Solitary Rossby Waves With Slowly Changing Topography And Forcing Dissipation In Stratified Flows

Rossby solitary wave is one of the major fluctuations of atmospheric and oceanic movement, and are intrinsic in the large-scale systems of fluid, in this thesis, the equations of Rossby waves in stratified fluid are derived from barotrophic quasi-geostrophic vorticity and lower boundary with slowly changing topography by using perturbation method and stretching transforms of time and space. First, we deduced the vorticity equation and lower boundary condition with generalized β plane approximation, then converted them into non-dimensional form and get the non-dimensional governing equation and boundary conditions, Then, long time and space scales are introduced. At last, the amplitude of Rossby waves is discussed under the long time and space variableξ、τ by using perturbation method.On the basis of quasi-geostrophic potential vorticity equation, the nonlinear Rossby waves in the geophysical fluid were investigated in this paper, considering the slowly changing topography、dissipation and external heating source.the major contents of this paper are as follows:In the first chapter, The research status and research methods and background of the research about the Rossby waves in the geophysical fluid were introducedIn the second chapter, Some approximate models for handling of the geophysical fluid were presented, Moreover, the quasi-geostrophic potential vorticity equation of the geophysical fluid in the baroclinic stratification model、the barotropic model and slowly changing topography in the lower boundary condition was deduced.In the third chapter, The generalized β plane approximation model was adopted, The β-plane approximation f=f_o+β(P_o is a constant) is extended into f=f_o+P_o(y)y, which include a nonlinear function βo(y) taking the place of β in the (3-plane approximation. Such an approximation can depict more precisely the motion of atmosphere and ocean, especially in the middle and high latitude regions, considering slowly changing topography in the boundary condition, the nonlinear KdV-Burgers equation is deduced by using perturbation method and stretching transforms of time and space method,which Rossby waves changing over time satisfies, the solution of solitary waves of KdV and mKdV equation and the time evolutions of the mass and the energy of the solitary waves are analyzed.In the four chapter, A summary of this paper was made and an outlook was also done to the direction for the future researches.