Abstract
The truncation error of difference solutions of the barotropic vorticity equation is considered, and it is shown that the physical phase velocity of the difference solution of the linearized vorticity equation becomes smaller than that of the true solution as an effect of use of the space difference, and larger as an effect of the time difference. And a method eliminating the computational noises which originate from the time difference is given. Some considerations on the truncation error of the non-linear term are also presented. Next, approximate solutions by the perturbation method are considered, and as an example of this method the problems on the energy exchange between the disturbances and general current are discussed. In the case of the long wavelength disturbances good approximate solutions can be obtained, but in the case of the shorter wavelength disturbances it is not. Asnecessary conditions for obtaining the approximate solutions, the laws of the kinetic energy conservation and the momentum transfer on the variation of the general current are adopted.
