海嘯是一種具有巨大能量的波，當其襲上海灘後，往往造成相當嚴重的破壞，而在近代研究中通常使用孤立波來模擬由遠海之地震所引發之海嘯，對於近岸的山崩或火山爆發所造成的海嘯，則是使用N-Wave來模擬。

　　在本篇論文中，我們主要探討在海灘斜坡上放置三角堤時，三角堤的形狀和位置對於孤立波最大溯升高度之影響。我們使用線性化之淺水波方程式來描述孤立波之溯升行為，並求得其最大溯升高度之積分式。接著我們利用漸近展開法得到最大溯升高度的近似解，並以此近似解來討論三角堤形狀及位置對於最大溯升高度之影響。

　　我們發現，三角堤的放置有時會消減最大溯升高度，但有時也會造成最大溯升高度的增加，而將三角堤放置在靠近岸邊處，對於增加或消減最大溯升高度的效果最好。

　　因此，我們可以透過變化三角堤的形狀和位置參數來控制最大溯升高度的增加和消減。當我們控制三角堤使其增加最大溯升高度時，便可以應用在增加海洋波浪發電效率上。我們也可以控制三角堤使其消減最大溯升高度，並應用在預防海浪侵襲海灘上。

　Tsunamis possess a huge amount of energy and can be extremely disastrous. It is therefore very important to study their propagation characteristics and runup on the beach. In this thesis, we model the tsunami by a solitary wave incoming from the sea, and investigate how placing a two-dimensional obstacle of triangular cross-section on an otherwise uniformly sloping beach would affect the runup of the solitary wave. In particular, the effects of the obstacle’s location and geometry on the maximum runup of the solitary wave are examined.

　Based upon the linearized shallow water wave equation, an integral expression is obtained for the runup of the solitary wave. Furthermore, the expression is asymptotically expanded to derive an approximate formula for the maximum runup of the solitary wave. Using the approximate formula, we then systematically examine the effects of the precise location, width, and height of the triangular obstacle on the maximum runup of the solitary wave.

　The results indicate that the presence of the triangular obstacle may decrease or increase the maximum runup of the solitary wave, depending upon the precise location and geometry of the obstacle, and the parametric demarcation between the two possibilities is determined. It is then hoped that the runup of the solitary wave can be controlled to some extent, provided that appropriate parameter control strategies can be devised.

[1]Liu, P. L.-F. , Synolakis, C. E. & Yeh, H. H. (1991) “Report on the international workshop on long-wave run-up.” J. Fluid Mech., 229, 675-688.

[2]Tadepalli, S. & Synolakis, C. E. (1994) “The run-up of N-waves on sloping beaches.” Proc. Royal soc. London, 445, 99-112.

[3]Tadepalli, S. & Synolakis, C. E. (1996) “Model for the leading waves of tsunamis.” Physica Rev. Let., 77(10), 2141-2144.

[4]Carrier, G. F. & Greenspan, H. P. (1958) “Water waves of finite amplitude on a sloping beach.” J. Fluid Mech., 17, 97-110.

[5]Carrier, G. F. (1966) “Gravity waves on water of variable depth.” J. Fluid Mech., 24, 641-659.

[6]Lautenbacher, C. C. (1970) “Gravity wave refraction by islands.” J. Fluid Mech., 41, 655-672.

[7]Spielvogel, L. Q. (1975) “Single-wave run-up on sloping beaches.” J. Fluid Mech., 74, 685-694.

[8]Synolakis, C. E. (1987) “The runup of solitary waves.” J. Fluid Mech., 185, 523-545.

[9]Kanoglu, U. & Synolakis, C. E. (1998) “Long wave runup on piecewise linear topographies.” J. Fluid Mech., 374, 1-28.

[10]Yu, J. & Mei, C. C. (2000) “Do longshore bars shelter the shore?” J Fluid Mech., 404, 251-268.

[11]Li, Y. & Raichlen, F. (2001) “Solitary wave runup on plane slopes.” J. Wtrwy., Port, Coast., and Oc. Engrg., 127, 33-44.

[12]Liu, P. L.-F. , Lynett, P. & Synolakis, C. E. (2003) “Analytical solutions for forced long waves on a sloping beach.” J. Fluid Mech., 478, 101-109.

[13]Carrier, G. F. , Wu, T. T. & Yeh, H. (2003) “Tsunami run-up and draw-down on a plane beach.” J. Fluid Mech., 475, 79-99.

[14]Pedersen, G. & Gjevik B. (1983) “Run-up of solitary waves.” J Fluid Mech., 135, 283-299.

[15]Langsholt, M. (1981) “Experimental study of wave run-up.” Cand.real. thesis, University of Oslo.

[16]Hall, J. V. & Watts, G. M. (1953) “Laboratory investigation of the vertical rise of solitary waves on impermeable slopes.” U.S. Army, Corps of Engrs, Beach Erosion Board, Tech. Memo no. 33.

[17]Kim, S. K. , Liu, P. L.-F. & Liggett, J. A. (1983) “Boundary integral equation solutions for solitary wave generation, propagation and run-up.” Coastal Engineering, 7, 299-317.

[18]Liu, P. L.-F. , Cho, Y.-S. , Briggs, M. J. , , U. & Synolakis, C. E. (1995) “Runup of solitary waves on a circular island.” J Fluid Mech., 302, 259-285.

[19]Lin, P. , Chang, K.-A. & Liu, P. L.-F. (1999) “Runup and rundown of solitary waves on sloping beaches.” J. Wtrwy., Port, Coast., and Oc. Engrg., 125, 247-255.

[20]Chang, K.-A. & Liu, P. L.-F. (1998) “Velocity, acceleration and vorticity under a breaking wave.” Phys. Fluids, 10, 327-329.

[21]Watts, P. (2000) “Tsunami features of solid block underwater landslides.” J. Wtrwy., Port, Coast., and Oc. Engrg., 126, 144-152.

[22]Baldock, T. E. , O’Hare, T. J. & Huntley, D. A. (2004) “Long wave forcing on a barred beach.” J. Fluid Mech., 503, 321-343.

[23]Gedik, N. , Irtem, E. & Kabdasli, S. (2005) “Laboratory investigation on tsunami run-up.” Ocean Engineering, 32, 513-528.

[24]Skjelbreia, J. E. (1987) “Observation of breaking waves on sloping bottoms by use of laser Doppler velocimetry.” Rep. No. KH-R-48, California Institute of Technology, Pasadena, Calif.