标题: 孤立波于阶梯式海堤之溯上研究
The Runup of Solitary Waves on Stepwise Sea Dikes
作者: 谢文绍
Wen-Shao Hsieh
吴永照
Yung-Chao Wu
土木工程学系
关键字: 阶梯式海堤;有限差分法;能量损失;孤立波;碎波;溯上;溃坝;Stepwise Sea Dikes;Finite Difference Method;Energy loss;Solitary Wave;Breaking;Runup;Dam Breaker
公开日期: 1999
摘要: 本文研究主要目的为探讨孤立波作用于传统斜坡与阶梯式斜坡之溯上高度;本数值模式考虑底床摩擦力,并可模拟孤立波通过底床变化区域时产生的未碎波与碎波波形变化过程并讨论能量损失对于孤立波溯上高度之影响;并藉此结果探讨阶梯式斜坡之平台长度对于溯上高度的影响,并选取相关研究内容之结果来加以验证,将经由数值解析所得之数值解与理论解及经由实验所得到的结果相互比较,以证明本数值模式之妥适性。
本文以有限差分法(finite difference method)中之间隔显性蛙跳法(staggered explicit leap-frog difference scheme)及引用Lax-Wendroff(1960)消散项对浅水方程式进行数值计算,由于此一消散式允许流场中产生不连续情形,能够计算其格点间因扩散而产生的突然变动,因此这个方法能够应用于模拟孤立波通过底床变化区域时所产生的碎波情形。本文发展之数值模式经模拟得到的数值解与Synolakis(1987)之解析近似解及实验值相互比较,可发现所得的溯上结果与Synolakis之趋势十分吻合。于不同条件之传统斜坡溯上结果中来说:未碎波的情况下,其斜坡坡度愈缓其溯上高度愈高;而于碎波情况下,其斜坡坡度愈缓则其溯上高度愈低,此结论与一般认为之结果有所不同。而传统斜坡与阶梯式斜坡溯上之数值模拟结果相互比较后得:相同的坡度及入射波高条件下阶梯式斜坡之最大溯上高度小于传统斜坡溯上高度;而于阶梯式斜坡之溯上模式中,相同的平均坡度条件下,其平台长度愈长时,溯上的高度较小。
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.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT880015004
http://hdl.handle.net/11536/65100
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