Topography and the Non-linear Rossby Wave in the Zonal Shear Basic Flow

Under semi-geostropical approximation, by means of phase angle function the non-linear ordinary differential equation is derived involving topography and zonal shear basic flow. Conditions for the existence of limited amplitude periodical and isolated wave solutions are directly obtained based on the qualitative theory of the ordinary differential equation. Analysis is thus made of the influence of topography and zonal shear flow on the existence of wave solution. Finally, explicit wave solutions are determined by function approaching with the result that topography and zonal shear flow affect not only the existence but also the form of waves, indicating the non-linear features of waves and the effect of topography and shear basic flow on undulation.