Study On The Effect Of The External Source And Thf Horizontal Component Coriolis Force On The Nonlinear Rossby Waves

In this thesis,the nonlinear wave problems of the Rossby solitary waves are investigated by employing the method of combination of the scale analysis,the theoretical derivations and symbolic computations.On the one hand,the amplitude evolution of the Rossby solitary waves are considered with the "Traditional Approximation" and the spheres effect of the Earth's rotation.On the other hand,starting from the quasi-geostrophic potential vorticity equation with the complete Coriolis force,including the dissipation,the external sources and the generalized beta effect,with the help of the perturbation method and reductive perturbation method,the various mathematical models for the amplitude evolution of the Rossby solitary waves are derived.By using the generalized Jacobi elliptic function expansion method,perturbation method and trial function method,the analytical solutions of the corresponding equations the above models are obtained and analyzed the effects of various factors on the generation,evolution,interaction of Rossby solitary waves,the specific content has the following parts.Firstly,for the inviscid,imcompressible barotropic fluid from quasi-geostrophic vorticity equation with the "Traditional Approximation" and the generalized ? plane approximation condition,the KdV equation is presented by using reductive perturbation method and the perturbation method considering the influence of the external source.Then,the(2+1)dimensional Zakharov-Kuznetsov(ZK)equation with the external source is derived by using similar method.Further,ZK-Burgers equation also is obtained.The solitary wave solutions of the corresponding equations the above models are obtained by using the generalized Jacobi elliptic function expansion method and sine-cosine method,the effects of the generalized beta plane approximation,dissipation and the external source are analyzed on the Rossby solitary waves.Secondly,starting from the quasi-geostrophic potential vorticity equation with the complete Coriolis force,including the dissipation,the external sources and the generalized beta effect,the one-dimensional mathematical models are derived by similar method,the results are the traditional approximation extension.Then,the solitary wave solutions of the corresponding models are obtained by using the generalized Jacobi elliptic function expansion method and perturbation method.Further,considering the characteristics of the multi-temporal scale of the earth fluid,the nonlinear Schrodinger equation and the nonlinear Schrodinger equation with the dissipation are obtained with the help of multiple scales and perturbation expansions.Then the solitary wave solutions are studied by using trial function method.The solutions are simulated by using MATLAB software,the results reveal that the horizontal component of the Coriolis parameters,the external source and the dissipation affect the phase speed,the breadth and the frequency on the Rossby solitary waves.At last,starting from the quasi-geostrophic potential vorticity equation with the complete Coriolis force including dissipation,the external sources and the generalized beta effect,the(2+1)dimensional Rossby solitary waves are derived by perturbation method and reductive perturbation method.Similar to the previous chapters,the solitary wave solutions of the corresponding models are obtained by using the generalized Jacobi elliptic function expansion method and perturbation method.By virtue of the analytical solution,the effect of the horizontal component of the Coriolis parameters,the external source and the dissipation is researched on the phase speed,the breadth and the frequency of Rossby solitary waves.