Two-point Spatial Correlation Research Articles

The Statistical Evaluation of the Flapping Motion in a Two-Dimensional Turbulent Jet

The flapping motion in a two-dimensional turbulent jet is analyzed statistically. The analysis is done by applying a continuous wavelet transform with Gabor mother wavelet to the experimental result of hot-wire anemometer. The analysis results show that the flapping motion is clearly recognized by the present new method. The flapping motion occurs at random, and the average time interval of flapping motion is about 6.1 times the flapping periods (0.24 sec). The average duration time of the flapping motion is about 1.7 times the flapping period (0.07 sec) and the one that continues over 3.0 times the flapping period is very few. The negative value of the two-point spatial velocity correlation substantially depends on whether the flapping motion arises or not. From these results, it is found that the flapping motion in a two-dimensional turbulent jet has a very important role to the properties of the jet though the flapping motion is a rare phenomenon.

Structure, scaling, and synthesis of proper orthogonal decomposition modes of inhomogeneous turbulence

By examining the proper orthogonal decomposition (POD) of turbulent channel flow and turbulent thermal convection in the inhomogeneous direction of each flow, it is found that the POD eigenfunctions separate into two types of modes having different structure and scaling. For these flows, the modes can be represented in the form of amplitude-modulated and phase-modulated oscillations in the wall-normal direction. The phase functions can be extracted by several means and they contain much of the physics embedded in the two-point spatial correlation function. The phase and envelope functions are analyzed to interpret POD mode behavior. The first several most energetic modes are large-scale and their structure is idiosyncratic relative to the rest of the modes and characteristic of the type of the flow. Outside this group of idiosyncratic modes, the remaining modes are less energetic, smaller scale, and asymptotically self-similar in the sense that the phases scaled using sequency correlate well and approach a single limiting curve with increasing order (mode number). This asymptotic phase function is characteristic of the type of turbulence, i.e., it differs between channel flow and thermal convection, despite it being small-scale and, therefore, presumably insensitive to the form of the boundary conditions. The work of Moser [“Kolmogorov inertial range spectra for inhomogeneous turbulence,” Phys. Fluids 6, 794 (1994)] provides an approximate relationship for the asymptotic phase function in terms of the distribution of viscous dissipation ϵ(y). A more general framework for this relationship is presented in which the idiosyncratic modes determine the energy distribution and the asymptotically self-similar modes determine the distribution of viscous dissipation. The foregoing results are exploited to develop a complete set of orthonormal basis functions that approximate the POD modes and possess convergence properties that are comparable to the optimal convergence of the exact POD and significantly better than those of conventional orthogonal polynomials. This procedure, called “synthetic POD,” uses only knowledge of the distribution of mean dissipation (or equivalently, the asymptotic phase function) without a priori computation of the more complicated two-point correlation functions.

On the correlation of heat release rate in turbulent premixed flames

Two-point spatial correlation of rate of change of fluctuating heat release rate dictates the sound emission from open turbulent flames and this correlation is not directly addressed in past studies. The results from Direct Numerical Simulation and laser diagnostics of turbulent premixed flames are analyzed to study this correlation function and the two-point spatial correlation of the fluctuating heat release rate. The analyses showed that these correlation functions can be represented very well using Gaussian functions. The integral length scale, ℓ, for the fluctuating heat release rate is about one to two planar laminar flame thermal thickness, δLo, and this is not influenced by turbulence Reynolds number and swirl. The length scale for the rate of change of fluctuating heat release rate is about δLo/4. The far field sound pressure levels of open turbulent premixed flames calculated by post processing RANS simulation results along with the above length scales compare very well with measured values.

