Turbulent Correlation Research Articles

Field correlations for off‐axis Gaussian laser beams in atmospheric turbulence

AbstractThe absolute field correlations in atmospheric turbulence are evaluated for the off‐axis optical Gaussian beam incidence. Evaluations in the practical range of the source and the turbulent medium parameters show that an increase in the diagonal length at the receiver plane causes the absolute field correlations of the off‐axis Gaussian beam to decrease. At a fixed receiver diagonal length, the off‐axis Gaussian beams having smaller displacement parameters and larger source sizes exhibit larger absolute field correlations. Comparing the absolute field correlations of the off‐axis Gaussian beams in atmospheric turbulence with their no turbulence counterparts, it is observed that the behavior of the absolute field correlation variations remains the same; however, the diminishing of the absolute field correlations in turbulence occurs at smaller diagonal lengths.

Investigation of the mixing layer of underexpanded supersonic jets by particle image velocimetry

The present experimental study focuses on some properties of the turbulence and the shock-cell structure in underexpanded supersonic jets, which are of practical relevance in air transport. Choked jets at fully expanded Mach numbers Mj=1.10, 1.15, 1.35 and 1.50 are investigated using particle image velocimetry. The strength of the shock-cell structure is studied from mean velocity profiles, both in the jet core and in the mixing layer. The general geometry of the latter and its location relatively to the mean shock-cell structure are established. Furthermore, detailed accounts of mixing layer thickness, turbulence levels, spatial correlations and intrinsic turbulence length scales are given. While the mean velocity variations related to the shock-cell structure extend up to the subsonic part of the studied jets, their mixing layer is found to be mostly located in the subsonic region. Some of the observed turbulence properties, like the mixing layer thickness and turbulence levels, are close to what is found for subsonic jets. The effect of the shock-cell structure on turbulence is however visible for Mj⩾1.35. The spatial correlations of turbulence are used to estimate intrinsic turbulence length scales and these are found to be of the order of the shock-cell length. These data are used to make some comments upon the generation mechanism of shock-associated noise, a noise component produced by imperfectly expanded supersonic jets.

Passively controlled supersonic cavity flow using a spanwise cylinder

An experimental investigation of a passively controlled open cavity with a length to depth ratio of six and freestream Mach number of 1.4 was conducted to investigate the mechanisms responsible for the observed surface pressure reductions. The passive control comes from placing a spanwise aligned cylinder in the boundary layer near the leading edge of the cavity. The two control configurations were isolated from previous experiments of the fluctuating surface pressure and correspond to a larger diameter rod near the top of the boundary layer and a smaller diameter rod placed near the wall. These were further analyzed using particle image velocimetry in an attempt to elicit the responsible mechanism for the flow control. The use of two-point statistics revealed the wall normal turbulent velocity correlation’s evolution became elongated in the wall normal direction. This suggests that the shear layer may be less-organized and consists of smaller-scale structures. The disturbance of the feedback receptivity loop is clearly demonstrated for the controlled configurations evidenced by weakened correlation signals between the aft wall sensor and positions on the cavity floor. The presence of the rod is shown to decrease the mean shear gradient, more effectively for the large rod placed at the top of the boundary layer, throughout the shear layer. The efficacy of the control leads to an initially thicker shear layer which spreads more rapidly and is clearly demonstrated by vorticity growth rates, mean, and turbulent flowfield statistics.

Separation & free-stream turbulence: implications for surface aerodynamics & heat transfer

Preliminary results from a Particle Image Velocimetry (PIV) investigation of the separation-reattachment flow over a flat plate are presented. The experiments address the effects of two key variables: flow approach angle (manipulated indirectly with a trailing edge flap) and free-stream turbulence level (introduced upstream with grids). The plate thickness Reynolds number is fixed throughout and lies within the transitional regime.In the first test series (I), it is shown that increasing the turbulence level and reducing the approach angle cause the mean leading-edge separation bubble to shrink. The effect of free- stream turbulence, in particular, diminishes progressively as its level is raised. In the second series (II), downstream development of the reattached boundary layer is found to unfold rapidly at first but plateau after approximately three bubble-lengths. Momentum thickness Reynolds and Stanton numbers develop independently of the free-stream turbulence thereafter, and are well described by shifted turbulent correlations. Heat transfer potential ultimately depends upon the balance between frictional loss, bubble size and downstream mixing.

