Abstract: 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 fric-tion are involved in the equations. Starting from the equations,we investigate the in-teraction 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 greaterthan the primary one and one Rossby wave packet with scale smaller than the primaryone grow exponentially through three wave interactions,the intrinsic frequencies of the secondary waves can be varied, The threshold and the variation of the intrinsic frequ-encies of the secondary waves are related to the Ekman friction frequency dismatchtopography and spatial evolution of the secondary Rossby wave packets.

Key words: composed incompressible hyper-elastic material, finite deformation dynamics, cavity formation, nonlinear periodic oscillation, topography, Rossby waves, non-resonant parametric instability