Effects of Injection and Main Flow Conditions on Supersonic Turbulent Mixing Structure

The effects of injection and main flow conditions on the turbulent structure produced by a gaseous sonic transverse injection into a supersonic airstream were investigated. The turbulent structure inherent in the mixing flowfield was characterized by the single-time two-point spatial correlations based on the concentration fluctuation and measured with acetone planar laser-induced fluorescence. Results revealed that the most intensively fluctuating region appeared on the 50%-averaged-concentration track, irrespective of the injection conditions. The highly correlated region, which indicates an organized large-scale structure, appeared as a tilting ellipse in the lower-compressibility cases and an ellipse almost parallel to the streamline in the higher-compressibility cases. These differences in structure result in the difference of the averaged jet width. The injection with the higher-compressibility condition showed more stable structures and slower development in the size due to suppression of the instability growth. The structure was likely to be stretched toward the averaged-velocity direction as the main flow Mach number increased. Increasing the velocity difference between the jet and main flow caused the large-scale eddies to appear more frequently.

Full 3D correlation tensor computed from double field stereoscopic PIV in a high Reynolds number turbulent boundary layer

The turbulence structure near a wall is a very active subject of research and a key to the understanding and modeling of this flow. Many researchers have worked on this subject since the fifties Hama et al. (J Appl Phys 28:388–394, 1957). One way to study this organization consists of computing the spatial two-point correlations. Stanislas et al. (C R Acad Sci Paris 327(2b):55–61, 1999) and Kahler (Exp Fluids 36:114–130, 2004) showed that double spatial correlations can be computed from stereoscopic particle image velocimetry (SPIV) fields and can lead to a better understanding of the turbulent flow organization. The limitation is that the correlation is only computed in the PIV plane. The idea of the present paper is to propose a new method based on a specific stereoscopic PIV experiment that allows the computation of the full 3D spatial correlation tensor. The results obtained are validated by comparison with 2D computation from SPIV. They are in very good agreement with the results of Ganapthisubramani et al. (J Fluid Mech 524:57–80, 2005a).

Scaling properties of one-dimensional cluster–cluster aggregation with Lévy diffusion

We present a study of the scaling properties of cluster–cluster aggregation with a source ofmonomers in the stationary state when the spatial transport of particles occurs by Lévyflights. We show that the transition from mean-field statistics to fluctuation-dominatedstatistics which, for the more commonly considered case of diffusive transport,occurs as the spatial dimension of the system is tuned through two from above,can be mimicked even in one dimension by varying the characteristic exponent,β, of the Lévy jump length distribution. We also show that the two-pointmass correlation function, responsible for the flux of mass in the stationarystate, is strongly universal: its scaling exponent is given by the mean-fieldvalue independent of the spatial dimension and independent of the value ofβ. Finally, we study numerically the two-point spatial correlation function whichcharacterizes the structure of the depletion zone around heavy particles in thediffusion-limited regime. We find that this correlation function vanishes with a non-trivialfractional power of the separation between particles as this separation goes to zero. Weprovide a scaling argument for the value of this exponent which is in reasonable agreementwith the numerical measurements.

STATISTICAL ANALYSIS OF WATER MASERS IN STAR-FORMING REGIONS: CEPHEUS A AND W75 N

We have done a statistical analysis of Very Long Baseline Array (VLBA) data of water masers in the star-forming regions (SFRs) Cepheus A and W75 N, using correlation functions to study the spatial clustering and Doppler-velocity distribution of these masers. Two-point spatial correlation functions show a characteristic scale size for clusters of water maser spots < or ~1 AU, similar to the values found in other SFRs. This suggests that the scale for water maser excitation tends to be < or ~1 AU. Velocity correlation functions show power-law dependences with indices that can be explained by regular velocity fields, such as expansion and/or rotation. These velocity fields are similar to those indicated by the water maser proper-motion measurements; therefore, the velocity correlation functions appear to reveal the organized motion of water maser spots on scales larger than 1 AU.

Spectral changes of the light produced by scattering from tissue

The effect of the two-point spatial correlation function of human tissue on the spectrum of scattered light is considered within the accuracy of the first Born approximation. An expression for the maximum of the spectrum of the scattered light at various scattering angles is derived. It is shown that for most biological tissues the spectrum of the backscattered light is centered at a higher frequency with respect to the incident spectrum.

