截谱模式方法与大气中的多重平衡现象

本文在介绍截谱模式方法的基础上,以强迫耗散的非线性准地转方程为例,用解析方法讨论了不同截断水平下模式方程对多重平衡态的影响。看出,截谱模式方法的最大成功之处在于揭示了大气中多重平衡现象。利用此法可将模式方程转化为耦合常微分方程组。特别是讨论平衡态时,归结为对代数方程的讨论。这就为揭示多重平衡现象和应用突变理论展示大气中突跳现象提供了可能。通过讨论也证实:随着截断水平的加大,平衡态分枝数随之增多,最终将进入“浑沌”状态。

The Method of Truncated Spectral Model and the Multiple Equilibration Characteristic in the Atmosphere

In the paper a method of truncated Spectral expansion is presented for the governing equation of the model. By means of the nonlinear quasi-geostrophic equation with forced disspation, We investigated that, several truncated levels have an influence up the multiple equilibration state. It is shown that, the method of truncated Spectral model clealy exhibits great excellence for establishment of the multiple equilibration phenomenon in the atmosphere. And we demsnstrated that, when truncated level was increased the number of bifurcation on the equilibration state increased all together. Finally it may appear a "chaotic behavior".