Effects of orography and horizontal diffusion on the generation of the asymmetric motion in the barotropic filtered model atmosphere

By using the barotropic vorticity equation including the effects of orography and horizontal diffusion, the linearized equation describing symmetric motion and that describing antisymmetric motion, and their analytic solutions, are presented. It can be found from the solutions that, regardless of the kind of motion, each solution consists of three waves: Rossby waves related to initial values; marching waves propagating at Rossby wave velocity; and stationary waves. The latter two are closely related to orography and horizontal diffusion. However, if the motion is symmetric at the initial instant, then the antisymmetric components of orography and of horizontal diffusion are likely to lead to the generation of antisymmetric motion. In the steady state, the symmetric flow is connected with symmetric orography and horizontal diffusion, and the antisymmetric flow with antisymmetric orography and horizontal diffusion. To verify the above analysis, three numerical experiments have been made. The results show that