Fourier projection method for measuring the two-point correlation of Laguerre–Gaussianmodes

The spatial distribution and signature of vorticity of Laguerre–Gaussian modes is analysedby measuring the two-point spatial correlation function of the one-dimensional projectionof the vortex field. We describe an interferometric approach, based on a Fourier projectionalgorithm, for the experimental determination of the two-point correlation function of thefull complex vortex field at the cross-section plane of the recorded interference pattern. Thetwo-point correlation at any transverse plane along the beam axis is retrievedby the angular spectrum of plane waves technique, allowing us to characterizethe vortex structure and spatial coherence along the direction of propagation.

Fresnel tomography and interferometric technique for characterizing Laguerre–Gaussian beams

The Fresnel tomograms of Laguerre–Gaussian beams are found and the relation of the two-point spatial correlation function with the tomographic map is discussed. The spatial distribution and signature of vorticity of Laguerre–Gaussian modes is analyzed by measuring the two-point spatial correlation function of the one-dimensional projection of the vortex field. An interferometric approach, based on a Fourier projection algorithm, for the experimental determination of the two-point correlation function of the full complex vortex field at the cross-section plane of the recorded interference pattern is also described; this approach allows one to characterize the vortex structure and spatial coherence along the direction of propagation.

Scalar Spatial Correlations in a Supersonic Mixing Flowfield

Single-time two-point spatial correlations of injectant concentrations in the supersonic mixing flowfield produced by a sonic transverse injection of air into a Mach 2.0 supersonic airstream were investigated using acetone planar laser-induced fluorescence data. Side-view and end-view contour maps were obtained in several planes to characterize the turbulent structure and three-dimensionality of the mixing flowfield. The correlation maps indicated an organized large-scale structure in the upper region of the jet. The side-view correlation maps revealed that the shape of the large dominating structure was elliptic and that its major axis turned from backward-leaning to forward-leaning as the reference point of correlation moved downstream. The end-view correlation maps showed that the instantaneous jet plume appeared by turns either in the top or in the lower sides of the time-averaged injectant plume in each cross section.

The Imperial IRAS-FSC Redshift Catalogue: luminosity functions, evolution and galaxy bias

We present the luminosity function and selection function of 60 micron galaxies selected from the Imperial IRAS-FSC Redshift Catalogue (IIFSCz). Three methods, including the 1/Vmax} and the parametric and non-parametric maximum likelihood estimator, are used and results agree well with each other. A density evolution proportional to (1+z)^3.4 or a luminosity evolution exp(1.7 t_L / \tau)$ where t_L is the look-back time is detected in the full sample in the redshift range [0.02, 0.1], consistent with previous analyses. Of the four infrared subpopulations, cirrus-type galaxies and M82-type starbursts show similar evolutionary trends, galaxies with significant AGN contributions show stronger positive evolution and Arp 220-type starbursts exhibit strong negative evolution. The dominant subpopulation changes from cirrus-type galaxies to M82-type starbursts at log (L_60 / L_Sun) ~ 10.3. In the second half of the paper, we derive the projected two-point spatial correlation function for galaxies of different infrared template type. The mean relative bias between cirrus-type galaxies and M82-type starbursts, which correspond to quiescent galaxies with optically thin interstellar dust and actively star-forming galaxies respectively, is calculated to be around 1.25. The relation between current star formation rate (SFR) in star-forming galaxies and environment is investigated by looking at the the dependence of clustering on infrared luminosity. We found that M82-type actively star-forming galaxies show stronger clustering as infrared luminosity / SFR increases. The correlation between clustering strength and SFR in the local Universe seems to echo the basic trend seen in star-forming galaxies in the Great Observatories Origins Deep Survey (GOODS) fields at z ~ 1.

