Abstract
A finite difference scheme for solving marching problems is designed. It is a two step iteration to simulate the backward difference method, i.e., first the tentative values at the later time stage are calculated by using the foreward difference and then the correction is made using these quantities. Applying this scheme to oscillatory equations, the high frequency oscillation is shown to be damped under certain conditions. Numerical integrations of the primitive equations for the so-called divergent barotrophic model were carried out by making use of this scheme. The result show that, because of an unbalanced initial state, gravity waves of fairly large amplitudes are initially generated. However, they are damped out with the lapse of time, while the quasi-geostrophic part of motions is kept less disturbed. For comparison, calculations were made for the same model and for the same initial conditions, by applying both the present method and the centered difference method commonly used. The two patterns thus calculated coincide in main features but differences are found in the distribution of divergence, especially near the boundary of the integration domain.
