Statistical Properties Of Turbulence Research Articles

REVERSE TRANSITION OF A TURBULENT BOUNDARY LAYER

Systematic experimental researches on reverse transition in the boundary layer on a heated plate are carried out, and the time-series of instantaneous velocity components and temperature fluctuation are measured, then the Reynolds stress, the production term and absorption term of turbulent energy are presented. From the experimental results, the characteristics and physics mechanism of reverse transition as well as statistical properties of turbulence during reversion are revealed.

Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom

For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be calculated using only one UPO sampled from the ensemble. Evidence to support this conclusion is obtained by generating the ensemble by Monte Carlo calculation for a statistical mechanical model described by a space-time Hamiltonian that is expressed in terms of Floquet exponents of UPOs. This result allows us to interpret the recent interesting discovery that statistical properties of turbulence can be obtained from only one UPO [G. Kawahara and S. Kida, J. Fluid Mech. 449, 291 (2001); S. Kato and M. Yamada, Phys. Rev. E 68, 025302(R) (2003)].

Non-Gaussian Statistics of Atmospheric Turbulence and Related Effects on Aircraft Loads

Non-Gaussian statistical properties of turbulence in the inertial range can be characterized in terms of an exponent (k) that defines the scaling of velocity increments together with a fractal dimension (D) that quantifies “intermittency.” A new method of data analysis, for measuring k and D ,i sp resented based on the collapsing of appropriately normalized probability distributions measured at different scales. The method is illustrated by its application to records of turbulence measured at low altitudes by a specially instrumented Gnat trainer aircraft. The resulting “multifractal” statistical description of velocity increments is consistent with results obtained by previous authors using a different method of analysis, based on the scaling of velocity structure functions, and with the predictions of recent theoretical models of physical processes in the inertial range. It is demonstrated how the results can be applied directly to the estimation of aircraft loads, using a new multifractal formulation of statisticaldiscrete-gust theory. Qualitative differences between the resulting estimated loads and the loads predicted by the statistical method prescribed in the current airworthiness regulations, the power-spectral-density method, are identified.

Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures

In the present paper the statistical properties of compressible isotropic turbulence are analyzed by means of direct numerical simulations. The scope of the work is to evaluate the influence of compressibility on the time evolution of mean turbulence properties and to quantify the statistical properties of turbulent structures, their dynamics and similarities with the incompressible case. Simulations have been carried out at various turbulent Mach numbers and compressibility ratios by using a conservative hybrid scheme that relies on an optimized weighted essentially nonoscillatory approach for the convective terms and compact differencing for the viscous contributions. In order to identify similarities with incompressible turbulence we have also carried out an analysis in the plane of the second (Q*) and third (R*) invariants of the anisotropic part of the deformation rate tensor. The simulations show that the joint probability density function (Q*,R*) has a universal structure, as found in incompressible turbulence. The study confirms that the enstrophy obeys a two-stage evolution, due to the competing mechanisms of vortex stretching and viscous dissipation; however, at high turbulent Mach numbers, compressibility effects, associated to the occurrence of shocklets, become important. Furthermore, the analysis of the controlling mechanisms of vorticity generation has shown that even for compressible turbulence the growth of enstrophy is associated to a preferential alignment of the vorticity with the intermediate eigenvector of the anisotropic part of the strain-rate tensor.

Universality of Intermittent Convective Transport in the Scrape‐off Layer of Magnetically Confined Devices

AbstractThis article describes briefly recent results on the universality of intermittent convective transport reported in the scrape‐off layer. We show that the statistical properties of turbulence are identical for four different magnetic fusion devices. The four devices are the PISCES linear plasma device, the Tore Supra tokamak with limiter configuration, the Alcator C‐MOD with divertor configuration and high magnetic field, and theMAST spherical tokamak where the walls are far from the last closed flux surface (LCFS). These four devices do not only have different magnetic configurations but also have four different probes designs. Nine different types of statistical analyses are used, here we present just a few. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Some Applications of a Driven Nonlinear Lattice: Statistical Properties of Turbulence and Control of Thermal Flow

A nonlinear lattice driven by both ends is an interesting system to study two different physical problems: the statistical properties of turbulence and the control of the thermal flow in a solid state device. Both of these applications rely on nonlinearity that couples modes, shifts their vibrational frequencies, and, in a lattice, allows for the existence of discrete breathers. By introducing a special form of dissipation that mimics viscosity, we can show that such a nonlinear lattice exhibits properties which are strikingly similar to various experimental results obtained in a turbulent von Kármán flow, while an appropriate choice of parameters allows a precise control of the heat flow in the lattice, and can even turn the system into a "thermal rectifier" which does not have the same thermal conductivity in the two directions. By providing a model sufficiently simple to be studied in details the application to turbulence may suggest some clues to understand general features of turbulence, while the possibility to control and direct a thermal flow, although it is still very far from a practical device, could open new possibilities for applications.

