The influence of topography on the nonlinear interaction of Rossby waves in the barotropic atmosphere

In the frame of weak nonlinear theory, a set of equations depicting the nonlinear interactions of barotropic Rossby waves are derived, the topography and Ekman friction are involved in the equations. Starting from the equations, we investigate the interaction of three Rossby wave packets with narrow-spread in wave vectors. When an intense primary pump Rossby wave with amplitude larger than a threshold propagates through the atmosphere, the amplitude of one Rossby wave packet with scale greater than the primary one and one Rossby wave packet with scale smaller than the primary one grow exponentially through three wave interactions, the intrinsic frequencies of the secondary waves can be varied. The threshold and the variation of the intrinsic frequencies of the secondary waves are related to the Ekman friction frequency dismatch, topography and spatial evolution of the secondary Rossby wave packets.