阻塞动力学研究进展与展望

简介了大气阻塞动力学在多平衡态理论和外源强迫的共振理论、孤立子及偶极子理论、强迫耗散ＫＤＶ动力学以及天气扰动的激发等几方面理论研究的进展。并对阻塞动力学的研究进行了展望。     

湿大气方程组解的渐近性质

研究无穷维Ｈｉｌｂｅｒｔ空间中,湿大气运动系统解的长期行为,在导得了湿大气运动方程是Ｈｉｌｂｅｒｔ空间中一个非常特殊的算子方程之后,利用算子的性质讨论了全局吸收集和全局吸引子的存在性,揭示出系统解的渐近行为表现在吸引子的结构上及系统向非绝热加热的非线性适应过程。最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同,从而给出长期天气或气候研究中简化方程组必须遵循的原则。     

强迫耗散非线性发展方程准完全平方守恒格式的构造

从描述大气和海洋运动的强迫耗散非线性发展方程出发，对强迫耗散非线性大气和海洋方程组显式差分格式的计算稳定性进行了分析，构造了一类强迫耗散性发展方程的显式准完全平方守恒差分格式，理论分析和数值试验证明，这类显式准完全平方守恒差分格式是计算稳定的．值得推广应用。     

一个Navier-Stokes算子方程广义能量的存在性

利用泛函理论,建立关于大气系统Navier-Stokes动力学方程组各变量的Hilbert空间,并将该方程组化为一个Hilbert空间中的非线性算子方程。在此基础上,为考虑方程的整体特征,通过必要的简化,将一个本质为欠定的偏微分方程组化为一个关于广义能量的非线性偏微分方程。由于该偏微分方程的非线性性质,试图考虑其弱解的存在性。经分析发现,在外源强迫为已知或固定的情况下,如果在湍流闭合过程,使关于广义能量方程的非线性项系数具有强椭圆性质,那么根据连续正规算子方程的投影解法,可以确定该非线性偏微分方程具有投影解,且投影解收敛于弱解,从而得出广义能量弱解的存在性。对于大气运动而言,其能量守恒是重要的,因此,最后对广义能量守恒进行了讨论,得到广义能量守恒的条件。     

热力强迫对湿斜压大气中南亚高压平衡态的影响

本文基于Lorenz的湿模式,引入地形效应并进行适当简化,在低谱近似下得到了描述大气运动的非线性耗散系统。讨论了在热力强迫与大气环流的非线性相互作用下,湿、斜压大气在参数空间的平衡态与南亚高压的流型分布及其东西摆动。结果表明:南亚高压典型的平衡态流型是西部型、东部型和带状高压,而且东西部流型的转换并非高压中心的连续位移,而是表现为一个高压中心消失后经过流场上的调整重新建立新的高压中心的过程。     

中国年降水气候振动的非线性动力学特征

从观测资料出发,利用反演方法,获得了描述我国17个站年降水气候振动的二阶非线性动力学方程组中的系数,并在无外源强迫的情况下对该非线性动力学方程组作了定性的分析,对17个站的年降水气候振动进行气候模拟试验。结果表明:我国大部分地区的年降水气候振动存在弱的非线性振动特征,17个站的年降水气候振动都可以看作是一个正阻尼的动力系统,在运动变化过程中,自身能量的变化dEdt<0,17个站年降水气候振动的固有频率的变化范围为0.6≤ω0≤1.417,其固有周期的变化范围为10.4≥T≥4.4年。从空间分布特征上可以看到,其固有周期的长短分布有明显的东西向特征。在17个站中,兰州、成都、重庆、南宁、福州、上海、温州地区的年降水气候振动是一个类似于具有渐软弹簧特性的非线性动力系统,而昆明、长春、哈尔滨、北京、广州、西安、厦门、长沙、南京、杭州地区的年降水气候振动是一个类似于具有渐硬弹簧特性的非线性动力系统,从其空间分布特征上看也有东西向特征。全国17个站年降水气候振动的动力系统都存在一个稳定的焦点,在无外源强迫作用时,各站的年降水气候振动将逐渐趋向于各自的稳定的焦点,但都不存在极限环。在仅考虑降水自身振动的情况下,利用我们反演得到的非线性动力学方程对年降水气候振动做模拟,位于内陆地区的模拟情况可以通过显著性水平检验,而靠近海洋的地区模拟效果没有内陆好。这一结果说明在降水气候振动中,靠近海洋地区的外源强迫影响作用比位于内陆地区大。     

近共振热力强迫作用下多重平衡态的激发、建立和转换(一)——多重平衡态的渐近解

本文通过一个含有近共振热力强迫和耗散、基本流有常数切变的二层准地转β-平面纬向周期性窄通道斜压模式,运用多尺度方法导出一投影在T—X时空平面的、包含强迫波—自由波—自由波非线性相互作用的、关于定常热强迫波上扰动的偏微分方程组.借助奇异摄动法解析地求得了此方程组的平衡态渐近解.结果得到,在很大的参数范围内都可存在多重平衡态.     

