孤立波於階梯式海堤之溯上研究

Abstract

本文研究主要目的為探討孤立波作用於傳統斜坡與階梯式斜坡之溯上高度；本數值模式考慮底床摩擦力，並可模擬孤立波通過底床變化區域時產生的未碎波與碎波波形變化過程並討論能量損失對於孤立波溯上高度之影響；並藉此結果探討階梯式斜坡之平台長度對於溯上高度的影響，並選取相關研究內容之結果來加以驗證，將經由數值解析所得之數值解與理論解及經由實驗所得到的結果相互比較，以證明本數值模式之妥適性。 本文以有限差分法（finite difference method）中之間隔顯性蛙跳法（staggered explicit leap-frog difference scheme）及引用Lax-Wendroff（1960）消散項對淺水方程式進行數值計算，由於此一消散式允許流場中產生不連續情形，能夠計算其格點間因擴散而產生的突然變動，因此這個方法能夠應用於模擬孤立波通過底床變化區域時所產生的碎波情形。本文發展之數值模式經模擬得到的數值解與Synolakis（1987）之解析近似解及實驗值相互比較，可發現所得的溯上結果與Synolakis之趨勢十分吻合。於不同條件之傳統斜坡溯上結果中來說：未碎波的情況下，其斜坡坡度愈緩其溯上高度愈高；而於碎波情況下，其斜坡坡度愈緩則其溯上高度愈低，此結論與一般認為之結果有所不同。而傳統斜坡與階梯式斜坡溯上之數值模擬結果相互比較後得：相同的坡度及入射波高條件下階梯式斜坡之最大溯上高度小於傳統斜坡溯上高度；而於階梯式斜坡之溯上模式中，相同的平均坡度條件下，其平台長度愈長時，溯上的高度較小。

This study investigates the solitary wave effect on traditional plain and stepwise slope, confirms that the height of the stepwise runup is smaller than the traditional plain slope when they are in the same average slope. In addition, the terrace is longer the runup is lower. The numerical model simulates the change of a nonbreaking solitary wave and a breaking solitary wave on sea dikes and discusses the influence of energy loss as well as the length of terrace on the runup height. Asymptotical analytic solutions and experiment results are selected to verify the accuracy of the present numerical model. The one-dimensional nonlinear shallow water equations are solved here numerically by Lax-Wendroff dissipative scheme. The dissipation term allows discontinuities, jumps, to arise and propagate naturally within the flow field. The dissipation also enables the computation to continue by diffusing the jump over a few space grids. Comparing the numerical results with Synolakis' experimental reveals the runup and trend of the numerical closely resemble each other. The runup of the non-breaking solitary wave increases as the slope gradient decrease. This phenomenon is contrary to the breaking solitary wave.