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1.
利用紧性理论，证明了扩散现象中出现的一类退缩抛物型方程组初边值问题解的存在性和唯一性。 相似文献
2.
利用锥映射不动点指数计算方法,结合极值原理、解耦方法得到了一类反应扩散方程组正平衡解的存在性和唯一性.分析过程表明,对此类微分方程组的解耦方法类似于代数方程中的消元法. 相似文献
3.
The three-dimensional stability problem is investigated for a family of velocity and density profiles similar in form to those expected for large-amplitude internal gravity waves near a critical level. These profiles exhibit regions of high shear and stable stratification alternating with regions of weak shear and unstable stratification. Analytical solutions are given for inviscid, neutral modes that are similar to those found under neutral conditions with stable stratification. Neutral modes form closed streamline patterns centered at locations of maximal shear, and are not strongly influenced by nearby regions of unstable stratification. Unstable modes are computed numerically. It is shown that the instability mechanism for these wave-like flows fundamentally three-dimensional in character and exhibits both shear and convective dynamics. For flows with parameter values below the neutral curves, unstable modes oriented in the streamwise direction undergo shear instability, while modes oriented orthogonally are convectively unstable. In addition to their intrinsic physical relevance, the results of this study have important implications for the physics and the numerical modeling of breaking internal gravity waves. Two-dimensional models will bias the breaking dynamics by eliminating the possibility for convection oriented in the transverse plane. 相似文献
4.
There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase- or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). As the attracting trajectory can sometimes lie close to the boundary of its basin of attraction, a small perturbation could quite easily make climate to jump between different histories, reducing the predictability. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronisation regimes on obliquity, precession or combinations of both, all over the history of the Pleistocene. 相似文献
5.
热带风暴中波动特征的研究进展和问题 总被引：9，自引：2，他引：9
在分析热带风暴眼壁和螺旋雨带中尺度波动特征最新研究的基础上，指出这些研究所忽略的问题，其中包括重力惯性波和涡旋Rossby波波解存在的前提条件和约束、理论分析与观测研究存在的差异等。提出一种基于准平衡动力条件下，热带风暴内中尺度扰动涡散运动共存时，区别于标准模混合的不可分的混合涡旋Rossby-重力惯性波，并讨论了位涡守恒条件下这一类不可分混合波的可能成波机制。利用高分辨率的模式大气资料，采用非对称波分量的分解方法分析了Bonnie飓风中的中尺度波动特征，结果表明，热带风暴中1波型扰动既具有涡旋波性质，但也存在散度扰动的变化，而2波型扰动则体现了明显的不可分混合波的特性。 相似文献
6.
NUMERICA STUDY OF THUNDERSTORM ELECTRIFICATION WITH A THREE-DIMENSIONAL DYNAMICS AND ELECTRIFICATION COUPLED MODEL—MODEL DESCRIPTION AND PARAMETERIZATION OF ELECTRICAL PROCESSES 
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下载免费PDF全文 A new three-dimensional dynamics and electrification coupled model has been developed forinvestigating the characteristics of microphysics,dynamics and electrification insidethunderstorms.This model is basically modified from a three-dimensional,time-dependent,anddual-parameter cloud model originally established in IAP(Institute of Atmospheric Physics)and atwo-dimensional axisymmetric cloud dynamics and electrification coupled model.Primarymodifications to the model include not only the coupling of electrification with dynamical andmicrophysical processes,but also the lightning discharge process and screening layer effect at thecloud top as well.Apart from including a full treatment of small ions with attachment to sixclasses of hydrometeors,the inductive and non-inductive charging mechanisms are more specificallyconsidered.A case simulation of July 19.1981 CCOPE is performed aiming to validate thepotential capability of the model.Comparison between model results and observations reveals thatthe model has the capacity to reproduce many of the observed characteristics of thunderstorms indynamical,microphysical,and electrical aspects. 相似文献
7.
