Non-linear waves in an atmospheric model

Weather forecasts are part of everyday life. People use them to decide on clothing, holiday destinations and as subject of conversations. Nowadays the forecasts are quite accurate up to a week ahead, whereas thirty years ago one could only rely on 2-days forecasts. Of course the results of the forecasts are easy to grasp, but how about the methods to obtain those results, e.g. the underlying theory? In chapter 2 we will state the governing equations of atmospheric flow. A physical aspect of the system, called the Coriolis effect, will then be described in more detail. After this we start looking for well-behaving solutions; traveling waves. This is done by transforming the system into new coordinates and manipulating the system in such way that we only need to solve one equation. In section 3 we obtain some qualitative results about waves under various conditions using phase plane analysis. Special attention is paid to connections between equilibrium points. Stability of the...Show moreWeather forecasts are part of everyday life. People use them to decide on clothing, holiday destinations and as subject of conversations. Nowadays the forecasts are quite accurate up to a week ahead, whereas thirty years ago one could only rely on 2-days forecasts. Of course the results of the forecasts are easy to grasp, but how about the methods to obtain those results, e.g. the underlying theory? In chapter 2 we will state the governing equations of atmospheric flow. A physical aspect of the system, called the Coriolis effect, will then be described in more detail. After this we start looking for well-behaving solutions; traveling waves. This is done by transforming the system into new coordinates and manipulating the system in such way that we only need to solve one equation. In section 3 we obtain some qualitative results about waves under various conditions using phase plane analysis. Special attention is paid to connections between equilibrium points. Stability of the solutions will be discussed briefly in section 4. In section 5 the model used in the first sections is compared to an other model; the Eady model. The Eady model uses a slightly different approach but will turn out to also be quite similar.Show less

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Non-linear waves in an atmospheric model