Experimental Investigations of an Internal Flow Generated by Porous Injection

Abstract An anisothermal channel flow generated by a porous injection is investigated in details for different Reynolds numbers of the injection in order to highlight the impact of the microstructure of porous material on the flow development. Two types of porous materials, being characterized by different matrices and pore sizes are studied: a coarse bronze porous plate (30% porosity and 100 μm average pore diameter) and a stainless steel porous plate (30% porosity and 30 μm average pore diameter). Particle image velocimetry, hot-wire anemometry, and cold wire thermometer measurements lead to the comparison of mean profiles, rms profiles, and energy spectra for the velocity and temperature fields. Two-point spatial correlations for the fluctuating velocity are also calculated. In the case of the coarse bronze plate, the flow is slightly fluctuating with big space coherence. In the opposite, the results obtained with the fine pore plate show a flow close to a fully developed turbulent channel flow. The comparison of the aerodynamic field with computational simulations based on a Reynolds-averaged Navier-Stokes (RANS) model underlines the difficulties to reproduce exactly the evolution of the mean and fluctuating velocities in all the explored part of the channel.

The spatial distribution of X-ray selected AGN in theChandradeep fields: a theoretical perspective

We study the spatial distribution of X-ray selected AGN in the framework of hierarchical co-evolution of supermassive black holes and their host galaxies and dark matter haloes. To this end, we have applied the model developed by Croton et al.(2006), De Lucia & Blaizot(2007) and Marulli et al.(2008) to the output of the Millennium Run and obtained hundreds of realizations of past light-cones from which we have extracted realistic mock AGN catalogues that mimic the Chandra deep fields. We find that the model AGN number counts are in fair agreement with observations, except at fluxes <1e-15 erg/cm^2/s. The spatial two-point correlation function predicted by the model is well described by a power-law relation out to 20 Mpc/h, in close agreement with observations. Our model matches the correlation length r_0 of AGN in the Chandra Deep Field North but underestimates it in the Chandra Deep Field South. When fixing the slope to gamma = 1.4, as in Gilli et al. (2005), the statistical significance of the mismatch is 2-2.5 sigma, suggesting that the predicted cosmic variance, which dominates the error budget, may not account for the different correlation length of the AGN in the two fields. While our results are robust to changes in the model prescriptions for the AGN lightcurves, the luminosity dependence of the clustering is sensitive to the different lightcurve models adopted. However, irrespective of the model considered, the luminosity dependence of the AGN clustering in our mock fields seems to be weaker than in the real Chandra fields. The significance of this mismatch needs to be confirmed using larger datasets.

Correlation properties of random electromagnetic beams in laser resonators

With the help of the generalized Huygens–Fresnel principle and the tensor approach for electromagnetic stochastic beams we investigate the behavior of their two-point spatial correlation properties on interaction with a laser resonator. In particular, the evolution of the degree of coherence, of the degree of cross-polarization and of the intensity correlations (at one and two points in space) is analyzed for typical beams and cavities. The theory is illustrated by numerical curves pertaining to various correlation properties of typical electromagnetic Gaussian Schell-model beams.

Unsteady characteristics of near-wall turbulence using high repetition stereoscopic particle image velocimetry (PIV)

This study is part of a project that is aimed at building dynamic boundary conditions near a solid wall, in order to reduce the large eddy simulation spatial resolution that is necessary in this region. The objective is to build a low-order dynamical system in a plane parallel to the wall, which will mimic the unsteady behaviour of turbulence. This dynamical system should be derived from a POD decomposition of the velocity field. The POD decomposition is to be applied on an experimental database of time-resolved velocity fields. In order to obtain the experimental database, a specific experiment of high-speed stereoscopic particle image velocimetry (PIV) has been performed. This experiment was carried out in the turbulent boundary layer of the LML wind tunnel. The plane under study was parallel to the wall located at 100 wall units. This database is validated via comparison with hot-wire anemometry (HWA). Despite some peak locking observed on the streamwise velocity component, the PDF and the power spectra are in very good agreement with the HWA results. The two-point spatial correlations are also in good agreement with the results from the literature. As the flow is time-resolved, space–time correlations are also computed. The convection of the flow structure is observed to be the most important effect at this wall distance. The next step is to compute the dynamical system and to couple it to a large eddy simulation.

