| This thesis describes a mathematical study of the evolution of Rossby waves in the atmosphere. These are large scale waves that result from the Earth's rotation. Analytical methods including Laplace transforms, multiple scaling and asymptotic expansions are used to obtain approximate solutions that describe the propagation of the waves. Each fluid variable in the governing equation is written as the sum of a basic steady term and a time dependent perturbation. In previous related studies the basic flow was considered to be a function of the latitude only, but in this thesis we study a configuration where the basic flow varies slowly with respect to the zonal variable. This is a more realistic representation of the general circulation of the real atmosphere. The governing equation includes these small parameters and depending on the relative magnitude of these parameters the problem can be linear or nonlinear. We consider the scalings that lead to linear problems and derive an approximate solution in each case. These approximate solutions describe interactions between the waves and the basic flow. |
