, 91: pp. 99-164, 1963.
[39]J. W. Deardorff, “A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Number”, Journal of Fluid Mech., Vol. 41, NO. 2, pp. 453-480, 1970.
[40]K. Abdolmaleki and M. T. Morris-Thoas, “Simulation of The Dam Break Problem and Impact Flows Using a Navier-Stokes Solver”, 15th Australasian Fluid Mechanics Conference , Sydney , Australia 13-17, 2004.
[41]K. H. Wang and A. T. Chwang, “Nonlinear impulsive force on a vertical cylinder”, in A. P. Boresi and K. P. Chong (eds), Engineering Mechanics in Civil Engineering, pp. 859–862, 1984.
[42]K. H. Wang and A. T. Chwang, “Flow around an impulsively starting vertical cylinder”, Advancements in Aerodynamics, Fluid Mechanics and Hydraulics, pp. 322–328, 1986.
[43]K. H. Wang and A. T. Chwang, “Free–surface flow produced by aWTelerating vertical cylinder”, Journal of Engineering Mechanics, NO. 7, pp. 1559–1566,1989.
[44]M. Gomez-Gesteira and R. A. Dalrymple, “Using a Three-Dimensional Smoothed Particle Hydrodynamics Method for Wave Impact on a Tall Structure”, Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 130, No. 2, pp. 63-69, 2004.
[45]M. J. Ketabdari , M. R. H. Nobari and M. M. Larmaei, “Simulation of waves group propagation and breaking in coastal zone using a Navier_Stokes solver with an improved VOF free surface treatment”, Applied Ocean Research, 30, pp. 130-143, 2008.
[46]M. LANDRINI, A. COLAGROSSI, M. GRECO and M. P. TULIN, “Gridless simulations of splashing processes and near-shore bore propagation”, Journal of Fluid Mechanics, Volume 591, , pp 183-213, 2007.
[47]P. A. Madsen and I. A. Svendsen, “Turbulence bores and hydraulic jumps”, Journal of Fluid Mechanics, pp. 1-25, 1983.
[48]P. D. Hieu, K. Tanimoto and V. T. Ca, “Numerical simulation of breaking waves using a two-phase flow model”, Applied Mathematical Modeling (Elsevier), 28, pp. 983–1005, 2004.
[49]P. D. Hieu and K. Tanimoto, “Verification of a VOF-based two-phase flow model for wave breaking and wave–structure interactions”, cean Engineering, 33, pp. 1565–1588, 2006.
[50]P. Guyenne and S. T. Grilli, “Numerical study of three-dimensional overturning waves in shallow water”, J. Fluid Mech., pp. 361-388, 2006.
[51]P. Lin and C. W. Li, “A σ-coordinate three-dimensional numerical model for surface wave propagation”, Int. J. Numer. Meth. Fluids, Vol. 38, pp. 1048-1068, 2002.
[52]P. Lin and C. W. Li, “Wave-current interaction with a vertical square Cylinder”, Ocean Engineering, Vol. 30, pp. 855-876, 2003.
[53]P. L. F. Liu, T. R. Wu, Raichlen, C. E. Synolakis and J. C. Borrero, “Runup and rundown generated by three-dimensional sliding masses”, J. Fluid Mech, pp. 107-144, 2005.
[54]Q. Zhang and P. L. F. Liu, “A numerical study of swash flows generated by bores”, Coastal Engineering, 55, pp. 1113-1134, 2008.
[55]R. A. Dalrymple and B.D. Rogers, “Numerical modeling of water waves with the SPH method”, Department of Civil Engineering, Johns Hopkins University, 2005.
[56]R. C. Ertekin and J. M. Becker, “Nonlinear diffraction of waves by a submerged shelf in shallow water”, ASME, New York, pp. 31-39, 1996.
[57]R. H. Cross, “Tsunami surge forces”, Journal of Waterways and Harbor Division, ASCE, Vol. 93, NO. 4, pp.201–231, 1967.
[58]R. Lohner, C. Yang and E. Onate, “On the simulation of flows with violent free surface motion”, Comput. Methods Appl, Mech, Engrg, 195, pp. 5597-5620, 2006.
