On the Solutions of the Primitive Equations of Motion in the Atmosphere

[摘要] It is first demonstrated that the solutions of the primitive equations of motion in both barotropic and baroclinic atmospheres which do not include noticeable meteorological noise can be derived by the perturbation method on the basis of usual geostrophic equations.Namely, the order of magnitude of each term in the equations of motion is estimated using the Rossby number, and the necessary solutions are expanded in the power series of the Rossby number. When the power series does not converge, a method how to treat is then shown especially for the balance equation and this method gives a new method solving the balance equation. It is next shown that when numerical integration is executed by the difference method, particular attention should be paid for an appearance of the secular term. And it is finally shown that though the total energy is conserved in the closed quasigeostrophic system but it is not conserved without neglecting the quantities of order of the Rossby number in the higher approximate system.

[学科分类] 大气科学