非穩態慣性流於可變性多孔介質之渠道

Abstract

本論文目的在於研究當淺水波通過一變動多孔介質層的發展。一個有特色的例子為潰壩問題所造成的波將分別在兩方向形成反射以及透射。論文其中包含理論的推導、實驗的方法、影像分析過程以及數值模擬。再推導統馭方程式過程中我們將會引進如何用漢米頓最小作用量原理說明附加質量的影響。影像分析過程中我們將會提供一個解決鏡像扭曲的簡單2D處理方式，除此之外我們將會呈現如何使用活塞完成無壩堤之潰壩實驗。最後將會使用實驗結果以及數值模擬結果去將慣量以及附加質量特性化在於波的發展過程。

The goal of the present thesis is to investigate shallow water flows propagating through a medium of variable porosity. One particular case considered is a dam-break wave partially reflected and transmitted at a vertical porous boundary. The contents of this thesis include the derivation of governing equations, experimental methods, image analysis and the numerical modeling. In the derivation of the governing equations we will introduce how to use the Hamilton’s principle of least action to account for added mass effects. Image processing will offer some sample way to solve the radial distortion problem in 2D. Besides, we will show how to use piston to do dam-break experiment without using a sluice gate. Finally, we use experimental and numerical results to characterize the influence of inertia and added mass on the wave propagation.