Some characteristics of barotropic atmosphere are illustrated by numerical modeling, basing on a potential vorticity equation with forcing, dissipation, and non -linear interaction. For the barotropic potential vorticity equation (named the barotropic model) on a β-plane channel its solution is a stationary, wave-like pattern under a certain thermal forcing, while a quasi-periodic oscillation betw een two essential flow patterns appears if north-south thermal heating and wave- like topography are added as the model forcing. The oscillation has a period abo ut 15d, very similar to atmospheric index cycle in middle and high latitudes. Th e low-index pattern corresponds to a blocking flow, whereas the high index one i s an intensive westerly flow. More oscillation solutions are expected when the e quation is under periodic boundary condition with a strong thermal forcing, and a similar quasi-periodic solution can be obtained, which also results from a wav e topography forcing. However, its low index pattern is symmetrical, and differe nt from the blocking pattern produced by the β-plane model. When the heating fo rcing becomes weak, there also exists a stationary solution. Therefore, the char acteristics of atmospheric index cycle may not be soundly manifested by an analy tical solution or numerical solution under periodic boundary condition using low -order spectrum method that approximates the barotropic model in the β-plane ch annel.