NUMERICA STUDY OF THUNDERSTORM ELECTRIFICATION WITH A THREE-DIMENSIONAL DYNAMICS AND ELECTRIFICATION COUPLED MODEL—MODEL DESCRIPTION AND PARAMETERIZATION OF ELECTRICAL PROCESSES* 下载免费PDF全文
下载免费PDF全文 SUN Anping YAN Muhong ZHANG Yijun ZHANG Hongf HUANG Meiyuan 《Acta Meteorologica Sinica》2002,16(1):107-122
A new three-dimensional dynamics and electrification coupled model has been developed for investigating the characteristics of microphysics,dynamics and electrification inside thunderstorms.This model is basically modified from a three-dimensional,time-dependent,and dual-parameter cloud model originally established in IAP (Institute of Atmospheric Physics) and a two-dimensional axisymmetric cloud dynamics and electrification coupled model.Primary modifications to the model include not only the coupling of electrification with dynamical and microphysical processes,but also the lightning discharge process and screening layer effect at the cloud top as well.Apart from including a full treatment of small ions with attachment to six classes of hydrometeors,the inductive and non-inductive charging mechanisms are more specifically considered.A case simulation of July 19.1981 CCOPE is performed aiming to validate the potential capability of the model.Comparison between model results and observations reveals that the model has the capacity to reproduce many of the observed characteristics of thunderstorms in dynamical,microphysical,and electrical aspects. 相似文献
8.
研究了随机滞后微分方程的一致有界和一致最终有界.利用Lyapunov函数和Razumikhin技巧,得到了一些关于随机滞后微分方程有界性新的Razumikhin定理,同时,证明随机滞后微分方程解的存在性,推广了相关的文献.最后,给出例子证实定理的有效性. 相似文献
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10.
在前文采用半地转近似和行波法来研究层结大气中的非线性波动的基础上,进一步探讨非线性方程及其级数近似方程的解的稳定性,波动解的存在条件和波动的一些特征。研究指出,在平衡点附近,将非线性方程用其级数近似方程代替是可行的、合理的。在初始拟能满足一定的条件下,椭圆余弦波和孤立波是存在的。文中还求得了椭圆余弦波解的周期、ｘ向波长和振幅以及孤立波的宽度和振幅。并指出,孤立波的宽度和振幅不但与波速有关,还与β因子和层结稳定度有关,而且在相同的某条件下,西行的混合Ｒｏｓｓｂｙ－重力孤立波比起东行的惯性重力孤立波来,宽度要小但振幅却大。 相似文献
11.
Motivated in part by the mathematical problems associated with the application of open boundary conditions to the hydrostatic primitive equations (PE), Browning et al. (1990, Dyn. Atmos. Oceans, 14: 303–332) proposed the use of the reduced system (RS) of equations to replace PE for oceanographic problems. The RS are essentially the Boussinesq equations (BO) with the non-hydrostatic terms in the vertical momentum equation multiplied by a constant δ2 ? 1. This artificially alters the physics (e.g. changing the intemal-inertial wave properties) to facilitate numerical integration, but the changes are assumed to have negligible effects on the dynamics of interest. We assess the accuracy and utility of the RS (following the guidelines for the choice of δ) by comparing numerical finite difference solutions of RS, PE and BO for initial-value problems involving three-dimensional instability of an ocean front and atmospheric frontal development in a two-dimensional Eady wave. Both explicit (BO, PE) and semi-implicit (BOSI, PESI) time-difference schemes are used for the Boussinesq and primitive equations. For RS, the same explicit scheme as for BO is used where δ ? 1 allows larger time steps than with the other explicit models. It is found that relative to BO solutions, the errors for RS are small but increase rapidly and monotonically with increasing δ (over a range consistent with the guidelines) and are greater than the errors for the other models. The use of BOSI allows time steps at least as large as those for RS and results in smaller errors than RS. For these problems, BOSI is the preferable model to replace PE. 相似文献
12.
