由於目前國內從事 Boussinesq 模式的研究仍採用弱非線性的 Boussinesq 方程式，故本文主要目的為發展一套高階全非線性Boussinesq 數值模式，以改善低階 Boussinesq 方程式之弱非線性及弱頻散性，並擴大模式之使用範圍，藉以模擬非線性波浪在變動底床之波場變化。本文並希望利用本文發展之模式計算由不同規則波波浪條件作用於不同斜坡底床之波場變化，並提出波浪之反射率及溯升的經驗公式，以利工程應用。

　　本文模式以 Wei 等人 (1995) 之二階非線性 Boussinesq 方程式為控制方程式，再加入 Kennedy 等人 (2000) 之方法以模擬波浪碎波及溯升。在數值模式的建立上，則參考 Wei 及 Kirby (1995) 之研究，為避免數值離散之捨去項造成數值頻散，建議在空間離散上，對一階微分項採四階精確度之中央差分法，二階以上之微分項則離散至二階準確度後進行計算，以解決數值頻散的問題。另外，Wei 和 Kirby (1995) 在計算網格上是以非交錯網格 (non-staggered grid) 進行離散，其會造成數值計算上有鋸齒狀波形的出現，會使得模式較不穩定，為改善此一情況，本文採用 Banijamali (1997) 提出的交錯網格 (staggered grid) 進行有限差分法之離散。在時間離散上，利用四階精確度之 Adams-Bashforth-Moultor 預測與修正 (predictor-corrector) 技巧。

　　模式分別計算規則波與不規則波通過潛堤及斜坡底床上的波場變化，計算結果並與理論值或試驗值進行一系列比較驗証，用以確認本文模式適用於近岸波場的模擬。本文模式同時計算 160 組於不同的規則波浪傳遞於各種斜坡底床上的波場分佈，並分析其堤面的溯升高度及堤前的波浪反射率，再根據 Hunt (1956) 之波浪溯升經驗公式及 Battjes (1974) 之波浪反射率經驗公式，將計算結果進行回歸分析，提出可適用於較廣泛範圍的經驗公式。

　　Within the past decades, the researches about Boussinesq equations in Taiwan have been focused on the weak nonlinearity ones. Therefore, to improve the weak nonlinearity and weak dispersion, the main purpose of this paper adopts a set of high-orders of all nonlinear Boussinesq numerical model by expanding the scope of application of the model to simulate the nonlinear wave field change in the varying bottom bed. This paper utilizes the model of this paper to calculate the wave field change that acted on different slope bottom beds by different regular wave terms, and provides the experience formula of wave runup and the reflection with favorable engineering application.

　　The model of this paper is based on the 2nd order fully nonlinear Boussinesq equations of Wei et al. (1995) and methods of Kennedy et al. (2000) to simulate wave breaking and runup. In terms of the numerical model, this paper adopts Wei and Kirby (1995) research. For preventing the model from dispersing because of canceling the items of numerical model, it is suggested that the first-order difference schemes is fourth-order accuracy and the 2nd-order above difference schemes is 2nd-order accuracy in space. Since the authors noticed that the use of non-staggered grid (according to Wei and Kirby (1995)) could have appearances of the cockscomb wave that it caused the numerical model to be unsteady, this paper adopts the staggered grid that was suggested by Banijamali (1997).

　　This model adopts a fourth-order Adams-Bashforth-Moultor predictor-corrector method to advance in time.
The model proposed in this paper calculates the wave field of the regular wave and irregular wave passing the submerged breakwater and the slopping bottom beds respectively. The check of the results with a series of the theory values or the testing values has confirmed this model suitable for the simulation of the wave fields near shore. This paper provides 160 groups of regular wave passing various slopping bottom beds, and the analysis of the wave runup and the reflection. Finally, this paper provides a large range of the experience formula based on the runup experience formula that proposed by Hunt (1956) and the reflection experience formula that proposed by Battjes (1974).

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