Lagrangian and Eulerian velocity intermittency

Usual turbulence experiments, based on the Taylor hypothesis, differ from true Eulerian measurements. This is the origin of the apparent discrepancy between a recent two point correlation analysis and the multiplicative cascade picture. Indeed, both Eulerian and Lagrangian observations perfectly agree with this picture. Received 19 June 2002 / Received in final form 29 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: bcastain@ens-lyon.fr     

Eulerian and Lagrangian Pictures of Non-equilibrium Diffusions

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the fluctuation-dissipation relations in that frame observed previously. The general considerations are illustrated on few examples of stochastic particle dynamics.     

非旋转性自由表面重力驻波的Euler与Lagrange方法解间的转换

对于等深水中的非旋转性重力驻波流场,本文用Euler与Lagrange两种方法求得其至三阶的解,根据同一粒流体质点在相同时间与位置处其流速值为唯一与质量守恒及在自由表面水位的Euler形式解与Lagrange形式解相同等特性,来推导其间互可转换.由一系列连续的Taylor级数展开,在考虑波动场中各流体质点的运动轨迹与运动周期条件下,将已知的Euler解转换成完全未知的Lagrange形式解.接着再将所得的Lagrange解转换成对应的Euler形式,均可得到完全相同的结果.由此可得知,在考虑波动场各流体质 关键词： 重力驻波 Euler与Lagrange解间的转换 质点运动轨迹     

非旋转性前进波Euler与Lagrange解间的转换

对等深水中非旋转性的前进重力波动场,以求得的Euler与Lagrange两种形式至第三阶的解,按照同一流体质点在相同时间与位置处其流速唯一与质量守恒性及在自由表面水位处Euler形式解与Lagrange形式解为同一值的特性,来推导二者可相互转换.由连续的Taylor级数展开,考虑波动场中各流体质点的运动轨迹与运动周期,将已知的Euler形式解转换成完全未知的Lagrange形式解,解决了以往成果中出现含时间的不合理的共振项,以及无法得到与Euler系统不同的Lagrange形式的流体质点运动频率与平均运动 关键词： 非旋转性前进波 Euler-Lagrange转换 质点运动轨迹 质点运动频率     

Lagrangian chaos and Eulerian chaos in shear flow dynamics

Shear flow dynamics described by the two-dimensional incompressible Navier-Stokes equations is studied for a one-dimensional equilibrium vorticity profile having two minima. These lead to two linear Kelvin-Helmholtz instabilities; the resulting nonlinear waves corresponding to the two minima have different phase velocities. The nonlinear behavior is studied as a function of two parameters, the Reynolds number and a parameter lambda specifying the width of the minima in the vorticity profile. For parameters such that the instabilities grow to a sufficient level, there is Lagrangian chaos, leading to mixing of vorticity, i.e., momentum transport, between the chains of vortices or cat's eyes. Lagrangian chaos is quantified by plotting the finite time Lyapunov exponents on a grid of initial points, and by the probability distribution of these exponents. For moderate values of lambda, there is Lagrangian chaos everywhere except near the centers of the vortices and near the boundaries, and there are competing effects of homogenization of vorticity and formation of structures associated with secondary resonances. For smaller values of lambda Lagrangian chaos occurs in the regions in the centers of the vortices, and the Eulerian behavior of the flow undergoes bifurcations leading to Eulerian chaos, as measured by the time series of several Galilean invariant quantities. A discussion of Lagrangian chaos and its relation to Eulerian chaos is given.(c) 2001 American Institute of Physics.     

Lagrangian and Eulerian Statistics from Direct Numerical Simulations of Turbulent Channel Flow

Lagrangian and Eulerian statistics are obtained from the direct numerical simulation of a turbulent channel flow. The Reynolds number is obtained to be Reτ = 100 （based on friction velocity and channel half-height）. The Lagrangian time microscales are compared to their Eulerian equivalents. It is found that the Lagrangian time microscales equal the Eulerian time microscales at the wall, but they are consistently larger than the Eulerian away from the wall. The Eulerian time scales are also found to be scaled by the propagation velocity rather than the mean velocity. The ratio of the Lagrangian to the Eulerian time microscales is found to be nearly constant away from the wall （y^＋ 〉 40）.     

