海气耦合振荡非线性动力系统的平衡态研究

本文利用一个正压地形强迫准地转方程与表层海温方程联立,在大尺度洋流可用Sverdrup流近似的假设下来封闭方程组。在这样一个海气相互作用系统中,考虑了海温场加热大气及大气环流通过风生流再分布海温场的两个基本过程。在低阶截谱及多尺度方法的简化下,建立一个海气耦合系统。并对耦合系统作相空间分析,解析地求得海气系统中的两类稳定的平衡态。指出由此可以解释一些长期环流异常的特征。     

INTERACTION OF FORCED WAVE, FREE WAVE AND ZONAL FLOW (Ⅰ)——BIFURCATION OF THE EQUILIBRIA——BIFURCATION OF THE EQUILIBRIA

In this paper, two level quasi-geostrophic model is used to set up a simple nonlinear inter-action model including a near resonant forced wave component, a near baroclinically un-stable free wave and a zonal flow component. The dynamic mechanisms of the transition ofhigh and low index and index cycle are discussed. In the first part, the weak nonlinear problem with near baroclinic instability and nearresonant forcing are analysed. The simple periodic solution resulting from bifurcation ofHadley cell to Rossby transient wave and the more complicated solutions resulting from thebifurcation of the wave equilibria to mixed state with both forced stationary wave and tran-sient wave are discussed.     

THE INTERACTION BETWEEN FORCED WAVE,FREE WAVE AND ZONAL FLOW(Ⅱ)——QU ALITATIVE ANALYSIS FOR THE TRANSITION AND oSCILLATION OF HIGH AND LOW INDEXES

In this second part, the so-called "discontinuous vibration analysing" method is used to discuss the qualitative features of the solutions in the system set up in Part I. The system and the phase space are divided into two subsystems and two subspaces, which are corresponding to the slow and fast varying processes respectively. The qualitative vector field and trajectories for solutions are analysed and the mechanisms for the transition and nonuniform oscillation of high and low indexes are discussed.     

强迫波、自由波和纬向气流的相互作用——Ⅰ.平衡态环流的分支

本文用二层准地转模式,建立了一个近共振强迫波和近斜压不稳定自由波的非线性相互作用模式,试图以此来研究高低指数转换和非均匀性振荡的动力学问题。在这第一部分中,首先分析临界斜压不稳定和近共振强迫共同作用的弱非线性问题。然后以Hadley环流向Rossby波分支所造成的简单周期运动开始,分析热强迫波平衡态向定常强迫波与瞬变移动性Rossby混合型态的分支,及其所造成的较为复杂的运动形态。     

THE MULTIPLE EQUILIBRIA IN THE COUPLED ATMOSPHERE-OCEAN SYSTEM

In this paper, a topography forced quasi-geostrophic baroclinic model and an SST (sea surface temperature) equation are used to set up a simple coupled atmosphere-ocean model The large-scale ocean current is nearly the Sverdrup flow. Two basic processes are considered in this system, i. e. the SST as a thermal forcing drives the atmospheric circulation and the ocean current produced by the wind redistributes the SST. Highly truncating and multiple scale method are used to simplify the model and obtain a low dimensional dynamic system. In this part, the qualitative vector in the phase space of the system is analysed and two stable equilibria are obtained. These two kinds of equailibria may be used to explain some features of the long-range anomalies of circulation.     

PERIODIC AND NONPERIODIC OSCILLATIONS OF NONLINEAR ATMOSPHERIC WAVES FORCED BY PERIODIC THERMAL FORCING——SYSTEM WITHOUT DISSIPATION

In this paper, a baroclinic stable system with periodic forcing is used to discuss the dynamics of wave amplitude near the resonant forcing instability.In the first part, the linear resonant condition and weakly nonlinear resonant problem are analysed and two distinct periodic solutions with larger and smaller amplitudes are solved respectively for system without dissipation. When external forcing varies between the existence domains for these two kinds of periodic solution, nonperiodic oscillation appears, i.e. the so-called "chaos" phenomenon.     

基于最大——最小贴近度的IOWA算子最优组合预测模型

将最大一最小贴近度与IOWA算子相结合,建立了基于最大一最小贴近度的IOWA算子最优组合预测模型,并且定义了在最大一最小贴近度下非劣性组合预测、预测方法优超等概念.在此模型下,研究了模型的非劣性组合预测及优性组合预测存在的充分条件.最后给出实例分析,表明该组合预测方法的有效性.     

在周期性热源强迫下,非线性大气强迫波振幅的非周期和准周期振荡——无耗散系统

本文从一个斜压稳定的非线性系统出发,在一个随时间周期变化的外源作用下,通过近共振强迫不稳定,讨论波幅振荡的动力学。第一部分,首先分析热强迫系统中的线性共振条件和弱非线性共振问题,然后解出无耗散动力系统中的大、小振幅两类周期解。当外源在两类不同的周期解的存在域内变化时,系统出现不规则的非周期振荡,即所谓“混沌”现象。     

PERIODIC AND NONPERIODIC OSCILLATIONS OF NONLINEAR ATMOSPHERIC WAVES FORCED BY PERIODIC THERMAL FORCING——SYSTEM WITH DISSIPATION

This is a continued paper of [1]. The dissipation is considered here for analysing the mul-tiple equilibria and their instability. It is found that the far super-resonant and sub-resonantequilibria are stable and the near super-resonant equilibrium is unstable. The numerical resultsfor the periodic varying forcing show that the two kinds of stable equilibria in the dissipativesystem can alternatively transform into an asymmetrical oscillation with a period same asthat of the forcing.     

在周期性热源强迫下,非线性大气强迫波振幅的非周期和准周期振荡——有耗散系统

本文是继文献[1],考虑了有耗散的动力系统,解析地分析了系统中的平衡态及其稳定性。指出了远超共振和次超共振平衡态的稳定性和微超共振平衡态的不稳定性。在考虑了周期性外源的作用,数值积分后发现,它可以在耗散系统中导致二类稳定平衡态的转换,形成与外源同周期的、但不对称的周期振荡。