大气平衡态的动力特征——Ⅰ:多平衡态的共面和非共面性质

本文设计了一个有地形、强迫源和摩擦耗散的球面正压低阶模型来研究大气平衡态的动力特征。在相空间中,存在各平衡态共存的非线性作用曲面、角动量平面和强迫耗散球面。多平衡态的共面特征反映着大气运动的全局行为。指出大气运动的非线性特征只为多平衡态的存在提供可能性,但不提供必然性。动能和位涡拟能的分析表明,不同平衡态处在不同的能级,具有不同的拟能态,在相空间上位于不同的能量球面上。了解各态间的动力差异有助于理解大气运动向定常态收敛和产生振荡的物理原因。这将在第Ⅱ部份深入讨论。     

大气平衡态的动力特征 I:多平衡态的共面和非共面性质

本文设计了一个有地形、强迫源和摩擦耗散的球面正压低阶模型来研究大气平衡态的动力特征。在相空间中,存在各平衡态共存的非线性作用曲面、角动量平面和强迫耗散球面。多平衡态的共面特征反映着大气运动的全局行为。指出大气运动的非线性特征只为多平衡态的存在提供可能性,但不提供必然性。动能和位涡拟能的分析表明,不同平衡态处在不同的能级,具有不同的拟能态,在相空间上位于不同的能量球面上。了解各态间的动力差异有助于理解大气运动向定常态收敛和产生振荡的物理原因。这将在第Ⅱ部份深入讨论。     

正压大气中尺度半平衡和准平衡动力学模式

应用描写正压大气运动的基本方程组，分析了中尺度大气运动的物理特征，指出非平衡强迫运动是引起中尺度重要天气演变的根本原因。中尺度动力学方程组是中尺度动力学理论研究的基础，因此，结合中尺度大气运动的基本特征，依据严格的尺度分析理论和摄动理论，简化基于流体力学和热力学的大气动力学方程组使之能够恰当地描述出中尺度运动的基本特征，对于中尺度动力学的发展是极为必要的。基于非线性平衡方程所得到的半平衡和准平衡动力学模式分别与半地转和准地转模式极为相似，它们可以较精确地描述中尺度大气运动的基本特征，因而，可作为中尺度动力学研究的理论基础。将准平衡动力学模式应用于中尺度涡旋系统的研究，结论表明中尺度平衡涡旋系统主要是受梯度风控制，其流场和气压场的发展演变则由一个演化方程来描写，获得了较为理想的结果。     

FURTHER STUDY ON THE PROPERTIES OF OPERATORS OF ATMOSPHERIC EQUATIONS AND THE EXISTENCE OF ATTRACTOR

The equivalent operator equation is derived from the full primitive nonlinear equations of theatmospheric motion and the properties and physical senses of the operators are studied.In theinfinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system withthe non-stationary external forcing is studied under the assumption of the bounded externalforcing.The existence theorems of the global absorbing set and the global attractor are obtained.Thus,the conclusions deduced from the large-scale atmosphere(Li and Chou 1996 a;1996 b)areextended to the general atmosphere.     

FURTHER STUDY ON THE PROPERTIES OF OPERATORS OF ATMOSPHERIC EQUATIONS AND THE EXISTENCE OF ATTRACTOR*

The equivalent operator equation is derived from the full primitive nonlinear equations of the atmospheric motion and the properties and physical senses of the operators are studied.In the infinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system with the non-stationary external forcing is studied under the assumption of the bounded external forcing.The existence theorems of the global absorbing set and the global attractor are obtained.Thus,the conclusions deduced from the large-scale atmosphere(Li and Chou 1996a;1996b) are extended to the general atmosphere.     

气候数值模拟研究中初始场衰减理论的理解和应用

根据对大气原始方程的定性理论和相空间的理论研究,初始场对数值模拟的作用会随着时间的增长而逐步衰减.文章分析初始场作用衰减理论的关键问题,通过对大气环流谱模式SAMIL和ECHAM的数值试验,在实际的计算环境中研究其初始场作用的变化情况.研究中使用到对舍入误差干扰的一种集合消减方法(REME),保证了验证试验所受舍入误差的影响小于给定的范围.结果表明有舍入误差存在的计算环境中,当初始差别较大时,其逐步衰减到一个波动值.而对于特别微小的初始场差别,其长期影响也应是衰减的,但由于计算精度有限,可能会出现增大到一个波动值的现象,这些结果与非线性误差理论所描述的误差饱和现象一致.试验得到了具体模式的衰减速率曲线,发现衰减需要的时间范围大约为40-60 d.文中还利用初始场作用衰减的理论探讨了如何解释初始场集合预报(IME)能够减少模拟结果误差的现象.     

