Study On Topographic Rossby Solitary Waves Based On Fourier Spectrum Method

In this thesis,the effect of topography on barotropic Rossby solitary waves is discussed.The Korteweg-de Vries(Kd V)and Boussinesq equations of nonlinear Rossby wave amplitude evolution are derived by means of Gardner-Morikawa transformation and perturbation expansion.The shooting method is used to solve the Sturm-liouville equation with fixed boundary conditions and the Fourier spectrum method is used to solve the Kd V and Boussinesq equations.Based on the numerical solutions of the equations obtained and the qualitative and quantitative analysis of the changes of the images when the parameters of the terrain change,the results show that,both the bottom topography and the rotation of the Earth have important effects on the propagation of nonlinear Rossby solitary waves.