海堤堤面波浪溯升及反射之研究

Abstract

本文建立二階全非線性布氏(Boussinesq)數值模式，以改善低階布氏方程式之弱非線性及弱頻散性，擴大模式之使用範圍，藉以模擬非線性波浪之變形，模式中並加入能量消散效應，以模擬波浪碎波效應及溯升和反射。在空間離散方面，一階微分項採四階精確度之中央差分法，高階微分項採二階精確度。本文以規則波和不規則波通過變動水深地形進行數值計算，並與試驗結果相互比較。本文針對160組不同條件的規則波浪，計算其傳遞於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，再將計算結果進行回歸分析，提出適用於較廣泛範圍的經驗公式。A Boussinesq numerical model is developed for describing wave setup and reflection using finite difference method. Nonlinear wave transformations are simulated in the proposed model. This model significantly improves the dispersion properties and makes them applicable to a wider range of water depths. The energy dissipation effect is taken into account for wave breaking, runup and reflection in the model. A fourth-order Adams-Bashforth-Moultor predictor-corrector method to advance in time and finite difference schemes with fourth-order accuracy in space are used. Numerical results and experimental datas are compared for both regular and irregular waves passing over a varying topography. The model is capable of simulating nonlinear wave transformation from deep water to shallow water. This investingation provides 160 groups of regular wave passing various sloping bottoms to investigate wave runup and reflection. The numerical result provides a large range of validity of the empirical formula.