Based on a barotropic vortex model, generalized energy-conserving equation was derived and twonecessary conditions of basic flow destabilization are gained. These conditions correspond to generalizedbarotropic instability and super speed instability. They are instabilities of vortex and gravity inertial waverespectively. In order to relate to practical situation, a barotropic vortex was analyzed, the basic flow of which issimilar to lower level basic wind field of tropical cyclones and the maximum wind radius of which is 500 km.The results show that generalized barotropic instability depending upon the radial gradient of relative vorticitycan appear in this vortex. It can be concluded that unstable vortex Rossby wave may appear in barotropic vortex.
In this paper, we discusses the spectrum distribution of baroclinic disturbances in tropical cyclone-scale vortices with the assumption that the basic flow does not vary with height. The semi-circle theorem for the unstable perturbation is obtained and the upper bound of growth rate can be estimated. The upper bound of instability growth rate increases with the increase of the maximum basic-state tangential wind speed, angular speed, inertial parameter, absolute vorticity, radial gradient of absolute vorticity and static stability. The upper bound of instability growth rate is greater for vortices of larger horizontal scale and smaller vertical scale and lower wave-number disturbances.
A three-layer theoretical model was established, in which the atmosphere is divided into three layers based on the Scorer parameter 12 , which is large in the middle layer and small in the other two layers. The wave number formula of lee waves was deduced with this theoretical model, and a typical example for the lee wave was calculated. Thus, the influence of changes in the thickness of every layer and values of the Scorer parameter in every layer was examined. The results show that the wavelength decreases with an increase in the thickness of the lower and the middle layers and is more sensitive to the changes in the middle layer. Therefore, if the changes in these two layers are different, the changes in the middle layer will dominate the changes in the wavelength. The results also show that the wavelength decreases with the increase in the value of 12 in every layer, among which the sensitivity to the 12 in the upper layer is the most striking. The calculation results reasonably can explain the influence of diurnal changes on the wavelength. The example was simulated using Advanced Regional Prediction System model, and the sensitivity experiments were performed to confirm the effects of the Scorer parameter profiles on the wavelengths. The simulated results are consistent with the calculated results.
