# 臺灣博碩士論文加值系統

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 本文以有限元素法探討非線性長波與離岸潛堤互制作用下，波浪透反 射現象及底床剪力作用情形。文中推導一般性的水深平均積分式，藉由水 深平均與水深線性擾流水平速度假設的不同分佈，估算長波傳遞現象水平 流速。相較於傳統長波理論以微擾參數分析頻散效應，而得低階 Boussinesq方程式組，並包含緩變底床變化；本文推導過程更為精簡通用 ，並具同等之效應。 本文計算孤立波與孤立波的互制、孤立波與離岸潛式結構物的互制，並分 析所產生之液面演變和相關物理量的變化。以有限元素法所建立的數值模 式，經由格網誤差測試，獲得最佳時距dt=0.01、格網尺寸dx=0.05，可達 到孤立波傳遞的精度要求。利用這個數值模式，可計算孤立波波高為0.4 倍靜水深和高度超過一半靜水深的高潛堤， 所產生之強烈非線性互制結 果。 本文分析的物理現象有：孤立波在平直底床渠道傳遞的數值模式測試。孤 立波在平直底床渠道傳遞的線性水平流速數學模式測試。兩對稱孤立波的 反向互撞、左右不對稱孤立波的反向互撞；單一孤立波與單一潛堤互制作 用、兩反向對稱孤立波與單一潛堤互制作用、單一孤立波與兩潛堤互制作 用、兩反向對稱孤立波與兩潛堤互制作用。
 This article utilizes the finite-element method to analyze the wavetransmission, reflection on the free surface and the shear stress on thechannel bottom caused by the interaction of a nonlinear long wave with an off-shore submerged structure. The content first focuses on the process ofdeveloping a general form for the depth-averaged model. By giving the uniformand linear distributions of horizontal velocity profiles, one can solve the depth-averaged continuity and momentum equations to analyze the phenomenon of waves propagation. As compared with the conventional long-wave theory, the dissipative effects included by the Boussinesq equations (BE) for the slowly varying bottom bed have been regained with the process simpler and moreconcise than that in the long-wave theory and with the same form as BE at thecomparable order. The present study calculates a solitary wave interacting with anothersolitary wave, and also calculates a solitary wave interacting with the off-shore submerged structure. From these one can obtain the evolution of the sur-face elevation and the relative variation of physical variables. The numericalmodel which is established by the finite-element method is testified throughgrid-dependency analysis to obtain the optimal grid size dx=0.05 and time stepdt=0.01 to match the accuracy requirement for a solitary wave propagating along a uniform- depth channel. This numerical model is then used to analyze the strongly nonlinear interaction for a solitary wave, with peak up to 0.4 times the water depth, passing over a submerged structure, with height more than a half the water depth. In all, the phenomena analyzed by this article are : a solitary wave propagating along a uniform channel in test cases by using uniform velocity and linear velocity distributions; two symmetrical or unsymmetrical solitary waves interacting with each other in the opposite directions; a solitary wave interacting with one structure or with two structures submerged at the channelbottom; two symmetrical solitary waves in the opposite directions interactingwith one structure or with two structures submerged at the channel bottom.
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 1 孤立波通過直角彎道波場分析 2 孤立波經直立壁防波堤繞射反射波場分析 3 應用不同波浪形態方程組解析初始孤立波傳遞現象 4 孤立波經河川彎道之數值分析

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