THE STABILITY AND CATASTROPHE OF NONLINEAR STRATIFICATION SYMMETRIC MOTION IN THE NONHYDROSTATIC BALANCE ATMOSPHERE

In this paper,based on the assumption of the geostrophic wind with linear horizontal and vertical shear,a nonlinear ordinary differential equation is constructed considering the atmospheric stratification with linear and nonlinear vertical shear.Furthermore,the instability criteria of nonlinear strutification symmetric motion have been obtained by discussing the convexity of Hamilton's function,and the catastrophe condition of nonlinear stratification symmetric motion is discussed.