本文應用Lynett及Liu (2004)發展之多層布式方程式(Mulit-layer Boussinesq equations)，模擬海底崩移(landslide)所引起的海嘯波之發展過程。為確認模式模擬底床變動的可行性，本文將Lynett及Liu (2002)使用的完全潛沒(submerged)海底崩移運動行為及地形公式重新建立於模式中，與Lynett及Liu (2004)的數值結果進行比對驗證，其比對結果呈現高度的吻合。
在完成模式驗證之後，模擬海底崩移的移動及幾何形狀沿用Lynett及Liu (2005)所提出的海底崩移運動行為及地形公式，此運動公式主要建立在Watts (1997)的運動公式上，但在考慮半潛沒(subaerial)之海底崩移的情況下，需分別計算靜水面上及靜水面下塊體崩移速度，再分別乘以潛沒體積比例，加總後才為整體運動速度。單一斜坡坡度下，當改變崩移時的拖曳係數、附加質量係數與崩移塊體比重，將使崩移塊體的速度及加速度受到影響，本文以完全潛沒之海底崩移，經由改變以上參數導致的速度及加速度變化，及崩移塊體最大厚度與起始水深，來觀察波浪產生的不同。速度量變化大、最大厚度越大與起始水深越淺均會造成較大之波浪。
另一方面考慮由多種坡度所組合成的斜坡，同時包含完全潛沒與半潛沒之海底崩移。本文描述在不同的地形條件下，海底崩移時造成的波浪通過不同斜坡坡度時的演化過程，同時比較最後溯升高度的差異。在完全潛沒的海底崩移情況下，當第一段斜坡，也就是較淺水處的斜坡坡度越緩，造成的溯升高度越高。當崩移停止時，崩移塊體所在之水深，影響溯升高度比起速度變化量大小還要來得大。而在半潛沒的海底崩移情況下，本文所模擬之不同斜坡坡度之崩移，對於溯升高度的影響差異不大。無論是完全潛沒或半潛沒的崩移，在達到最大溯升高度的時間，均會因坡度的變緩而延後。

In this work we simulate tsunamis generated and evolution process by landslides using multi-layer Boussinesq equations developed by Lynett and Liu (2004). To ensure the ability of modeling landslide-induced tsunamis, the landslide motion and geometry created by Lynett and Liu (2002) are re-established in the present model, and the results show a high agreement with the numerical results by Lynett and Liu (2004).
Based on the formula of landslide motion and geometry by Lynett & Liu (2005), the effects of relevant parameters are discussed. By varying drag coefficient, added-mass coefficient and specific gravity of slides, the time-dependent velocity and acceleration of slides would be changed. Particularly, the slide-induced waves become larger when the variation of velocity becomes larger, the maximum thickness of the slide is thicker, or the slide body is close to the water surface.
The composite slopes are considered for simulating landslide-induced wave propagation including both subaerial and fully submerged landslide. Particularly, the process of waves passing through different slopes and the runup height are discussed in this study. For the cases of submerged landslide, the runup becomes higher as the first slope becomes milder. When landslides stop, the depth of slide body is more than variation of velocity for the runup height. However, there is no significant difference for runup height between the different slope angles when landslide is subaerial.

1.
Ataie-Ashtiani, B. & Najafi-Jilani, A., “A high-order Boussinesq-type model with moving bottom boundary: applications to submarine landslide tsunami waves,” International Journal for Numerical Methods in Fluids, Vol. 53, pp. 1019-1048 (2007).
2.
Di Risio, M., Bellotti, G., Panizzo, A. & De Girolamo, P., “Three-dimensional experiments on landslide generated waves at a sloping coast,” Coastal Engineering, Vol. 56, pp. 659-671 (2009).
3.
Di Risio, M. & Sammarco, P., “Analytical modeling of landslide-generated waves,” Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, No. 1, pp. 53-60 (2008).
4.
Enet, F. & Grilli, S.T., “Experimental study of tsunami generation by three-dimensional Rigid underwater landslides,” Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 133, pp. 442-454 (2007).
5.
Enet, F., Grilli, S.T. & Watts, P., “Laboratory experiments for tsunamis generated underwater landslides: comparison with numerical modeling,” Proceeding of the Thirteenth International Offshore and Polar Engineering Conference, pp. 372-379 (2003).
6.
Fine, I. V., Rabinovich, A. B., Bornhold, B. D., Thomson, R. E. & Kulikov, E. A., “The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling,” Marine Geology, Vol. 215, pp. 45-57 (2005).
7.
Fritz, H. M., Hager, W.H. & Minor, H.-E., “Landslide generated impulse waves. 1. Instantaneous flow fields,” Experiments in Fluids, Vol. 35, pp. 505-519 (2003a).
8.
