Dynamics Research Of Nonlinear Rossby Solitary Waves Under The Influence Of Unsteady Disturbance

Since J.S.Russell observed the solitary waves firstly, the research on solitarywaves has become an advanced subject in mechanics, physics, applied mathemat-ics, atmospheric and oceanic sciences and so on, and has significant theoreticaland real meaning. The research on Rossby solitary waves is an important branchof the theme.In this thesis, the generation, evolution, interaction of Rossby solitary waveswhich excited by unsteady perturbation in barotropic and stratified fluid of difer-ent depth are investigated by employing the method of combination of theoreticalanalysis, symbolical computation and numerical simulation, especially here dissi-pation efect is considered. The former research commonly focused on the efectof steady perturbation on the Rossby solitary waves, while in the paper we con-sider the efect of unsteady perturbation on the generation, evolution, interactionof Rossby solitary waves, which has important theoretical and application value.Firstly, for the inviscid, incompressible barotropic fluid of diferent depth,from the quasi-geostrophic vorticity equation including topography and dissipa-tion, with the help of the perturbation method and stretching transform of timeand space, one-dimensional models governing the amplitude of Rossby solitarywaves are derived. By using the Jacobi elliptic function expansion method andperturbation method, the analytical solutions of corresponding homogeneous e-quations of the above models are obtained, the speed, dissipation efect and so onof Rossby solitary waves are discussed and the conservation laws of Rossby soli-tary waves are derived. By virtue of the pseudo-spectral method, the numericalsimulation of models are carried out. With the help of these water-fall plots, theefects of topography(unsteady topography, wavy topography) on Rossby solitarywaves are discussed under diferent states(resonant state, supercritical state, sub-critical state). The discussion can be used to explain the ocean phenomenon thatthe wavy bottom forcing can prevent wave breaking to some extent.Next, the inviscid, incompressible stratified fluid of diferent depth is con- sidered. By using the same method and procedure, the models governing theamplitude of Rossby solitary waves in the stratified fluid are derived. Comparingwith the former models, the nonlinearity is stronger in these models. Some ofthem are the generalization of the former models. By numerical simulation, theefect of unsteady external source on Rossby solitary waves are discussed and theblock and oscillation phenomenon which happen in ocean and atmosphere areexplained.Finally, the two-dimensional Rossby solitary waves in barotropic fluid arestudied. Similar to the previous chapters, the two-dimensional classical Rossbysolitary waves model with dissipation efect is derived. The conservation laws oftwo-dimensional Rossby solitary waves are analyzed. By employing the sin andcos function method, the periodical solutions and the solitary-wave-like solutionsof model are obtained. By virtue of the analytic solution, the efect of dissipa-tion on the amplitude, speed and width of Rossby solitary waves is researched.Meanwhile, the research of two-dimensional algebraic Rossby solitary waves isfirst carried out, and the modified two-dimensional BO-Burgers model, modifiedtwo-dimensional ILW-Burgers model are derived. It enlarges the research scopeof two-dimensional Rossby solitary waves model. The research in the paper is abeneficial supplement for nonlinear Rossby waves dynamics.