海床地形如何影響水波行進之研究

Abstract

在流體動力學中，研究水波是一個很重要的主題。在我的論文裡，我所考慮的是一個二維理想流體，在適當地加入不可壓縮的性質以及忽略黏滯力的影響下，重新簡化這個問題。雖然目前已經有許多數值還有實驗的方法提出，但是這些方法有時候並沒有辦法賦予我們較顯而易見的物理意義。更由於，這類問題所會遇見較麻煩處理的邊界條件還有不特定的地形起伏。所以我在這裡使用微擾法以適當選取邊界條件下所得的格林函數去幫助我解得較一般的解析解。同時，把所得的解析解和前人的結果做一些比較。

Surface gravity wave has long been an important topic in the study of hydrodynamics. Here, we consider a two-dimensional surface wave for an incompressible, inviscid fluid and pay special attention to its interaction with the topography at the bottom. We use a Green’s function approach coupled with an appropriate perturbation calculation to compare with previous works, which involve experimental study, numerical simulation, or very cumbersome theoretical calculations that usually do not directly tell what is going on in a physically intuitive manner. Our aim in this work is to give a physically more appealing approach that can complement the works done by previous researchers. We also apply our approach to definite problems for comparison.