S. P. Meacham K. K. Pankratov A. F. Shchepetkin V. V. Zhmur 《Dynamics of Atmospheres and Oceans》1994,21(2-3)
We show that an arbitrarily oriented ellipsoid of uniform potential vorticity, embedded in a background flow described by a quadratic streamfunction, is an exact solution of the quasigeostrophic equations governing motion in a uniformly stratified, unbounded fluid. This type of flow includes plane horizontal shear and strain as well as uniform vertical shear of a unidirectional horizontal flow. We derive ordinary differential equations describing the motion of such a vortex and discuss some aspects of their solutions. We note the existence of steady states (solutions in which the vortex is in equilibrium with the background flow), of periodic solutions near these steady states, of non-periodic trajectories which nervertheless remain in the vicinity of the steady states, and of solutions which represent the shearing out of the vortex by the background flow. We try to use this information to propose partial answers to the question of when a given horizontal or vertical shear flow is likely to destroy a vortex and when a vortex might survive external shear and strain. 相似文献
13.
湿大气方程组解的渐近性质 总被引：4，自引：0，他引：4
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。 相似文献
14.
Helicity Dynamics of Atmospheric Flow 总被引：17，自引：0，他引：17
Helicity is an important physical variable which is similar to the energy and enstrophy in three-dimensional fluid. It can be used to describe the motion in the direction of fluid rotation and also can be regarded as a new physi-cal variable in turbulence theory. In recent years, it has been used in atmospheric dynamics. In this paper, helicity of atmospheric flow, especially helicity in the boundary layer and in the vicinity of front was discussed. These results show that helicity is usually positive in the boundary layer due to the effect of friction. The helicity of boundary layer flow is larger in anticyclone than that in cyclone, resulting from the different wind structures of boundary layers in an-ticyclone and cyclone under the geostrophic momentum approximation. It is possible that the helicity is negative at certain height in the baroclinic boundary layer. The influences of nonlinearity and baroclinity on the helicity are im-portant. The so called “Cloud Street” in the boundary layer is related to the dynamics of helicity. Helicity in the at-mosphere can be expressed as the temperature advection under some conditions, so helicity would be allowed to des-cribe the frontogenesis and development of frontal structure. The amplitude of helicity increases with time in the frontogenesis. A large gradient of helicity is generated in the region located to the northeast of the surface low and in which the front is formed. In warm frontal region, as well as behind the trough of temperature, the helicity is positive, while the helicity is negative in cold frontal sector and in the ahead ridge of temperature. The largest helicity occurs in the boundary. 相似文献
15.
G.R. Flierl V.D. Larichev J.C. McWilliams G.M. Reznik 《Dynamics of Atmospheres and Oceans》1980,5(1):1-41
We derive exact nonlinear solutions to the inviscid quasigeostrophic two-layer equations. The solutions represent isolated eddies with an amplitude that decays rapidly away from the eddy. They translate steadily either to the east (if there is a barotropic component in the fringes of the eddy) or either to the east or rapidly to the west (if the exterior field has only a baroclinic mode structure). They are strong in the sense that all of the fluid within a finite radius from the center is carried along with the eddy as it translates. The solutions have a characteristic north-south antisymmetry with the nonlinear vortex pair interactions being an essential feature of the dynamics. However, we also show that radially symmetric perturbations of a special form but arbitrary amplitude can be superimposed on the basic solutions; thus the antisymmetric structure may to some extent be masked. We show nondimensional dispersion relationships: atmospheric and oceanic planetary wave phenomena do fall in the range of parameters where theory predicts solitary eddy solutions can exist. 相似文献
16.
赵鸣 《Acta Meteorologica Sinica》1992,(3)
In this paper, the eddy coefficient and the treatment for dividing layers of Estoque's numerical model in modernPBL dynamics have been applied to derive order-zero and order-one analytic solutions over large-scale topography,the solutions are used to obtain the divergence and vertical velocity, improving the previous results. 相似文献
17.
Zhao Ming 《Acta Meteorologica Sinica》1992,6(3):332-344
In this paper, the eddy coefficient and the treatment for dividing layers of Estoque's numerical model in modern PBL dynamics have been applied to derive order-zero and order-one analytic solutions over large-scale topography,the solutions are used to obtain the divergence and vertical velocity, improving the previous results. 相似文献
18.
