中层大气受迫 Rossby 波包的非线性相互作用Ⅰ.理论分析

本文研究了中层大气受迫Ｒｏｓｓｂｙ波包非线性三波相互作用问题．理论分析得出，如果仅有最大波长或最小波长的波包受外源作用，系统仅能维持受迫波包的运动，平衡状态下外源能量不向另两个波包传递；仅有中等波长波包受外源作用时，随着外源强度的增加，系统的平衡态会发生分岔，并且在分岔点以后，中等波长波包的波幅不再增大，但大气高度愈高该振幅饱和值愈大，外源增大的能量全部通过非线性相互作用馈送给其他两个波包，从而外源可以维持三个波包的长期等幅运动．本文还给出了系统中有两个受迫Ｒｏｓｓｂｙ波包时系统的平衡态和稳定性条件，这时无论三个波包的尺度关系如何，外源能量均能在三个波包之间传递，因此外源也可以维持三个波包的运动．进一步的结果和波包的演化过程将通过数值计算给出．

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.