The oscillation between Rossby wave and zonal flow in a barotropic fluid

The eigenvalue approach is adopted to study briefly the linear barotropic instability of Rossby wave motion. It is discovered that the doubling time of barotropically unstable Rossby wave motion is quite realistic provided the amplitude of basic Rossby wave motion is calculated depending on the order of magnitude of meridional wind, permitted by the synoptic scale of motion. The main object of the present study is to deal with the quasi-linear barotropic instability of Rossby wave motion by including the nonlinear product term of perturbation in the basic flow equation. It is found that there is a regular periodic oscillation between the basic Rossby wave motion and the perturbation zonal flow. The oscillation occurs on the time scale of "weeks" which is in agreement with observational facts