應用間接特徵匹配法模擬波浪之布拉格共振

Abstract

本文將應用（蔡等，2011）所發展之間接特徵函數展開法（indirect eigenfunction matching method, IEMM）模擬波浪通過沙漣底床或是複合式沙漣下其反射率與透過率之變化。此法不但改良傳統階梯近似法（Takano, 1960）之計算上效率不彰的缺點，更能任意退化成轉換矩陣法（Miles, 1967）與平面波近似法（Lamb, 1937）。倘若假設任意底床剖面可以視作一連串垂直階梯所組合，每個階梯面上均滿足速度連續與壓力連續條件，則波浪與結構物之間的波場變化可藉由一連串包含水平速度的未知係數所組成之方程組聯合解之。不同於一般緩坡方程式受限較陡或是曲率較大之底床地形，IEMM均可對波浪作用於任意底床地形給予精確的與廣泛的計算。另外，本文在探討波浪通過沙漣底床與系列潛堤之布拉格共振現象中，發現IEMM的解可穩定快速收斂，而且較一般緩坡方程式的數值解精確許多。An indirect eigenfunction matching method (IEMM) which can be arbitrarily reduced to plane-wave approximation (Lamb, 1937) and transfer-matrix method (Miles, 1967) was developed by (Tsai et al., 2011). The matching conditions are represented by the horizontal velocities at the steps in the solution procedure if the bottom profile is in terms of successive flat shelves separated by abrupt steps. The approximated wave field is thus obtained by solving a system of linear equations with unknown coefficients which represents the horizontal velocities under a proper basis. In this article, we are going to study waves propagating over a sinusoidally ripple bed and a doubly-sinusoidally varying topography by IEMM. Furthermore, The present model would be also compared with other method. The Bragg resonance would be discussed as well.