Turbulence imaging and applications using beam emission spectroscopy on DIII-D (invited)

Two-dimensional measurements of density fluctuations are obtained in the radial and poloidal plane of the DIII-D tokamak with the Beam Emission Spectroscopy (BES) diagnostic system. The goals are to visualize the spatial structure and time evolution of turbulent eddies, as well as to obtain the 2D statistical properties of turbulence. The measurements are obtained with an array of localized BES spatial channels configured to image a midplane region of the plasma. 32 channels have been deployed, each with a spatial resolution of about 1 cm in the radial and poloidal directions, thus providing measurements of turbulence in the wave number range 0<k⊥⩽3 cm−1. A 5 (radial)×6 (poloidal) channel grid provides time-resolved images near the outer midplane at the sampling frequency of 1 MHz, thus providing a modest spatial resolution, high throughput, high time resolution turbulence imaging system. The images and resulting movies have broad application to a wide variety of fundamental turbulence studies: imaging of the highly complex, nonlinear turbulent eddy interactions, measurement of the 2D correlation function, and S(kr,kθ) wave number spectra, and direct measurement of the equilibrium and time-dependent turbulence flow field. The time-dependent, two-dimensional turbulence velocity flow-field is obtained with time-delay-estimation techniques.

Statistical Properties of Turbulence: A New Approach to Characterize Transport in Fusion Plasmas

A view of recent experimental results and progress in the characterization of the statistical properties of edge turbulence in fusion plasmas is given. The study of the dynamical interplay between fluctuations in gradients, turbulent transport and radial electric fields has shown that these parameters are strongly coupled both in tokamak and stellarator plasmas. The size of turbulent events increases when the plasma deviates from the average density gradient. The radial velocity of fluctuations is of the order of 20 m/s for transport events associated with a small deviation from the most probable gradient. On the contrary, the effective radial velocity increases up to 500 m/s for transport events in which the local gradient increases significantly above the most probable gradient. These results suggest a link between the size of transport events and the nature of transport (diffusive versus non-diffusive) in the plasma boundary region. The dynamical relationship between fluctuations in gradients and transport is strongly affected by the presence of sheared poloidal flows, heating power and the proximity to instability thresholds. There is also experimental evidence that the turbulent transport is strongly coupled with fluctuations in parallel flows, reflecting that parallel flows might, at least partially, be driven by turbulent mechanisms. Using the same methods developed for the study of turbulence, the statistical properties of the radial propagation of edge localized modes (ELMs) in the SOL of JET have also been investigated. ELM events propagate radially with effective velocities in the range of 1000 m/s, again showing a link between the radial velocity and the size of transport events. At such high velocities, the radial propagation competes strongly with parallel loss to the divertor plates and may therefore be an important mechanism transporting particles to the main chamber walls of fusion devices. This work emphasizes the importance of the statistical description of transport processes in fusion plasmas as an alternative approach to the traditional way of characterizing transport based on the computation of effective transport coefficients (i.e. diffusion coefficients) and on average quantities (i.e., average correlation lengths).

Stabilization of ion temperature gradient driven turbulence and formation of an internal transport barrier in a tokamak

The formation of an internal transport barrier (ITB) in a tokamak plasma due to the stabilization of ion temperature gradient (ITG) driven turbulence is analyzed using a three-dimensional turbulence code [Garbet et al., Phys. Plasmas 8, 2793 (2001)]. Two mechanisms leading to a reduction of turbulent transport are studied. First, a bifurcation to an improved confinement state obtained by increasing the heating power above a threshold value with a monotonic q profile is presented. This bifurcation occurs due to a spontaneous increase of self-generated E×B rotation shear. Then, the effect of low and negative magnetic shear on the ITG driven turbulence and transport is studied. The beneficial effects of low order minimum safety factor and low curvature of the safety factor profile are shown in these simulations by varying the magnetic configuration in a large range. The evolution of the statistical properties of turbulence during the ITB formation is presented.

Universal wall‐boundary conditions for turbulence‐transport models

AbstractIn the industrial design process of fluids engineering devices, the use of numerical simulation is of ever increasing importance. The predictive quality of such simulations is often governed by the representation of turbulence. Virtually all industrial simulations mimic the influence of turbulence by a closure model based on transport equations for statistical turbulence properties. Besides the derivation of such transport‐equation models, the adequate formulation of wall‐boundary conditions has come into the focus of attention. Conventional boundary conditions rely on the validity of specific flow conditions pertaining to the wall‐shear stress and the resolution properties of the computational grid in the wall‐adjacent region. Since the shear stress is part of the simulation result, this approach—strictly speaking—requires the anticipation of the solution. Moreover, it significantly affects the efficiency and flexibility of the simulation due to the associated mesh constraints. The principal aim of this research is the development of a universal boundary condition. Examples included show encouraging results for attached and separated flows.

