Analysis of Relative Diffusion in Homogeneous Isotropic Turbulence

The relative diffusion in homogeneous isotropic turbulence is studied in this letter. The mean square of the separation (Y²)∝t³ has been shown by the mean-field approximation as well as the analysis based upon the assumption that the particle displacement has the Gaussian distribution. The analytical results are in agreement with the conclusion of Richardson 4/3 law.     

Homogeneous Isotropic Turbulence: Geometric and Isometry Properties of the 2-point Velocity Correlation Tensor

The emphasis of this review is both the geometric realization of the 2-point velocity correlation tensor field B_ij (x,x′,t) and isometries of the correlation space K³ equipped with a (pseudo-) Riemannian metrics ds²(t) generated by the tensor field. The special form of this tensor field for homogeneous isotropic turbulence specifies ds²(t) as the semi-reducible pseudo-Riemannian metric. This construction presents the template for the application of methods of Riemannian geometry in turbulence to observe, in particular, the deformation of length scales of turbulent motion localized within a singled out fluid volume of the flow in time. This also allows to use common concepts and technics of Lagrangian mechanics for a Lagrangian system (M^t, ds²(t)), M^t ? K³. Here the metric ds²(t), whose components are the correlation functions, evolves due to the von Kármán-Howarth equation. We review the explicit geometric realization of ds²(t) in K³ and present symmetries (or isometric motions in K³) of the metric ds²(t) which coincide with the sliding deformation of a surface arising under the geometric realization of ds²(t). We expose the fine structure of a Lie algebra associated with this symmetry transformation and construct the basis of differential invariants. Minimal generating set of differential invariants is derived. We demonstrate that the well-known Taylor microscale λ_g is a second-order differential invariant and show how λ_g can be obtained by the minimal generating set of differential invariants and the operators of invariant differentiation. Finally, we establish that there exists a nontrivial central extension of the infinite-dimensional Lie algebra constructed wherein the central charge is defined by the same bilinear skew-symmetric form c as for the Witt algebra which measures the number of internal degrees of freedom of the system. For turbulence, we give the asymptotic expansion of the transversal correlation function for the geometry generated by a quadratic form.     

受大气湍流影响的光学波前模拟方法研究

介绍了模拟自适应光学系统中受大气湍流影响的光学波前的四种方法，即基于Zernike多项式的K—L函数展开法、小波法、Fourier法以及ARMA法。分析比较了四种方法模拟精度和速度。结果表明，前两种方法不论是精度还是速度上都比较好，更适合湍流波前的模拟。     

Dynamics Behaviors and Scaling in Intermittent Turbulence of a Shell Model

In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on fo-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function.     

Role of Clustering Coefficient on Cooperation Dynamics in Homogeneous Networks

Based on previous works, we give further investigations on the Prisoners＇ Dilemma Game （PDG） on two different types of homogeneous networks, i.e. the homogeneous small-world network （HSWN） and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game （SG） on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.     

Lagrangian Velocity Fluctuations in Fully Developed Turbulence: Scaling, Intermittency, and Dynamics

New aspects of turbulence are uncovered if one considers the flow motion from the perspective of a fluid particle (known as the Lagrangian approach) rather than in terms of a velocity field (the Eulerian viewpoint). Using a new experimental technique, based on the scattering of ultrasound, we have obtained a direct measurement of particle velocities, resolved at all scales, in a fully turbulent flow. We find that the Lagrangian velocity autocorrelation function and the Lagrangian time spectrum are in agreement with the Kolmogorov K41 phenomenology. Intermittency corrections are observed and we give a measurement of the Lagrangian structure function exponents. They are more intermittent than the corresponding Eulerian exponents. We also propose a novel analysis of intermittency in turbulence: our measurement enables us to study it from a dynamical point of view. We thus analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that displays extremely long-range correlations in time. Theoretically, we study a Langevin equation that incorporates these features and we show that the resulting dynamics accounts for the observed one-point and two-point statistical properties of the Lagrangian velocity fluctuations. Our approach connects the intermittent statistical nature of turbulence to the dynamics of the flow.     

可激发介质湍流的耦合同步及控制

利用相互耦合方法实现了两个处于湍流态的可激发系统的精确同步，给出了确定耦合系数的方法，计算了最大横向Lyapunov指数.并基于相互耦合，将处于湍流态的可激发系统与两个处于不同状态的可激发系统进行相互耦合，实现了用两种不同方法对湍流态的稳定控制. 关键词： 可激发介质 湍流控制 同步 耦合系数     

非Kolmogorov大气湍流对径向部分相干阵列光束瑞利区间和湍流距离的影响

基于广义的Huygens-Fresnel原理和非Kolmogorov谱模型,推导了无线光通信系统中径向分布部分相干高斯-谢尔模型阵列光束在非Kolmogorov大气湍流中传输时瑞利区间z_R和湍流距离z_T的解析表达式,对瑞利区间和湍流距离随湍流参量和光束参量的变化情况进行了数值分析.结果表明:不论是相干还是非相干合成,径向分布部分相干高斯-谢尔模型阵列光束的z_R和z_T均随湍流广义指数α的增大非单调变化,当α=3.11时,z_R和z_T取最小值,此时阵列光束扩展最大;相干合成比非相干合成的光束扩展要小,但其受湍流的影响更大;对于相干合成而言,径向分布半径r0越大,合成光束的z_R和z_T就越大,而非相干合成的z_R和z_T不受r0的影响;不论是相干还是非相干合成,阵列子光束数目对合成光束的z_R和z_T没有影响;当光束相干参量β足够小或波长λ足够大时,大气湍流对阵列光束z_R的影响可以忽略.     

地物散射和大气湍流导致的激光闪烁统计

通过分析大气湍流和地物散射对传输激光束的调制机理，运用双随机统计理论研究了空－地－空传输路径空载探测器接收到光闪烁统计问题。闪烁统计由大气湍流和地物（岩石，海洋和森林等）散射的联合效应给出，分析中采用最速下降法处理概率积分，获得了与岩石，海洋和森林二大类地物散射体对应的闪概率密度函数，广义Ｃｈｉ－Ｓｑｕａｒｅｄ地面散射与大气湍流综合调制效应明显地压缩了概率分布的宽度并使分布函数的峰值移向归一化强度     

Atmospheric Turbulence and Internal Gravity Waves Examined by the Method of Artificial Periodic Irregularities

A method for studying the Earth’s ionosphere at altitudes of the mesosphere and lower thermosphere based on creating artificial periodic irregularities in the ionospheric plasma by means of powerful radio waves is breafly described. Methods for determining the temperature and density of the neutral component and the velocity of vertical and turbulent motions by measuring the characteristics of the signal backscattered by the irregularities are described. The results of experiments performed on a SURA heating facility aimed at a comprehensive investigation of the natural processes occurring in the Earth’s lower ionosphere due to the propagation of atmospheric waves and turbulent phenomena are examined. Based on measurements of the amplitude and phase of the signal scattered by periodic irregularities, the most important characteristics of the neutral and plasma components of the Earth’s atmosphere at altitudes of the mesosphere and lower thermosphere are determined. Further research on the subject is discussed.     

Fully Developed Turbulence and the Multifractal Conjecture

We review the Parisi-Frisch (Proc. Int. School of Physics “E. Fermi”, pp. 84–87, North-Holland, Amsterdam, 1985) MultiFractal formalism for Navier-Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.