Statistical properties of turbulence: An overview

We present an introductory overview of several challenging problems in the statistical characterization of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.     

Decay of counterflow turbulence in superfluid <Superscript>4</Superscript>He

We summarize recent experiments on thermal counterflow turbulence in superfluid ⁴He, emphasizing the observation of turbulence in the normal fluid and its effect on the decay process when the heat flux is turned off. We argue that what is observed as turbulence in the normal fluid is a novel form of coupled turbulence in the superfluid and normal components, with injection of energy on the scales of both the (large) channel width and the (small) spacing between quantized vortices. Although an understanding of this coupled turbulence remains challenging, a theory of its decay is developed which accounts for the experimental observations.     

Dynamics of passive-scalar turbulence

We present the first study of the dynamic scaling or multiscaling of passive-scalar turbulence. For the Kraichnan version of passive-scalar turbulence we show analytically, in both Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is obtained but with different dynamic exponents. By developing the multifractal model we show that dynamic multiscaling occurs in passive-scalar turbulence only if the advecting velocity field is itself multifractal. We substantiate our results by detailed numerical simulations in shell models of passive-scalar advection.     

A study on turbulence modulation via an analysis of turbulence anisotropy-invariants

We investigate the turbulence modulation by particles in a turbulent two-phase channel flow via an analysis of turbulence anisotropy-invariants. The fluid turbulence is calculated by a large eddy simulation with a point-force two-way coupling model and particles are tracked by the Lagrangian trajectory method. The channel turbulence follows the two-component turbulence state within the viscous sub-layer region and outside the region the turbulence tends to follow the right curve of the anisotropy-invariant....     

Decay of pure quantum turbulence in superfluid 3He-B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.     

Varieties of dynamic multiscaling in fluid turbulence

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations, which we derive. We check this explicitly by detailed numerical simulations of the Gledzer-Ohkitani-Yamada shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time and time-dependent structure functions show multiscaling.     

Density fluctuation spectrum in whistler turbulence

We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k−7/3 spectrum, where k is a characteristic wavenumber.     

GEOMETRIC REALIZATION OF THE TWO-POINT VELOCITY CORRELATION TENSOR FOR ISOTROPIC TURBULENCE

A new geometric view of homogeneous isotropic turbulence is contemplated employing the two-point velocity correlation tensor of the velocity fluctuations. We show that this correlation tensor generates a family of pseudo-Riemannian metrics. This enables us to specify the geometry of a singled out Eulerian fluid volume in a statistical sense. We expose the relationship of some geometric constructions with statistical quantities arising in turbulence.     

Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation

We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence.We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation.The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence.Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles.We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall.     

湍流理论的近代发展

这篇论文的内容是关於不可压缩流体的湍流理论近代发展的综合性介绍舆分析。我们首先评述了根据Reynolds的平均运动方程所建立的混合长度理论。其次,分析关於均匀各向同性湍流的主要理论工作。第三,讨论了运用Reynolds的平均运动方程和根据速度涨落方程求得的速度关联函数的动力学方程来处理具有Reynolds剪应力的普通湍流运动问题。同时说明这个方法虽然能够给出比混合长度理论舆实验较为接近的理论结果并能提出速度涨落平方平均值的理论分布,但是由於在求出的速度关联的动力学方程中出现高次元的速度关联,它继续地导致不封闭的微分方程组因而遇到不易克服的困难。因此,从以上湍流理论发展的回顾和最近关於均匀各向同性湍流在后期衰变运动的涡性结构工作,我们在最后提出了对今后湍流理论研究工作的新看法:湍流运动的基本组成部分是流体粘性作用所引起的涡旋运动;这个涡旋运动的动力学根据是用平均的方法后Navier-Stokes方程所导出的Reyonlds的平均运动方程典带度涨落方程。我们并着重说明Reynolds认识到湍流运动可分作平均运动与涨落运动的重要性。今后的理论工作则在於求这两组动力学方程的涡旋运动解,而这种类型的解并须满足像Колмогоров在高Reynolds数运动的局部各向同性湍流理论中所提出的统计条件,方能使解满足惟一性并可舆实验结果相比较。     

Turbulence decay rate as a measure of flow dimensionality

The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite-depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads to increased bottom damping. The anomaly coefficient, which characterizes the deviation of damping from the one derived using a quasi-two-dimensional model, can be used as a measure of the flow dimensionality. Experiments in turbulent layers show that when the anomaly coefficient becomes high, the turbulent inverse energy cascade is suppressed. In the opposite limit turbulence can self-organize into a coherent flow.     

