具有溼度和對流的大氣淺水波方程式的邊界問題之研究

Abstract

本計畫研究，我們主要是想從理論研究探討和數值模擬驗證的觀點來研究具有溼度和 對流的單層和雙層大氣淺水波模式的邊界值問題。本計畫的模式探討中，為了增加對 大氣動態的更加了解，引進在天氣預測和大氣研究中兩個重要的物理因子(溼度和對 流)。 本計畫研究的目的有兩方面:首先，我們將研究這個模式在提出邊界條件下數學的可解 性;之後，我們也將提出適當的數值方法來驗證所以提出的邊界條件的適切性。

In this research proposal, we intend to study boundary value problems for one-layer and two-layer shallow water models of the atmosphere with moisture and convection from the from the theoretical and computational point of view. In this project, to have better understanding of the large-scale atmospheric dynamics, the moisture effect and convection which play an essential role in the weather and climate are considered. Our goals are two-fold: first, we will study the well-posedness of the systems with the proposed boundary conditions; secondly, we will propose suitable numerical methods to demonstrate the suitability of the proposed boundary conditions.