本研究以數值模式模擬三維海嘯之上溯。研究案例為2010年10月25日Mentawai海嘯。經現場調查，該海嘯於Sibigau島呈現特殊之衝擊現象。該島嶼內陸大多數之植生被摧毀，然而沿海之植生卻僅受極有限之破壞。由於此處沿海地形後方有一陡峭之斜坡，本研究推估此地形對於湧潮破壞行為將產生影響。此假說若成立，代表未來於海嘯攻擊下，山邊離岸之建築物亦可能遭受海嘯之破壞。為研究此一現象，本文以數值方法進行模擬與分析。模擬案例包括與實驗數據之驗證，及三維Sibigau海嘯溢淹模擬。
於實驗驗證部分，本研究與新加坡南洋理工大學黃振華教授之實驗結果進行比對。該實驗以孤立波模擬海嘯波入射與上溯，並探討孤立波上溯後，湧潮施於細圓柱之水平力和轉動彎矩。數值模擬求解三維紊流大渦模式（LES），並以Morison公式推估海嘯力。比對結果發現數值模式於海嘯湧潮之水位與流速預測方面有良好之結果，而海嘯力之推估亦有合理之準確度。
本研究並探討三種不同峭壁角度之流場行為。研究發現，三種角度之峭壁造成湧潮之反彈，並進而對峭壁前之結構物及底床造成第二次衝擊。此現象說明Sibigau島出現之現象即有可能為峭壁反彈波所造成。為確認此現象，本研究進一步進行實際尺度之溢淹模擬。
Sibigau島之溢淹模擬分兩個部分，其一為以COMCOT海嘯數值模式進行Mentawai海嘯之模擬，模擬分三層巢狀網格進行。其中第三層網格置於Sibigau島，解析度為120 m。第二部分以三維LES-VOF模式進行，並將COMCOT第三層計算結果作為LES-VOF之入流邊界條件。模擬結果發現，海嘯波入射後以海嘯湧潮上溯，並於撞擊至山壁後反彈，反彈波之位置符合Sibigau島內陸樹林被摧毀之區域。

In this study, we use a 3D numerical model to simulate the processes of tsunami run-up. The study case is the Mentawai tsunami happened in October 25, 2010. The field survey showed an interesting phenomenon that most of the vegetation inland was destroyed, while, in contrary, only limited damage observed at the coastal area. Because a steep cliff is located right behind this area, we assume that this special topography might be one of the reasons. If this hypothesis sustains, the hillsides buildings might also under the tsunami threat. To study this case, the numerical method is adopted. Validation with experimental data and Sibigau tsunami simulation are included.
As for the model validation, the simulation results are compared with the experimental data obtained from Professor Zhenhua Huang in Singapore Nanyang Technological University. In the experiment, a solitary wave is used to represent the tsunami incident wave. The force and bending moment from the run-up bore acting on a small circular cylinder are recorded. Our numerical model solves 3D Large-Eddy Simulation（LES）model, and estimate the tsunami force by Morison formula. The result shows that the numerical model is able to predict the bore height and velocity field accurately, and reasonable accuracy on the force prediction.
We also study the flow characteristics of three cliff angles. The result shows that the rebounded bore is presented in all of the cases. This rebounded bore causes the second impact on the structures at the toe of the cliff. It might explain phenomenon observed on Sibigau Island. To confirm this hypothesis, this study precedes the overflow simulation in the real scale.
The complete tsunami simulation on Sibigau Island is divided into two parts. The first part is the 2D simulation of the Mentawai tsunami by COMCOT model. Three layers of nested grids are adopted. The third layer focuses on Sibigau Island with a resolution of 120m. The second part is the 3D simulation by LES-VOF model. The third-later COMCOT result is adopted as the inflow boundary condition. The result shows that the tsunami waves transforms into tsunami bores, and then rebound after reaching the hill. The position of the rebounded wave consists with the field observation.

