| In the atmosphere and ocean, there are already many important results for nonlinear Rossby wave. This thesis just focused on some problems about nonlinear Rossby waves.Content of this thesis is divided into three parts. The first part is to introduce the research progress in Rossby waves. The second part is to introduce some preliminary knowledge:basic equations, Jacobi elliptic functions and solutions of Kdv equations. There are two sections in the third part. The first section is to deal the research object, which is based on Rossby wave of a nonlinear Boussinesq model with basic flow. We studied travelling wave equations by the method of semi-geostrophic approximation. Then we used Taylor scries expansion to isolate the characteristics of the linear Rossby wave, and identified the Rossby wave elliptical cosine wave and solitary wave. Finally, the influence of the basic flow for nonlinear Rossby wave is analysed; In the second section, the model of modified Burger with basic flow is studied, the travelling wave solutions and Taylor scries expansion method are adopted.We obtained the analytical solutions of ultra-long wave. |
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