本文建立二階全非線性Boussinesq 數值模式，改善低階 Boussinesq 方程式之弱非線性及弱分散性，以模擬近岸高非線性波浪變形。針對二階全非線性 Boussinesq 數值模式之邊界條件加以改良，在開放邊界處設立海綿層邊界，由理論分析求得海綿層內函數之遞減型式及阻尼係數。結果顯示阻尼係數為相對水深之函數，計算時可由實際的波浪條件來決定最佳係數，減少往昔數值計算時參數選定所用試誤法之不確定性，增進數值計算之效率和精度。並進行斜坡底床與潛堤地形之數值驗証，包括規則波與不規則波造波，以証明本文模式的適用性。
　　應用本文發展之非線性波浪模式，模擬波浪通過非等坡度底床之變形現象，包括淺化、碎波、波浪再生、溯升以及水位揚升等，觀測波浪於近岸地形之實際水位變化。並針對不同波浪條件與不同坡度底床下，統計分析碎波參數、堤面波浪溯升高度及堤前反射率間之關係，提出修正的經驗式以擴大適用範圍。
　　最後分析規則波和不規則波波浪通過沙漣底床時產生的布拉格反射現象，與 Miles (1981) 理論之反射率公式、Hsu 等人 (2003) 之演進型態緩坡方程式計算結果以及試驗資料作比較。結果顯示不規則波於主共振和次諧波共振處之反射率小於規則波，而不規則波之反射率帶寬則大於規則波。並針對布拉格反射之影響因素，包括沙漣個數、沙漣高度及沙漣間距等，進行一系列的數值模擬及分析探討。結果顯示增加沙漣個數及沙漣高度，可使主共振反射率變大；而加大沙漣間距時雖主共振反射率減小，但次諧波共振反射率則變大。

　To improve the weak nonlinearity and weak dispersion of the classical Boussinesq equation, a 2nd-order fully nonlinear Boussinesq model based on Wei and Kirby (1995)’s scheme is established in this study. This model also uses the eddy viscosity technique to model breaking, and a “slotted beach” to simulate run-up phenomena. The damping coefficients of the sponge layer boundary in this model are derived theoretically. The present result differs from former researches in which the free parameters in the damping coefficients are suggested by numerical tests to control the effect of the sponge layer. Numerical experiments show that the proposed damping coefficients work efficiently on reducing the energy of reflected waves from the sponge layer. The numerical tests are performed to verify the applicability and validity of the present model.
　The present model is performed to simulate the deformation of waves propagating over the varying topography, including shoaling, breaking, recovery, runup and setup, etc. With different wave conditions and beach slopes, numerical analysis of the surf similarity parameter, runup elevation and reflection coefficient result in extended range of the empirical formulas.
　This study is also applied to simulate the Bragg reflection of monochromatic and random waves due to artificial sand ripples. The numerical results are compared with the theoretical solutions of Miles (1981), and with the corresponding results using the evolution equation for mild slope equation of Hsu et al. (2003) and the experimental data. For the monochromatic wave, the present model can predict the reflection coefficients of the primary and second-harmonic resonance well. For the random waves, the reflection coefficients of the primary resonance are smaller and the reflection bandwidth is wider than the monochromatic wave, so the Bragg reflection of random waves is different from that of the monochromatic wave. In addition, present model is applied to study the affecting factors of the Bragg reflection, including the number, the height and the spacing of artificial sand ripples.

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