摘要 i
Abstract iii
致謝 v
目錄 vi
圖目錄 ix
表目錄 xiv
第一章 緒論 1
1-1前言及研究動機 1
1-2 研究方法 2
1-3 本文架構 2
第二章 文獻回顧 7
第三章 模式與數值方法 12
3-1模式簡介 12
3-2流體體積法 12
3-3 連續方程式與動量方程式 14
3-4 大渦模擬法 16
3-5部份網格法 17
3-6 真實地形導入模組 18
3-7 COMCOT結果導入模組 19
第四章 模式驗證與研究案例 23
4-1 LES-VOF模式驗證 23
4-2 問題描述 23
4-3 實驗設置與數值模式設定 23
4-4 結果驗證 25
4-5水平力與實驗比較結果討論 27
4-6 研究案例一：孤立波上溯與不同角度之陡坡撞擊之互制 28
4-6-1 流體深度之比較 29
4-6-2 水平力之比較 30
4-6-3 彎矩力之比較 31
4-7 真實地形模擬 32
第五章 研究案例二：台灣第三核電場海嘯衝擊之研究 102
5-1 問題描述 102
5-2 海嘯情境設置 103
5-3 三維LES-VOF模式設置 104
5-4 海嘯上溯水位和流速分析 105
5-5 建物受力分析 106
5-6小結 107
第六章 結論與建議 126
參考文獻 128
附錄一 模式數值方法 133
A.1 有限體積法 133
A.2 大渦模擬法 134
附錄二 COMCOT簡介 138
附錄三 三維VOF-LES模式輸入檔 140
附錄四 口試委員意見表 153

[1] Baldock, T. E., Cox, D., Maddux, T., Killian, J., Fayler, L., “Kinematics of breaking tsunami wavefronts: A data set from large scale laboratory experiments.” Coast. Eng. J., Vol.56, pp. 506–516, 2009.
[2] Borrero, J. C., Fritz, H. M., Suwargadi, B. W., Li, L. L., Qiang, Q., Pranantyo, I. R., Synolakis C. E., Skanavis, V., “Field Survey of the Southern Mentawai Islands following the 25 October, 2010 Earthquake and Tsunami.”, 2011.
[3] Chuang, M. H., “Developing a Two-way Coupled of Moving Solid Method for Solving Landslide Generated Tsunamis.” Master dissertation, National Central University, 2009.
[4] Chen, M. Z., “3D Numerical Simulation on the Scouring Problem Induced by Tsunami Flood.” Master dissertation, National Central University, 2011.
[5] Deardorff, J. W., Peskin, R. L., “Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow.”, Phys. Fluids, Vol.13, pp. 584-595, 1970.
[6] Dodd, N., “Numerical model of wave run-up, overtopping, and regeneration.”, J. Waterway, Port, Coastal, Ocean Eng, Vol.124, pp. 73-81, 1998. [7] Frigaard, P., Burcharth, H. F., “Wave Loads on Cylinders.”, CEEC COMETT Seminar on Wave and Ice Forces on offshore structures, 1989.
[8] Germano, M., Piomelli, U., Moin, P., Cabot, W. H., “A dynamic subgridscale eddy viscosity model.”, Phys. Fluids A, Vol.3, pp.1760-1765, 1991.
[9] Hosoda, A., Maruyama, k., “Disaster Survey Report：Washed Away of Bridge by the Great East Japen Earthquake.”, 2011.
[10] Hill, E. M., Borrero, J. C., Huang, Z. H., Qiu, Q., Banerjee, P., Natawidjaja, D. H., Elosegui, P., Fritz, H. M., Suwargadi, B. W., Pranantyo, I. R., Li, L. L., Macpherson K. A., Skanavis V., Synolakis, C. E., Sieh, K., “The 2010 Mw 7.8 Mentawai earthquake: Very shallow source of a rare tsunami earthquake determined from tsunami field survey and near-field GPS data.”, J. Geophys. Res., Vol.117, 2012.
[11] James, S., Jaberi, F. A., “Large Scale Simulations of Two-Dimensional Nonpremixed Methane Jet Flames.” Combustion and Flame, Vol.123, pp. 465-487, 2000.
[12] Kakinuma, T., Tomita, T., “3D Numerical Simulation of Tsunami Runup.”, IEEE Techno-Ocean, Vol.1, pp. 146-151, 2004.
[13] Kim, S. k., Liu, P. L. F., and Ligget, J. A., “Boundary integral Equation Solutions for Solitary wave generation,propagation and run-up.”, Coatal Engineering, Vol.302, pp.299-317, 1983.
[14] Lilly, D. K., “A proposed modification of the Germano subgrid-scale closure method.”, Phys. Fluids A, Vol.4, pp.633-635, 1992.
[15] Liu, P. L. F., Cho, Y. S., Yoon, S. B., and Seo, S. N., “Numerical simulations of the 1960 Chilean tsunami propagation and inundation at Hilo, Hawaii, In Recent development in tsunami research.”, M. I. El-Sabh（ed）, Kluwer Academic, Dordrecht, The Netherlands, pp. 99-115, 1994.
[16] Liu Ph. L. F., Cho Yo S., Briggs M. J., Kanoglu U., Synolakis C. E., “Run-up of solitary waves on a circular island.”, J. Fluid Mech., Vol.302, pp. 259–285, 1995.
[17] Liu, P. L. F., Wu T. R., Raichlen, F., Synolakis, C. E., Borrero, J. C., “Runup and rundown generated by three-dimensional sliding masses.”, J. Fluid Mech., Vol.536, pp. 107-144, 2005.
