THE NONLINEAR INTERACTION OF FORCED ROSSBY WAVE PACKETS IN THE MIDDLE ATMOSPHERE I.THEORICAL ANALYSIS

The problem of the stability of the forced Rossby wave packets which are nonlinearly interacted resonantly in the middle atmosphere is examined analytically.The expression of the stationary state and the condition of the stability are given.When there is only one forced wave packet, if its lengthscale isn't between that ofthe other two, the forced wave will not translate its energy to the others in thestationary state, the others are exhausted by Rayleigh friction. But if the wavelengthof the forced wave is between the other two, the stationary state bifurcates to another stable one as the intensity of the forcing increasing to some value. After thebifurcation, the amplitude of the forced wave will not vary with the forcing, but itincreases with the atmosphere height, the energy increased is translated to otherwave packets eventually. When there are two forced wave packets, the system willtend to stationary states with nonzero wave amplitudes of all three wave. Moreresults will be given through numerical analysis.