Fractal dimension of superfluid turbulence

Superfluid turbulence consists of a disordered tangle of quantized vortex filaments which interact with each other and with the normal fluid. We develop a kinematic model of normal-fluid turbulence to study superfluid vortex tangles at finite temperatures and show by numerical simulation that the system of filaments has a fractal dimension larger than one. We find that the fractal dimension is directly related to the vortex-line density and is independent of temperature over a wide range.     

Nondiffusive suprathermal ion transport in simple magnetized toroidal plasmas

We investigate suprathermal ion dynamics in simple magnetized toroidal plasmas in the presence of electrostatic turbulence driven by the ideal interchange instability. Turbulent fields from fluid simulations are used in the nonrelativistic equation of ion motion to compute suprathermal tracer ion trajectories. Suprathermal ion dispersion starts with a brief ballistic phase, during which particles do not interact with the plasma, followed by a turbulence interaction phase. In this one simple system, we observe the entire spectrum of suprathermal ion dynamics, from subdiffusion to superdiffusion, depending on beam energy and turbulence amplitude. We estimate the duration of the ballistic phase and identify basic mechanisms during the interaction phase that determine the dependencies of the character of suprathermal ion dispersion upon the beam energy and turbulence fluctuation amplitude.     

Computational fluid dynamic modeling of gas flow characteristics of the high-power CW CO2 laser

To increase the photoelectronic conversion efficiency of the single discharge tube and to meet the requirements of the laser cutting system,optimization of the discharge tube structure and gas flow field is necessary.We present a computational fluid dynamic model to predict the gas flow characteristics of high-power fast-axial flow CO 2 laser.A set of differential equations is used to describe the operation of the laser.Gas flow characteristics,are calculated.The effects of gas velocity and turbulence intensity on discharge stability are studied.Computational results are compared with experimental values,and a good agreement is observed.The method presented and the results obtained can make the design process more efficient.     

A numerical investigation of vortex-coupled superfluidity

We have performed numerical simulations of quantized vortex lines in a model of normal fluid turbulence. The results are used to discuss the idea, put forward to explain some recent experiments, that in isothermal turbulent helium flow the high density of vortex lines locks the two fluid components together.     

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper,we present a direct numerical simulation(DNS) of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number(Re = 1) in a three-dimensional straight channel flow for the first time,using the Giesekus constitutive model for the fluid.In order to generate and maintain the turbulent fluid motion in the straight channel,a sinusoidal force term is added to the momentum equation,and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field.Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS.The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.     

Density fluctuations on mm and Mpc scales

We will in this Letter report on suggestive similarities between density fluctuation power versus wavenumber on small (mm) and large (Mpc) scales. The small scale measurements were made in fusion plasmas and compared to predictions from classical fluid turbulence theory. The data is consistent with the dissipative range of 2D turbulence. Alternatively, the results can be fitted to a functional form that cannot be explained by turbulence theory. The large scale measurements were part of the Sloan Digital Sky Survey galaxy redshift examination. We found that the equations describing fusion plasmas also hold for the galaxy data. The comparable dependency of density fluctuation power on wavenumber in fusion plasmas and galaxies might indicate a common origin of these fluctuations.     

Kinetic modeling of a high power fast-axial-flow CO2 laser with computational fluid dynamics method

A new computational fluid dynamics (CFD) method for the simulation of fast-axial-flow CO2 laser is developed.The model which is solved by CFD software uses a set of dynamic differential equations to describe the dynamic process in one discharge tube.The velocity,temperature,pressure and turbulence energy distributions in discharge passage are presented.There is a good agreement between the theoretical prediction and the experimental results.This result indicates that the parameters of the laser have significant effect on the flow distribution in the discharge passage.It is helpful to optimize the output of high power CO2 laser by mastering its kinetic characteristics.     

Numerical comparison of Riemann solvers for astrophysical hydrodynamics

The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.