An Eulerian–Lagrangian Approach¶to the Navier–Stokes Equations

We present a formulation of the incompressible viscous Navier–Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced. Received: 13 May 2000 / Accepted: 22 September 2000     

Characterisation of the Eulerian and Lagrangian accelerations in the intermediate field of turbulent circular jets

A rich data-set of Lagrangian trajectories from 3D particle tracking velocimetry is used to study the structure of various acceleration components, vorticity, and strain in the intermediate field of a circular jet at Reynolds number Re = 6000. The total acceleration is decomposed into three distinctive sets: (1) streamwise–radial; (2) tangential–normal; and (3) local–convective components. Probability density function (PDF) and joint distributions of each set are characterised at various radial locations from the jet core within a streamwise band 16 ≤ x/d_h ≤ 17, where d_h is the diameter of the pipe. The PDF of the relative angle between the acceleration components and the velocity vector is also included to aid the characterisation. Results show that the acceleration components are described by two distinctive distributions: one of them exhibits symmetry and heavy tails, while the other is best fitted by a power-law type. The tails of acceleration PDFs are heavier with larger radial distance from the core. The increased departure from the Gaussian distribution with the distance from the core is a result of the increasing turbulence levels promoted by the mean shear. The variation of the third and fourth moments between the streamwise–tangential and the radial–normal accelerations indicate the anisotropy of the jet. Joint PDF of each acceleration decomposition exhibits distinctive distribution that appears to depend from the distance from the jet core. However, the vorticity and strain show similar PDF across radial distances. Finally, complementary analysis of a jet from a semicircular pipe shows the footprint of the nozzle geometry in the acceleration structure of jets.     

Modeling material responses by arbitrary Lagrangian Eulerian formulation and adaptive mesh refinement method

In this paper we report an efficient numerical method combining a staggered arbitrary Lagrangian Eulerian (ALE) formulation with the adaptive mesh refinement (AMR) method for materials modeling including elastic–plastic flows, material failure, and fragmentation predictions. Unlike traditional AMR applied on fixed domains, our investigation focuses on the application to moving and deforming meshes resulting from Lagrangian motion. We give details of this numerical method with a capability to simulate elastic–plastic flows and predict material failure and fragmentation, and our main focus of this paper is to create an efficient method which combines ALE and AMR methods to simulate the dynamics of material responses with deformation and failure mechanisms. The interlevel operators and boundary conditions for these problems in AMR meshes have been investigated, and error indicators to locate material deformation and failure regions are studied. The method has been applied on several test problems, and the solutions of the problems obtained with the ALE–AMR method are reported. Parallel performance and software design for the ALE–AMR method are also discussed.     

Transports of air particulate matters in the atmospheric boundary layer-numerical studies using Eulerian and Lagrangian methods

Transports of air particulate matters(PM) from face sources in the atmospheric boundary layer(ABL) are investigated by the Eulerian single fluid model and the Lagrangian trajectory method,respectively.Large eddy simulation is used to simulate the fluid phase for high accuracy in both two approaches.The mean and fluctuating PM concentrations,as well as instantaneous PM distributions at different downstream and height positions,are presented.Higher mean and fluctuating particle concentrations are predicted by the Eulerian approach than the Lagrangian one.For the Lagrangian method,PM distributions cluster near the ground-wall because of the preferential dispersion of inertial particles by turbulence structures in the ABL,while it cannot be obtained by the Eulerian single fluid method,because the two-phase velocity differences are neglected in the Eulerian method.     

多物质流体动力学方法与结构动力学方法结合的流固耦合计算技术

建立一种基于重叠网格空间覆盖判断的流固耦合计算技术,把流场计算的Euler多物质流体动力学计算过程和Lagrange结构动力学计算过程相结合以描述流固间的相互作用.介绍该计算技术的具体实现过程,讨论提高几何判断效率、避免耦合遗漏、流固计算时间步协调等处理技术.应用建立的流固耦合计算程序模拟爆炸容器中爆炸流场对容器内部结构、容器壳体的作用过程.计算结果表明其可以反映流场发展过程、流场结构相互作用和结构的运动变形和破坏过程.     

Smooth decomposition of random fields

The Smooth Decomposition (SD) method was introduced to analyze discrete-time signals and generalized to continuous-time vector-valued random processes. The SD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random process and the covariance matrix of the associated time-derivative random process which defines the decomposition basis. This paper presents a new extension of the SD to continuous-time and continuous-space vector-valued random processes, classically named random fields. This generalization is a major step since one now deals with operators in infinite-dimensional spaces and not matrices. It is shown that in this new context the main properties of the SD are preserved. Applied to the responses of randomly excited continuous mechanical systems, the SD can be considered as an output-only analysis tool. Moreover, two natural orderings are defined to classify the decomposition terms which permit to interpret the SD in terms of modal analysis or in terms of Karhunen–Loève analysis.     

Optical polarimetry of random fields

The state of polarization of an optical field provides detailed information concerning both the radiation emission processes and the intricate interaction between light and matter. We report here a novel approach for characterizing the polarization properties of electromagnetic fields for which the electric field vector at a point may fluctuate in three dimensions. Using probes which couple all three components of the field, we were able to extract the polarized and unpolarized components of such fields. Our results constitute the proof of concept for what could be called three-dimensional optical polarimetry.     

Martin-Dynkin boundaries of random fields

Analogous of exit spaces of Dynkin [4] for Markov processes are constructed for random fields introduced by Dobrushin [2].     

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.