孤立波在階梯式親水性海堤之溯上研究

Abstract

本文以有限差分法（Finite difference method）中之間隔顯性蛙跳法（staggered explicit leap-frog finite difference scheme）對淺水方程式（Shallow water Equations）進行數值計算，以所建立之數值模式，並於其中加入底部磨擦，以模擬未碎孤立波（nonbreaking solitary wave）之波形變化，及未碎孤立波對直立岸壁前配置潛堤、輻射邊界前配置潛堤、斜坡與階梯式斜坡之溯上（runup）研究，並探討階梯式斜坡之平台長度對溯上高度的影響，文中並選取前人相關於本研究內容之結果來加以驗證。另外，本研究除了探討數值解析結果之數值波形與理論波形及實際波形之比較外，期能更確實的描述波浪之溯上、溯下（rundown）等現象。由於底床磨擦對於長波具相當重要性，所以吾人在數值模式中分別以有無加入磨擦來做比較，分別將所得之數值結果與Synolakis（1996，1987）之解析近似解作比較，可發現加入底部磨擦項之結果與實際現象較為吻合。對於階梯式斜坡來說，加入不透水底床底部磨擦項之結果，此數值結果較為穩定。由此可證明加入底部磨擦項之結果與實際現象較為吻合。於階梯式斜坡之模式中，吾人可得知，當平台長度愈長時，溯上與溯下均會愈小。在最大溯上高度之探討中，則結果與Synolakis（1996，1987）之解析近似解相吻合。

This study simulates the wave deformation of a nonbreaking solitary wave and the reflected back by a vertical wall and radiation condition behind a submerged breakwater, the runup on a linear sloping wall and a stepped sloping wall. The extent to which they influence the height of a runup is also examined using various segment lengths of a stepped sloping wall. In addition, the explicit leap-flog finite difference scheme with staggered grid is used to solve the shallow water equations which consider the bed shear stresses. In light of the importance of bed shear stresses in the long wave, comparing the simulated results of bed shear stresses and without bed shear stresses with those of the asymptotic analytic solution of Synolakis (1996,1987) reveals that the results with bed shear stresses more closely correspond to the analytical solutions than those without bed shear stresses. For a with stepped sloping wall, the simulated results are also more stable by considering bed shear stresses. In sum, results obtained from bed shear stresses approximate the actual physical phenomenon better than those without bed shear stresses. And for discussion on the height of runup, the segment length of stepped sloping wall is more longer, the runup and rundown are more shorter. It fits the Synolakis (1996,1987)'s asymptotic analytic solution.