Research On Nonlinear Rossby Wave With Complete Coriolis Force

Rossby solitary wave is one of the major fluctuations of atmospheric and oceanic movement,and are intrinsic in the large-scale systems of fluid.Based on the quasi-geostrophic potential vorticity equation with complete Coriolis force,the evolution of the nonlinear Rossby waves including the two contents of this thesis:In the first place,in barotropic fluids,the evelution of the amplitude of Rossby wavepacket with the zonal weakly shearing and nonslowly,satisfies the nonlinear Schrodinger equation.The results show the horizontal component of the complete Coriolis force has some effects on the Rossby wave packet,at the same time,beta effect and topographic effect are also important to the Rossby wave packet.And the eigenvalue problem of the basic flow in the presence of linear weak shear is also considered.In the second place,using reasonable approximation of the equatorial ? plane,the evolution of the amplitude of the nonlinear Rossby wave under the effect of topography and dissipation satisfies the inhomogeneous Benjamin-Davis-Ono-Burgers(BDO-Burgers)equation by employing the perturbation method and stretching transforms of time and space.Results by example show the effects of the horizontal component of the Earth's rotation and the underlying surface on Rossby waves.The equation can be reduced to the results of former in special cases.