Abstract: In this paper,discussing the stability of three classes of steady groundstate in the two-dimensional compressible adiabatic and non-dispersive at mosphere,it is exactly demonstrated that the stability of these groundstates is decided by their engine matrix +:a.the groundst at es are stable if + is positive definite in set G+Γ.b.the groundstates are unstable if + is negative definite in set G+Γ.