Based on the barotropic equations regarding terrain in the z coordinate system, obtaining the first-order approximation by using the small parameter method, and then analyzed shear wave and vortex wave and the relationship between them in theory. It was concluded that the wave caused by the wind shear includes the shear wave, the inertial wave and the gravity external wave, which belong to the two-way scattered wave. When considering terrain slope, the necessary condition of wave stability is related to the square of wave number, the contribution of terrain slope to stability fluctuation depends on the zonal distribution of the basic flow. Without considering terrain slope, the basic flow exists north-south shear and the wavelength is longer, there will be wave instability. Vortex wave instability is a special case of shear wave instability, which means the wave of the shear line develops into low vortex through the unstable development of the fluctuation, and shows that the shear line under certain conditions can induce low vortex, which is conducive to the formation of the extreme weather events.
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