海-气振荡子的动力行为与不稳态演化的研究

DYNAMIC BEHAVIOR AND UNSTABLE STATE EVOLUTION OF OCEAN-ATMOSPHERE OSCILLATOR

从数学上严格证明了非线性随机海-气振荡子模型存在一个稳定的极限环;随后转换成Fokker-Planck方程(FPE),从非平衡系统动力学角度首次研究ENSO从不稳态向稳态演化的问题。研究表明:(1)当初始处于不稳定的状态向稳态演化时,在最不稳定流型的决定下,系统只向一对对称的稳态演化,一稳态释为准正常的气候状态;另一稳态释为异常气候状态,即强ENSO状态;(2)若初始条件分布不在原点,由确定性方程可知,系统将向反对称的稳态演化,但在随机力的作用下,产生了与确定系统有本质区别的结果,即当t→∞时,绝大部分概率仍然对半地分布在对称势井内,而反对称势井内几乎不存在概率分布,计算结果与观测事实相吻合;(3)从动力学宏观理论上来看,准气候正常态与强ENSO是两个平衡态,遵循统一的动力学理论框架,它们有相同的时空尺度;ENSO是南方涛动和El Ni^no循环的统称,将它们纳入统一的框架体系来研究,说明它们的合理性;但从微观理论上看,南方涛动、El Ni^no和La Nina三者又反映出气候不同的位相,如何反映出El Ni^na和La Nina位相转换等,应建立它们本身的动力学框架。

It is mathematically and thoroughly proved in this paper that the nonlinear stochastic ocean-atmosphere oscillator model possesses a stable limit cycle; then the model equations are transformed into the Fokker-Planck equation （FPE）, and the evolution of E1 Nifio-Southern Oscillation （ENSO） from unstable state to stable state is studied from the point of view of nonequilibrium system dynamics for the first time. The system evolution from an initially unstable state to a steady state has been studied in this paper in terms of FPE expansion theory, and under the dominance of the most unstable manifold the system evolves towards only to a pair of symmetric steady states： one is considered as quasi-normal climatic state, and the other as anomalous climatic state, i.e. strong ENSO state. This study indicates that even if the initial distribution is not at the origin state, known from the deterministic equations the system will evolve towards antisymmetric steady states, however under the effect of stochastic forcing, the system exhibits intrinsic differences from deterministic systems, i.e. when t→∞, the overwhelming majority probability still distributes half-and-half in a pair of symmetric potential wells, and there is almost no probability distribution in a pair of antisymmetric potential wells. This is in consistent with observational facts. Viewed from dynamic macro-theory, quasi-normal climate state and strong ENSO state are two equilibrium states, follows an unified dynamic theoretical framework, and have the same temporal/spatial scales; ENSO is a joint name of Southern Oscillations and El Nifio cycles and bring them into an unified framework system in study is reasonable. However viewed from dynamic micro-theory, Southern Oscillations, El Nino and La Nina reflect different phases of Climate, in order to reflect the phase transition between El Nifio and La Nina, it is necessary to establish their dynamic frameworks respectively.