Baroclinic Instability of a Time-Dependent Zonal Shear Flow.

In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss baroclinic instability, not only to apply the potential vortex equation directly, but also to deal with shear of basic flow. The stability and oscillatory shear ability of Rossby waves are studied based on the two-layer Phillips model in the β plane; then, we summarize the baroclinic instability of time-dependent zonal shear flows. The multiscale method is used to eliminate some terms of natural frequency oscillations of nonlinear operators in the third-order expansion, thus generating an equation about the amplitude of the lowest-order Rossby wave in the long-time variable. The large amplitude perturbation begins to decrease, which produces the desired behavior. After the amplitude decreases for some time, the amplitude of Rossby waves can still be found to oscillate periodically with the time variable. [ABSTRACT FROM AUTHOR]