Effects Of Geostrophic Horizontal Component And Topography On Geophysical Fluid

Belonging to large-scale geophysical fluid, geostrophic effect which results from Coriolis force has a profound impact in many aspects. In recent years, the effects of Coriolis force’s horizontal component in geophysical fluid is attaching more and more attention by researchers, who also point out that the influence of the horizontal component in geophysical fluid could not be completely ignored. Furthermore, the effects of external force and dissipation, such as topography, friction in the geophysical fluid, had been discussed and studied, especially some new factors of global climate change indicating the slow changes of topography over time. Although the changes are not noticeable in short time, its effect in mathematics by space-time transformation analyzing process could not be ignored.On the basis of quasi-geostrophic potential vorticity equation, the nonlinear Rossby waves in the geophysical fluid were investigated in this paper, considering the geophysical horizontal component and the slowly changing topography. The major contents of this paper are as follows:The research status and research methods about the Rossby waves in the geophysical fluid were introduced in the first chapter.Some approximate models for handling of geophysical fluid were presented in the second chapter. Moreover, the quasi-geostrophic potential vorticity equation of geophysical fluid in the baroclinic stratification model and the barotropic model was deduced.The generalized β plane approximation model was adopted in the third chapter. And considering the complete Coriolis force, the nonlinear Korteweg-de Vries-Burgers(Kd VBurgers) equation is deduced by using power series expansion method, which Rossby waves changing over time satisfies. In addition, Rossby waves’ dispersion relation which is combined with Coriolis parameter horizontal component and topography effects interaction is derived.Rossby waves is influnced by large topography, friction and heat effect in barotropic fluid and it was researched in the fourth chapter. The inhomogeneous modify Korteweg-de Vries(m Kd V) equation, which nonlinear Rossby waves amplitude changes over time in the effect of topography, heat, friction and external source, was derived by using reductive perturbation method.A summary of this paper was made in the fifth chapter, and an outlook was also done to the direction for the future researches.