[59]R. Lohner, C. Tang, and E. Onate, “Simulation of flows with violent free surface motion and moving objects using unstructured grids”, Int. J. Numer. Meth. Fluids, 53, pp. 1315–1338,2007.
[60]S. B. Pope, “Turbulent flows”, Cambridge University Press, 2001.
[61]S. B. Pope, “Ten questions concerning the large-eLESy simulation of turbulent flows”, New Journal of Physics, 35, 2004.
[62]S. Hibber and D. H. Peregrine, “Surf and run-up on a beach: a uniform bore,” Journal of Fluid Mechanics, pp. 323-345, 1979.
[63]S. M. Hosseini, M. T. Manzari and S. K.Hannani, “A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17, No. 7, pp. 715-735, 2007.
[64]S. Nakamura and Y. Tsuchiya, “On shock pressure of surge on a wall” Bulletin of the Disaster Prevention Research Institute, Vol. 23, NO. 12, pp. 47–58, 1973.
[65]S. Osher and J. A. Sethian, “Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” Journal of Computational Physics, 79, pp. 12-49, 1988.
[66]S. Shao and E.Y. M. Lo, “Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface”, Adv. Water Resour, 26, pp. 787–800, 2003.
[67]S. Vincent, T. N. Randrianarivelo, G. Pianet and J. P. Caltagirone, “Local penalty methods for flows interacting with moving solids at high Reynolds numbers”, Computers & Fluids, 36, pp. 902–913, 2007.
[68]T. Nagayoshi, A. Minato, M. Misawa, A. Suzuki, M. Kuroda and N. Ichikawa, “Simulation of Multi-dimensional Heterogeneous and Intermittent Two-Phase Flow by Using an Extended Two-Fluid Model”, Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 40, No. 10, pp. 827–833, 2003.
[69]T. R. Wu, “A numerical study of three-dimensional breaking waves and turbulence effects”, PhD dissertation, Cornell University, 2004.
[70]T. R. Wu and P. L. F. Liu, “A large eLESy simulation model for tsunami and runup generated by landslides”, in Advances in Coastal and Ocean Engineering, Vol. 10 (ed. by Liu, P. L.-F., Yeh, H. and Synolakis, C.), World Scientific Publishing, 2009a.
[71]T. R. Wu and P. L. F. Liu, “Numerical study on the three-dimensional dam-break bore interacting with a square cylinder”, in Nonlinear Wave Dynamics (ed. Lynett, P.), World Scientific Publishing, 2009b.
[72]T. W. H. Sheu, C. H. Yu and P. H. Chiu, “Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows”, Journal of Computational Physics, 228, pp. 661-686, 2009.
[73]W. Cabot and P. Moin, “Approximate wall boundary conditions in the large-eLESy simulation of high Reynolds number flow”, Flow Turb. Combust., Vol. 63, pp. 269-291, 2000.
[74]W. J. Rider and D. B. Kothe, “Reconstructing Volume Tracking”, Journal of Computational Physics, Vol. 141, pp.112-152, 1998.
[75]W. Mo, K. Irschik, H. Oumeraci and P. L. F. Liu, “A 3D numerical model for computing non-breaking wave forces on slender piles”, J. Engrg. Math, Vol. 58, pp. 19-30, 2007.
[76]W. Rodi, “Turbulence models and their application in hydraulics – A state-of-the-art review”, I.A.H.R. publication, 1980.
[77]X. Wang, and P. L. F. Liu, “An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami”, Journal of Hydraulic Research, Vol. 44, NO. 2, pp. 147-154, 2006.
[78]Y. Fukui, M. Nakamura, H. Shiraishi, and Y. Sasaki, “Hydraulic study on tsunami”, Coastal Engineering, Japan, Vol. 6, pp. 67–82, 1963a.
[79]Y. Liu, M. Xue, and D. K. P. Yue, “Computations of fully nonlinear three-dimensional wave--wave and wave--body interactions”, Part 2. Nonlinear waves and forces on a body, J. Fluid Mech., pp.41 – 65, 2001.
[80]Y. Watanabe and H. Saeki, “Three-dimensional large eLESy simulation of breaking waves”, Coasal. Engng., Vol. 41, pp. 281-301, 1999.