Abstract
When a system of the primitive equations of motion, the thermodynamic equation andthe continuity equation is expressed in the nondimensional form, the Rossby number and the Richardson number will appear in the coefficients of these equations as parameters. It is well known that when the solutions of the system are expanded into the power series of the Rossby number, zero order solutions of the Rossby number correspond to the quasi-geostrophic solutions. But in this paper, it is shown by using the linearized system that the exact criterion of the baroclinic instability is determined by the first order solutions which is one order higher than the quasi-geostrophic solutions. It is also shown that when the horizontal gradient of the static stability in the basic current is taken into account, unstable waves exist in both the very long and the very short wavelength regions, besides the well-known unstable wavelength region.
