Boussinesq模式在過去的二十年內，已經被廣泛的應用於近岸波浪變形以及波浪與地形的互制作用(interaction)，並獲得相當的成功(e.g. Hsiao et al. 2002；Lynett 2004；Hsiao et al. 2005；Hsiao et al. 2010)。另外，Boussinesq模式的應用範圍涵蓋了淺水至中等水深區，並可以準確的模擬近岸地形變化對波浪之影響。由於Boussinesq模式為一水深積分之型式，因此降低了模擬問題的維度，同時大幅減少計算時間。

為了確認此高階Boussinesq模式之適用範圍，本文使用了一系列的數值模擬進行驗證。並將模擬結果與前人試驗資料比對。其中包括孤立波於一斜坡(斜率為1:19.85)上的溯升及溯降過程，不同非線性之孤立波於一緩坡(斜率為1:60)上的溯升以及行進時的波形變化，不同水深下的孤立波通過位於一斜坡(斜率為1:20)上的海堤結構物之波浪變形與其越波量，最後則是模擬規則正弦波於一斜坡式(斜率為1:10)堤防的平均越波量。經由數值模擬結果與試驗資料在水位變化、空間自由液面以及越波量的比對有一定的吻合度。

為了瞭解長波在臺灣東部海岸可能造成之損害，本文以Boussinesq模式模擬孤立波入射至台東縣台東市、宜蘭縣壯圍鄉以及花蓮縣新城鄉的實際底床及近岸海堤。並以統計所得之250年重現回歸期的外海波高疊加最大暴潮偏差作為入射條件。在本文模擬結果中，呈現了孤立波在真實底床上的各種現象，如淺化、碎波、溯升以及越波等。其中較為特別的是，為明白不同之波浪條件對越波量造成的影響，於花蓮縣新城鄉將採用相同非線性的孤立波與規則波為入射條件，並分析比較其越波量之差異；而在台東縣台東市及宜蘭縣壯圍鄉則以不同非線性之孤立波進行模擬，也探討了波浪非線性對於越波量的影響為何。另外，本文亦有對在臺灣東部海岸各地之瞬時越波量時序列作分析探討。

The Boussinesq model has been extensively used in simulating water waves transformation nearshore in the past twenty years, with considerable success (e.g. Hsiao et al. 2002；Lynett 2004；Hsiao et al. 2005；Hsiao et al. 2010). In addition, the Boussinesq model can accurately capture the wave evolution from intermediate to shallow water depths. Since the Boussinesq model is a depth-integrated model, the dimensions of physical problems can be reduced by one and thus greatly lessen the computational cost.

To validate this higher-order Boussinesq model, a series of numerical tests are conducted, including the runup and rundown process of solitary wave propagating a slope(inclination 1:19.85), the distinct nonlinearity solitary waves evolution over a mild slope(inclination 1:60), the tsunami-like solitary waves impinging and overtopping an impermeable sloping(inclination 1:20) seawall under different water depth. Finally, the average overtopping rate of the regular sinusoidal waves on a simple levee was examined. Based on the comparison of simulated results and experimental data including surface elevation, wave profile snapshot as well as overtopping volume, the fairly good agreement is found.

To investigate probable disaster in Taiwan eastern coasts caused by long waves, the model was applied to determine the extreme condition as a solitary wave attacks irregular seawalls at Taitung;Ilan and Hualien coast in eastern Taiwan. The surge level and maximum wave height are obtained from statistical analysis based on 250 years return period. Wave shoaling, wave breaking, runup as well as wave overtopping are all presented in our simulated results. The time-series of wave overtopping discharge are analyzed under various bathymetry and nonlinearity to calculate the wave overtopping rate.

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