Results from measurements of long-wave radiative flux divergence on calm, cloudless nights from within an urban canyon are presented. Results show the existence of three-dimensional (volume) radiative divergence in the canyon-air system. The results are compared with air temperature cooling rates (energy storage change) in the canyon. With calm, cloudless conditions, radiative divergence is the dominant mechanism controlling air temperature changes. In the early part of the night this results in air cooling, but radiative warming was commonly observed after midnight. Canyon-air volume radiative divergence is found to be considerably less than that observed previously above roof-level, and in rural areas. Measured cooling rates in the canyon are poorly predicted by a surface-oriented cooling approach. This again points to the importance of the atmospheric radiation balance. 相似文献
19.
大气环流模式中云系的超级参数化方案及其特征线方法之研究 总被引：1，自引：0，他引：1
就大气环流模式中如何有效处理云系,我们的目标:建立能考虑各种尺度和各种过程之间相互作用的多重尺度云系动力学(下称:云系超级参数化),并应同时考虑如下云的几何学与辐射传输两个问题:1)云的几何学,考虑如何描写云内结构的三维不均匀性和表面特征的几何不光滑性;2)云的辐射,考虑复杂云结构的辐射计算问题,并最终在大气环流模式中具体实现.本研究是理论部分,主要论述云系超级参数化框架和计算方法问题,主要结论如下:1)阐明了从多重尺度角度研究大气模式中云系的超级参数化方案是完全必要的.2)本云系超级参数化方案是3维完全Euler流体方程组,保留了全Coriolis力,Ertel全PV守恒,考虑声波等对云和降水微物理过程的影响.该云系超级参数化方案需要与大气大尺度动力学方程组进行耦合.3)关键问题为确定云系局部解的存在时间长度,不必考虑整体解.因为在实际大气中各物理量的不光滑,甚至不连续和间断,是有充分的物理意义的.大气中的间断除粘性和热传导等不可逆过程外,同时伴随着成云致雨的相变过程.4)在可积性和连续性条件下,证明了特征线的存在性;在Lipshitz条件下,证明了特征线的存在性和唯一性.5)给出了特征线积分的Picard方法的具体计算步骤,并同时给出了特征线积分稳定步长的具体条件.6)沿着特征线,初始场随着时间的推移,将发生平移、旋转与纯变形三种位移的几何和,这就是球面上平流方程的保形问题. 相似文献
20.
Aixia Feng Zhiqiang Gong Qiguang Wang Guolin Feng 《Theoretical and Applied Climatology》2012,109(3-4):635-643
We introduce bilayer networks in this paper to study the coupled air–sea systems. Results show that the framework of bilayer networks is powerful for studying the statistical topology structure and dynamics in the fields of ocean and atmosphere. Based on bilayer networks, the inner and cross interactions of the sea surface temperature (SST) field and the height field are displayed, and the main three-dimensional air–sea interaction pattern is identified. The formation of the main pattern can be explained by the “gearing between the Indian and Pacific Ocean (GIP)” model; therefore, the pattern existence can be confirmed reliably. Furthermore, lead–lag analysis reveals the trigger processes of the “GIP”. That is, the anomalies of the tropical mid-eastern Pacific Ocean SST (TMEPO-SST) appear first; then, through the Walker circulation, the 850-hPa geopotential height over the Pacific Islands responds to the anomalies of the TMEPO-SST 2 months later; finally, the tropical Indian Ocean SST (TIO-SST) responds to the anomalies of the height 1 month later through the Asian monsoon circulation. Therefore, the impacts of the TMEPO-SST to the TIO-SST show 3 months later through the air–sea interactions between the components of the main three-dimensional air–sea interaction mode. The new framework uncovers already-known as well as other novel features of the air–sea systems and general circulation. The application of complex network theory and methodology to understand the complex interactions between the oceans and the atmosphere is promising. 相似文献