[18] Murakami, S., "Overview of Turbulence Models Appied in CWE-1997.", 2nd European & African Conference on Wind Engineering Genova, Italy, June, p. 22-26, 1997.
[19] Mohapatra, P. K., Eswaran, V., Bhallamudi, S. M., "Two-Dimensional Analysis of Dam-Break Flow in Vertical Plane.", J. Hydraulic Engineering, Vol.125, No.2, pp. 183-192, 1999.
[20] Mohapatra, P. K., Bhallamudi, S. M., Eswaran, V., "Numerical Simulation of Impact of Bores against Inclined Walls.", J. Hydraulic Engineering, Vol.126, No.12, pp. 942-945, 2000.
[21] Megawati, K., Shaw, F., Sieh, K, Huang, Z., Wu, T.-R., Lin, Y., Tan, S. K., Pan, T.-C., "Tsunami hazard from the subduction megathrust of the South China Sea Part I. Source characterization and the resulting tsunami.", J. Asian Earth Sciences, Vol.36 , pp. 13-20., 2009.
[22] Newman, A. V., Hayes, G., Wei, Y., Convers, J., "The 25 October 2010 Mentawai tsunami earthquake, from real-time discriminants, finite-fault rupture, and tsunami excitation.", Geophys. Res. Lett., Vol.38, 2011.
[23] Nistor I., Palermo, D., Cornett, A., Taofiq Al-Faesly, "Experimental and Numerical Modeling of Tsunami Loading on Structures.", 2011.
[24] Okada, Y. , "Surface deformation due to shear and tensile faults in a half-space.", Bull. Seism. Soc. Am., Vol.75, pp. 1135-1154, 1986.
[25] Ramsden, J. D., "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.
[26] Ramsden, J. D., "Forces on a Vertical Wall due to Long Waves, Bores, and Dry-Bed Surges.", J. Waterway, Port, Coastal, Ocean Eng, Vol.122, pp.134-141, 1996.
[27] Robert, G. D., and Robert, A. D., "Water Wave Mechanics For Engineers and Scientists.", ced Series on Ocean Engineering, Vol 2, 2000.
[28] Synolakis, C.E., "The runup of solitary wave.", J. Fluid Mech., Vol.185, pp. 523-545, 1987.
[29] Stansby, P.K., Hunt, A.C., Xu, R., Taylor, P.H., Borthwick, A.G.L., Feng, T., Laurence, D.R., “Wave overtopping from focussed wave groups, experiments and modeling.”, Proc. 2nd IMA Conf. Flood Risk Assessment., 2007.
[30] Unjoh, S., ”Damage Investigation of Bridges affected by Tsunami during 2004 North Sumatra Earthquake, Indonesia.”, 2009.
[31] UNEP, “After the Tsunami Rapid Environmental Assessment.”, 2005.
[32] Udo, K., Sugawara, D., Tanaka, H., Imai, K., Mano, A., “Impact of the 2011 Tohoku Earthquake and Tsunami on Beach Morphology along the Northern Sendai Coast.”, Coast. Eng. J., Vol.54, 2012.
[33] Verman, B., Geurts, B., Kuerten, H., “Large-eddy Simulation of the Turbulent Mixing Layer.”, J. Fluid Mech., Vol.339, pp. 357-390, 1997.
[34] Wilde, P., Sobierajski, E., Romanczyk, W., “Determination of Coefficients in Morison Formula by a Kalman Filter.”, Coast. Eng. J., pp.1769-1780, 1993.
[35] Wu, T. R., “A Numerical Study of Three - dimensional Breaking Waves and Turbulence Effects”, Ph.D. Dissertation, Cornell University, 2004.
[36] Yang, C., Lin,B. L., Jiang, C. B., Liu, Y., “Predicting near-field dam-break flow and impact force using a 3D model”, J. Hydraulic Res., Vol.48, pp. 784-792, 2010.
[37] Yeh, H., “Tsunami Bore Runup”, Natural Hazards, Vol.4, pp. 209-220, 1991.
[38] Yen Y. T. and K. F. Ma, “Source-Scaling Relationship for M 4.6–8.9 Earthquakes, Specifically for Earthquakes in the Collision Zone of Taiwan.”, Bull. Seism. Soc. Am., Vol.101, pp. 464-481, 2011.
[39] 許泰文, “近岸水動力學”, 中國土木水利工程學會, 2003.
[40] Techet, A. H., “Morrison’s Equation”, 2004. <http://web.mit.edu/13.42/www/handouts/reading-morrison.pdf>
[41] New York Post, March 13, 2011. <http://www.nypost.com/p/news/international/nuclear_power_station_explodes_in_lMAD34kuD0536Cb4hSAFMP>
[42] USAtoday, March 13, 2011. <http://www.usatoday.com/news/world/2011-03-12-japan-reactor_N.htm>