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Spectral Reduction: A Statistical Description of Turbulence

A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be recovered from the time-averaged predictions of the reduced model. A Liouville theorem leads to inviscid equipartition solutions. Excellent agreement is obtained with two-dimensional forced-dissipative pseudospectral simulations. For the two-dimensional enstrophy cascade, logarithmic corrections to the high-order structure functions are observed.

Drag reduction in turbulent channel flow by phase randomization

Results of numerical simulations of plane turbulent channel flow are presented in which a forcing is introduced which derives from the randomization of selected Fourier modes. In all cases, the randomization is introduced uniformly throughout the channel. The properties of the resulting turbulence are strongly dependent on both the wave numbers whose phases are randomized and the forcing frequency. Two principal wave-number bands have been selected. The first includes a selected subset of the largest length scales of the turbulence. Forcing in this band results in a fully sustained maximum mass flux increase above that of normal turbulence of 30%, which translates into a drag reduction of 58%. Many of the statistical properties of the simulated drag-reduced turbulence generated in this manner are in good qualitative agreement with the statistical properties of turbulence observed in experiments in which drag reduction is achieved through the introduction of small concentrations of long-chained polymers into the flow. In a second set of simulations, the phases of the intermediate and smallest wavelengths were randomized. Forcing at these scales of motion results in a drag increase. Speculations on the mechanism of the drag reduction by phase randomization are offered.

Statistical properties of defect-mediated turbulence.

We study some statistical properties of a turbulent state described by a generalized Ginzburg-Landau equation and characterized by topological defects.

Imperfect turbulent mixing in chemical reactors: Coupling between chemical and hydrodynamic modes.

The effective rate of a chemical reaction is a complex combination of purely chemical effects and of effects related to transport phenomena or, more generally, to the spatial degrees of freedom. This coupling is analyzed in the limiting case of almost ideal mixing, taking into account the spatiotemporal correlations of the turbulent velocity field. A weak-noise expansion permits the deduction of an effective eddy diffusivity which is a function not only of the statistical properties of turbulence but also of the chemical kinetics. An application to the problem of thermal ignition is outlined.

Turbulent structure of a flat plate turbulent bounday layer diffusion flame. Production and transfer mechanism of a turbulent kinetic energy.

Turbulent properties of a diffusion flame formed in a flat plate boundary layer have been investigated experimentally. The flame is formed in the boundary layer with 10 m/s free stream velocity, when a fuel (Hydrogen/Nitrogen mixture) is uniformly injected through a porous wall. Statistical properties of turbulence up to third order cross correlations, mean temperature and mean values of stable species have been measured. The profiles of production, advection and turbulent diffusion of the turbulent kinetic energy and the cross correlation of two velocity components were calculated from measured data. These profiles show that the turbulent structure can be essentially treated as that of an isothermal shear flow even around the flame zone.

Turbulence and its effect upon the transmission of sound in water

When sound is transmitted in the sea the amplitude of the received signal is found to fluctuate. Various causes of signal fluctuations are discussed and the possibility of turbulence in the water causing some acoustic signal fluctuation is put forward. The statistical properties of turbulence are discussed and a theoretical prediction for the amount of signal fluctuation likely to be expected for a given degree of turbulence is made. Practical measurements, both of signal amplitude fluctuations and of the energy distribution of turbulent eddies agree very closely with the theoretical predictions.

Standardization of Gustiness Values from Aircraft

Abstract A universal turbulence standardization technique is described which is based quantitatively on the atmospheric turbulence itself rather than on the effects it products on an aircraft. It provides a single turbulence intensity number which may be measured continuously in flight in a variety of ways, and, with knowledge of the aircraft type and speed, can be linearly related to the rms value of vertical accelerations of the aircraft. The universal intensity number concept as applied here is an extension for aircraft use of the inertial subrange concept of atmospheric turbulence. In the inertial subrange all the statistical properties of turbulence of wavelengths less than a few hundred meters (the wavelength range which dominates gust loading for most aircraft) can be simply related to a single number. The intensity measurement also has value as a basic meteorological parameter, and has proven to be particularly useful in diffusion studies. The intensity scale is derived from various turbulence pow...

On the eddy diffusivities for momentum and heat

From a simple consideration, the eddy diffusivities for momentum and heat are shown to be equal in terms of statistical properties of turbulence. A universal semi-empirical expression for the eddy diffusivities in a turbulent shear flow is obtained in terms of the distance from the solid boundary and flow properties.

Turbulent Processes as Observed in Boundary Layer and Pipe

Certain statistical properties of turbulence observed in a boundary layer and in fully developed pipe flow are compared. Differences and likenesses are shown, and in particular certain common properties are found which appear to be indicative of processes governing the finer structure and controlling the origin, form, and life cycle of turbulent motions. An attempt is made to point out some of these processes. Attention is called to a region of high turbulent activity near the wall.