Research On Nonlinear Rossby Wave With Complete Coriolis Force And The Slowing Terrain

In this thesis,the nonlinear wave problems of the Rossby solitary waves are investigated by employing the method of combination of the scale analysis and the theoretical derivations.The amplitude evolution of the Rossby solitary waves are considered with complete Coriolis force and the spheres effect of the Earth’s rotation.On the one hand,in positive fluid,based on the geostrophic vorticity equation with complete Coriolis force,the amplitudes of Rossby wave in the slowedterrain of tangential zonal flows are deduced by the perturbation method,which satisfies the nonhomogeneous mKdVBurgers equation.The solitary wave solutions of the corresponding equtions the above models are obtained by using the generalized Jacobi elliptic function expansion methods and the effects of various factors are analyed on the Rossby solitary waves.On the other hand,the non-homogeneous BDO-Burgers equations with slowly varying topography are derived using the spatio-temporal elongation change,which involves the twodimensional terrain.The results show that the horizontal component of Coriolis force will have a certain influence on Rossby wave with the change of time.At the same time,the β effect,shear elementary stream and terrain effects are important factors to induce Rossby waves.