Semicircle Theorem on the Spectral Distribution in Symmetrical Instability with Wave-Cisk
WAVE-CISK对称不稳定谱点分布的半圆定理

The spectral distribution of symmetrical distribution with Wave-CISK under anelastic approximation is studied. The semicircle theorem on the spectral distribution in symmetrical instability with Wave-CISK is obtained. The theorem can estimate the supremum of the growth rate of the instability. It is found that under Wave-CISK, the heating feedback and stratification stability parameter have important influences on the growth rate. The stronger the heating feedback and vertical shear of basic flow, the larger the supremun of the growth rate. Also the simpler the structure of disturbance in vertical direction, the larger the supremum. Condition to make symmetric instability under the anelastic approximation is harsher than under Boussinesq approximation.