Fritz, H. M., Hager, W.H. & Minor H.-E., “Landslide generated impulse waves. 2. Hydrodynamic impact craters,” Experiments in Fluids, Vol. 35, pp. 520-532 (2003a).
9.
Fuhrman, D. R. & Madsen, P. A., “Tsunami generation, propagation, and run-up with a high-order Boussinesq model,” Coastal Engineering, Vol. 56, pp. 747-758 (2009).
10.
Grilli, S. T., Vogelmann, S. & Watts, P., “Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides,” Engineering Analysis with Boundary Elements, Vol. 26, pp. 301-313 (2002).
11.
Grilli, S. T. & Watts, P., “Modeling of waves generated by a moving submerged body. Applications to underwater landslides,” Engineering Analysis with Boundary Elements, Vol. 23, pp. 645-656 (1999).
12.
Grilli, S. T. & Watts, P., “Tsunami generation by submarine mass failure. I: modeling, experimental validation, and sensitivity analysis,” Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 131, pp. 283-297 (2005a).
13.
Grilli, S. T. & Watts, P., “Tsunami generation by submarine mass failure. II: predictive equations and case studies,” Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 131, pp. 283-297 (2005b).
14.
Hayir, A., Seseogullari, B., Kilinc, İ., Erturk, A., Cigizoglu, H. K., Kabdasli, M. S., Yagci, O. & Day, K., “Scenarios of tsunami amplitudes in the north eastern coast of Sea of Marmara generated by submarine mass failure,” Coastal Engineering, Vol. 55, pp. 333-356 (2008).
15.
Israeli, M. & Orszag, S. A., “Approximation of radiation boundary conditions,” Journal of computational physics, Vol. 41, pp. 115-135 (1981)
16.
Liu, P. L.-F., Wu, T.-R., Raichlen, F., Synolakis, C. E. & Borrero, J. C., “Runup and rundown generated by three-dimensional sliding masses,” Journal of Fluid Mechanics, Vol. 536, pp. 107-144 (2005).
17.
Lynett, P., Borrero, J. C., Liu, P. L.-F. & Synolakis, C. E., “Field survey and numerical simulations: A review of the 1998 Papua New Guinea tsunami,” Pure and Applied Geophysics, Vol. 160, pp. 2119-2146 (2003).
18.
Lynett, P., Wu, T.-R. & Liu, P. L.-F., “Modeling wave runup with depth-integrated equations,” Coastal Engineering, Vol. 46, pp. 89-107 (2002a).
19.
Lynett, P. & Liu, P. L.-F., “A numerical study of submarine-landslide-generated waves and run-up,” Proceeding of the Royal Society of London, A 458, pp. 2885-2910 (2002b).
20.
Lynett, P. & Liu, P. L.-F., “A two-layer approach to wave modeling,” Proceeding of the Royal Society of London, A 460, pp. 2637-2669 (2004a).
21.
Lynett, P. & Liu, P. L.-F., “Linear analysis of the multi-layer model,” Coastal Engineering, Vol. 51, pp. 439-454 (2004b).
22.
Lynett, P. & Liu, P. L.-F., “A numerical study of the run-up generated by three-dimensional landslides,” Journal of Geophysical Research, Vol. 110, C03006 (2005).
23.
Masson, D. G., Harbitz, C. B., Wynn, R. B., Pedersen, G. & Løvholt, F., “Submarine landslides: processes, triggers and hazard prediction,” Philosophical Transactions of the Royal Society, A 364, pp. 2009-2039 (2006).
24.
Najafi-Jilani, A. & Ataie-Ashtiani, B., “Estimation of near-field characteristics of tsunami generation by submarine landslide,” Ocean Engineering, Vol. 35, pp. 545-557 (2008).
25.
Qiu, L.-C., “Two-Dimensional SPH Simulations of Landslide-Generated water waves,” Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, pp. 668-671 (2008).
26.
Ward, S. N., “Landslide tsunami,” Journal of Geophysical Research, Vol. 106, 11 201-11 215 (2001).
27.
Watts, P., “Water waves generated by underwater landslides,” Ph.D. thesis, California Institute of technology. (1997)
28.
Watts, P., Grilli, S. T., Kirby, J. T., Fryer, G. J. & Tappin, D. R., “Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model,” Natural Hazards and Earth System Sciences, Vol. 3, pp. 391-402 (2003).
29.
Wei, G., Kirby, J. T., Grilli, S.T. & Subramanya, R., “A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves,” Journal of Fluid Mechanics, Vol. 294, pp. 71-92 (1995).
30.
Yuk, D., Yim, S.C. & Liu, P. L.-F., “Numerical modeling of submarine mass-movement generated waves using RANS model,” Computers & Geosciences, Vol. 32, pp. 927-935 (2006).