Abstract

fulfilment of the requirements for the Degree of Master of Science. I confirm that this is my own work and the use of all material from other sources has been properly and fully acknowledged. i Acknowledgements I would like to thank my supervisor, Maarten Ambaum, for his help and encouragement throughout this project. I am extremely grateful for his guidance and useful suggestions. Thanks also to my family for their support, and to all the other M.Sc. students for making this year so enjoyable. Special thanks to Dan for cooking me numerous dinners and picking me up from the department whenever I’ve worked here after dark. This dissertation and my year of study at Reading University has been financed by the National Environmental Research Council. ii The generation of gravity waves by topography is examined in this study. These waves are important in the atmosphere on all scales. Their interaction with the mean flow has implications for global atmospheric circulation. They also feature prominently in localised weather in mountainous or hilly regions. The equations of motion for an homogeneous layer of fluid flowing over a symmetric, one dimensional, isolated mountain are studied and it is found that there is a critical mountain height above which the solution becomes discontinuous. An expression for this critical height is derived. A numerical model is developed to solve the nonlinear shallow water equations in a homogeneous layer and the results it produces are compared with established results. The theory of stratified flow is presented. The effect of approximating continuous vertical profiles of buoyancy frequency and velocity by a finite set of discrete layers is discussed and this multilayer approach is further investigated with the aid of an extension of the single layer numerical model written by the author. The results are compared to established solutions and suggestions are put forward for further work. Contents 1

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