Abstract
The influence of topography and the planetary \(\beta \) effect on the linear stability of barotropic vortex and two-layer baroclinic vortex by considering cylindrical topography and vortex with stepwise relative vorticity profiles in the quasi-geostrophic approximation. After considering the planetary \(\beta \) effect, it is found that the planetary \(\beta \) effect has a great influence on the instability of middle and high latitude vortex. In the barotropic mode, the dipoles formed by unstable regions under the influence of the planetary \(\beta \) have a tendency to block westward movement. In baroclinic mode, the upper dipole is gradually destroyed and squeezed the upper dipole.
