THE STABILITY OF THREE CLASSES OF STEADY BASIC STATES IN THE TWO-DIMENSIONAL COMPRESSIBLE ATMOSPHERE^*

In this paper,the stability of three classes of steady basic states in the two-dimensional compressible adiabatic and non-dissipation atmosphere is discussed,and the following property is exactly demonstrated that the stability of these basic states is decided by their engine matrix A in two ways:(a)the basic states are stable if A is positively definite in set,and (b) the basic states are unstable if A is negatively definite in set.