Nonlinear three- wave interaction among barotropic rossby waves in a large- scale forced barotropic flow

In this paper, the coupling equations describing nonlinear three-wave interaction among Rossby waves including the forcing of an external vorticity source are obtained. Under certain conditions, the coupling equations with a constant amplitude forcing, the stability analysis indi-cates that when the amplitude of the external forcing increases to a certain extent, a pitchfork bifurcation occurs. Also, it is shown from numerical results that the bifurcation can lead to chaotic behavior of “strange” attractor. For the obtained three-variable equation, when the amplitude of modulated external forcing gradually increases, a period-doubling bifurcation is found to lead to chaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forced barotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explain in part 30-60-day low-frequency oscillations observed in mid-high latitudes.     

THE EFFECTS OF EXTERNAL FORCING,DISSIPATION AND NONLINEARITY ON THE SOLUTIONS OF ATMOSPHERIC EQUATIONS*

Based on the primitive equations of the atmosphere,we study the effects of external forcing.dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria.From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.     

THE EFFECTS OF EXTERNAL FORCING,DISSIPATION AND NONLINEARITY ON THE SOLUTIONS OF ATMOSPHERIC EQUATIONS

Based on the primitive equations of the atmosphere,we study the effects of external forcing.dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.Theresults show that the asymptotic behavior of solutions of the forced dissipative nonlinear system isessentially different from that of the adiabatic non-dissipative system,the adiabatic dissipativesystem,the diabatic non-dissipative system and the diabatic dissipative linear system,and that thejoint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria.From this we can conclude that the important actions of diabatic heating and dissipation must beconsidered in the models of the long-term weather and the climate.     

Progress in the Study of Nonlinear Atmospheric Dynamics and Predictability of Weather and Climate in China (2007--2011)

Recent progress in the study of nonlinear atmospheric dynamics and related predictability of weather and climate in China (2007-2011) are briefly introduced in this article. Major achievements in the study of nonlinear atmospheric dynamics have been classified into two types:(1) progress based on the analysis of solutions of simplified control equations, such as the dynamics of NAO, the optimal precursors for blocking onset, and the behavior of nonlinear waves, and (2) progress based on data analyses, such as the nonlinear analyses of fluctuations and recording-breaking temperature events, the long-range correlation of extreme events, and new methods of detecting abrupt dynamical change. Major achievements in the study of predictability include the following:(1) the application of nonlinear local Lyapunov exponents (NLLE) to weather and climate predictability; (2) the application of condition nonlinear optimal perturbation (CNOP) to the studies of El Nin o-Southern Oscillation (ENSO) predictions, ensemble forecasting, targeted observation, and sensitivity analysis of the ecosystem; and (3) new strategies proposed for predictability studies. The results of these studies have provided greater understanding of the dynamics and nonlinear mechanisms of atmospheric motion, and they represent new ideas for developing numerical models and improving the forecast skill of weather and climate events.     

Hurricane predictability: are there simple linear invariants within these complex nonlinear dynamical systems?

Summary Forecasting the tracks of hurricanes is a problem of immense importance. It is a major scientific exercise in solving the complicated set of mathematical equations that govern the behavior of atmospheric flow in general and hurricanes in particular. Moreover, hurricanes rank as the most devastating of all natural phenomena, in terms of loss of life and destruction of property. Hitherto, unlike many other atmospheric and oceanic systems, hurricanes have defied rapid advances in prediction of their motion, and progress has been of the order of a mere one percent or so reduction per annum in mean 48 hour forecast position errors over the past two decades. A research program aimed at estimating inherent and actual mean absolute forecast position errors, has produced an apparent paradox. Despite the fact that the equations governing hurricane motion are a complex, coupled, nonlinear set of dynamical equations, there is very strong evidence for the existence of an underlying simple, linear, invariant behavior. The original aim of the research program was to determine the lower limits of mean hurricane forecast position errors and to quantify them out to 72 hour leadtime. The appearance of the paradox meant that the focus shifted first to examining and explaining the paradox. Attention then turns to showing that the mean forecasts errors are still a very large 40 to 50 percent lower than the mean position errors currently being achieved in practice by state-of-the-art models numerical weather prediction (NWP) models. Revised December 14, 1999