THE CORRELATION FUNCTION OF OPTICALLY SELECTED GALAXY CLUSTERS IN THE SLOAN DIGITAL SKY SURVEY

We measure the two-point spatial correlation function for clusters selected from the photometric MaxBCG galaxy cluster catalog for the Sloan Digital Sky Survey (SDSS). We evaluate the correlation function for several cluster samples using different cuts in cluster richness. Fitting the results to power-laws, $\xi_{cc}(r) = (r/R_0)^{-\gamma}$, the estimated correlation length $R_0$ as a function of richness is broadly consistent with previous cluster observations and with expectations from N-body simulations. We study how the linear bias parameter scales with richness and compare our results to theoretical predictions. Since these measurements extend to very large scales, we also compare them to models that include the baryon acoustic oscillation feature and that account for the smoothing effects induced by errors in the cluster photometric redshift estimates. For the largest cluster sample, corresponding to a richness threshold of $\Ng\ge 10$, we find only weak evidence, of about $1.4-1.7\sigma$ significance, for the baryonic acoustic oscillation signature in the cluster correlation function.

Growing length scale in gravity-driven dense granular flow

We report simulations of a two-dimensional, dense, bidisperse system of inelastic hard disks falling down a vertical tube under the influence of gravity. We examine the approach to jamming as the average flow of particles down the tube is slowed by making the outlet narrower. Defining coarse-grained velocity and stress fields, we study two-point temporal and spatial correlation functions of these fields in a region of the tube where the time-averaged velocity is spatially uniform. We find that fluctuations in both velocity and stress become increasingly correlated as the system approaches jamming. We extract a growing length scale and time scale from these correlations.

표면조도가 있는 난류경계층 내 난류구조

Turbulent coherent structures near rod-roughened wall are investigated by analyzing the database of directnumerical simulation of turbulent boundary layer. The surface roughness rods with the height k/δ =0.05 are arranged periodically in Reδ = 9000 . The roughness sublayer is defined as two-point correlations are not independent of streamwise locations around roughness. The roughness sublayer based on the two-point spatial correlation is different from that given by one-point statistics. Quadrant analysis and probability-weighted Reynolds shear stress indicate that turbulent structures are not affected by surface roughness above the roughness sublayer defined by the spatial correlations. The conditionally-averaged flow fields associated with Reynolds shear stress producing Q2/Q4 events show that though turbulent vortices are affected in the roughness sublayer, these are very similar at different streamwise locations above the roughness sublayer. The Reynolds stress producing turbulent vortices in the log layer ( y /δ = 0.15) have almost the same geometrical shape as those in the smooth wall-bounded turbulent flows. This suggests that the mechanism by which the Reynolds stress is produced in the log layer has not been significantly affected by the present surface roughness.

Vortical structures in the turbulent boundary layer: a possible route to a universal representation

A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by stereoscopic particle image velocimetry (SPIV) in a plane normal both to the mean flow and the wall. The characteristics of the experimental data allow us to focus on the spatial organization within the logarithmic region for Reynolds numbersReθup to 15000. On the basis of the now accepted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two-point spatial correlations and the use of linear stochastic estimation (LSE). These analyses confirm that the shape of the most probable coherent structures corresponds to an asymmetric one-legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near-wall region belowy+=150, densely populated with strongly interacting vortices; and the region abovey+=150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall-normal independences of these quantities are achieved when scaling with the local Kolmogorov scales. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead us to revisit the equation for the mean square vorticity fluctuations, and to propose a new balance of this equation in the near-wall region. This analysis and the above results allow us to propose a new description of the near-wall region, leading to a new scaling which seems to have a good universality in the Reynolds-number range investigated. The possibility of reaching a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is suggested.