本文使用平面二維數值模式來模擬孤立波通過不均勻底床與防坡堤等結構物所產生的波形演變。模式之基本控制方程為弱非線性、弱頻散作用之一般化Boussinesq(gB) Wu (1981)方程組使用二階精度之時空中央差分與兩時階平均法來離散貼壁座標gB方程組，由矩陣法逐線連續疊代求解斷面平均流速 及水面高 ，直至所有變數完全收斂後，便可獲得具時間精度之數值結果。模式應用前首先評估初始孤立波形在均勻水深時，使用不同格網、時間間距計算，振幅與波形之結果，以獲得爾後計算分析之最佳格網尺寸。再進一步，利用此模式模擬孤立波經傾斜坡底床淺化過程中，波高、波長隨著水深而變，波動之非線性量因水深漸減而累增，使得波形尖銳度變大、波浪速度變慢的情形。並考量若至岸側遇直立壁防波堤，所造成波溯升之現象;由壁反射後，孤立波之主波後將有附屬波（secondary wave）的本文分別產生。並探討孤立波在不同坡度、或同一坡度但不同斜坡長度作用下，波形的變化差異。另為瞭解孤立波與實際複合地形之波形變化，考慮地形為一斜坡至較淺陸棚（continental shelf）的底床，由計算結果發現孤立波受陸棚水深的影響，主波會分離出附屬尾波及產生一微小反射波往回傳遞。不同的斜波長，將影響在於附屬尾波分離，但對最終附屬尾波的波高影響並不大;而不同陸棚高度，使主波於陸棚附近的波高變化有明顯差別，至於發展至陸棚後方的波高以不再影響而變化，而陸棚高度對附屬尾波、及反射波的波高也都有很大的影響。當孤立波進入斜坡中途額外加一平台，將產生分波現象，平台尾端也有一反射波出現往回傳遞，而最後整個波形變化為主波與二次波都會有再次分離的現象。最後考慮孤立波斜向入射定斜坡底床為之波傳過程，波形變化因不同斷面而波形變化不一樣，前斷面波峰受淺化影響較後斷面波峰大。

This thesis discussed the application of a two-dimensional numerical model to the long wave shoaling on a plane slope and its final interaction with a vertical-faced breakwater in water or a shelf. The model equations for an initial solitary waves evolved in shallow water are the generalized Boussinesq (gB) equations (wu, 1981), which are suitably applied to the weakly nonlinear, weakly dispersive waves on an uneven bottom. By using the second-order scheme based on the central difference and time-average process, the discretized gB equations in a boundary-fitted grid are solved to get a time-accurate solution by TDMA (tridigonal matrix algorithm) with line-by-line iteration. To validate the model, the author first assessed the optimum grid size by examing a solitary-wave with a permanent waveform propagation in a uniform depth. Then, the wave height and wave-length during shoaling over a constant slope increase with the depth decreased, resulting from enhancement of nonlinearity. If the vertical wall of a breakwater is set up at the coast end, the runup and reflection of the solitary wave there can generate the secondary trailing waves following the primary wave system. In the present study the effects of various slopes or the effects of various inclined lengths at the constant slope on the deformation of wave shape are considered. In addition, the complex topography of bottom is also studied through the simulation of waves over a continental shelf behind the slope. As to the soliton reflection, the spatial phase lag, the wave pattern and the maximum run-up on the vertical-faced breakwater during the reflecting process were also discussed. After reflecting, the solitary-wave is still affected by the original uneven bottom. The wave steepness of the solitary-wave becomes smaller, and its velocity slows down gradually caused by the increasing water depth.

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