Evaluation of augmented RSM for interaction of homogeneous turbulent mixture with shock and rarefaction waves

Interaction of shock or rarefaction waves with turbulent mixtures is challenging for turbulence models. A recent article has shown how results from linear interaction analysis (LIA) can be synthesised into transfer matrices relating upstream and downstream second-order turbulent correlations. These results have been obtained in the limit of axisymmetric weakly turbulent mixture. The current article is devoted to the evaluation of three augmented Reynolds stress models (RSMs) for the same kinds of interaction with weakly turbulent mixtures. Corrections aimed at improving the compatibility with LIA are finally proposed for one of these RSMs.

THREE-FLUID, THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SOLAR WIND MODEL WITH EDDY VISCOSITY AND TURBULENT RESISTIVITY

We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for themore » Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are compared with plasma and magnetic field observations on WIND, Ulysses, and Voyager 2 spacecraft.« less

Characterization of the Turbulent Magnetic Integral Length in the Solar Wind: From 0.3 to 5 Astronomical Units

The solar wind is a structured and complex system, in which the fields vary strongly over a wide range of spatial and temporal scales. As an example, the turbulent activity in the wind affects the evolution in the heliosphere of the integral turbulent scale or correlation length [λ], usually associated with the breakpoint in the turbulent-energy spectrum that separates the inertial range from the injection range. This large variability of the fields demands a statistical description of the solar wind. We study the probability distribution function (PDF) of the magnetic-autocorrelation lengths observed in the solar wind at different distances from the Sun. We used observations from the Helios, ACE, and Ulysses spacecraft. We distinguished between the usual solar wind and one of its transient components (interplanetary coronal mass ejections, ICMEs), and also studied solar-wind samples with low and high proton beta [βp]. We find that in the last three regimes the PDF of λ is a log-normal function, consistent with the multiplicative and nonlinear processes that take place in the solar wind, the initial λ (before the Alfvénic point) being larger in ICMEs.

A note on the relationship between turbulent coherent structures and phase correlation.

Various definitions of coherent structures exist in turbulence research, but a common assumption is that coherent structures have correlated spectral phases. As a result, randomization of phases is believed, generally, to remove coherent structures from the measured data. Here, we reexamine these assumptions using atmospheric turbulence measurements. Small-scale coherent structures are detected in the usual way using the wavelet transform. A considerable percentage of the detected structures are not phase correlated, although some of them are clearly organized in space and time. At larger scales, structures have even higher degree of spatiotemporal coherence but are also associated with weak phase correlation. A series of specific examples are shown to demonstrate this. These results warn about the vague terminology and assumptions around coherent structures, particularly for complex real-world turbulence.

Effect of ultrasound on mass transfer during electrodeposition for electrodes separated by a narrow gap

This work reports an investigation on mass transfer by ultrasound agitation during electrodeposition on electrodes separated by a narrow inter-electrode gap. Polarisation experiments were performed to identify the mass transfer limiting current. The limiting current density was used to calculate mass transfer boundary layer thicknesses which were used to develop mass transfer correlations. Experiments were carried out using a cell with parallel copper discs which were positioned at gaps of 1, 0.5 and 0.15cm. The distance between the ultrasonic probe and electrodes was varied between 3 and 1.5cm. The polarisation data showed clear limiting current plateaux when the distance between the electrodes was larger, however significant distortions were observed when the gap was 0.15cm. It was found that lower ultrasound powers of 9–18W/cm2 provided more effective agitation at narrower electrode gaps than powers exceeding 18W/cm2. Sherwood correlations showed that in this system, developing turbulence occurs for larger inter-electrode spacing, whereas for narrow electrode gaps fully turbulent correlations were obtained. A 2-D current distribution model showed that potential distortions that were observed in the polarisation data were caused by the close placement of the metallic US probe to the two parallel electrodes.

Radial correlation reflectometry at oblique probing wave incidence (linear scattering theory predictions)

Turbulence radial correlation length measurements by making use of Doppler reflectometry are analysed in this paper assuming the linear (in density perturbation amplitude) regime of the probing wave scattering. Based on the Born approximation applicable in this case, we get a general integral representation of the scattering signal amplitude, which is then analysed in detail both analytically and numerically. Asymptotic analytical evaluation of the scattering signal amplitude gives a criterion on the incidence angle, exceeding which leads to suppression of the poor localized forward scattering contribution to the Doppler reflectometry signal. In the latter case, fast decay of correlation in the two frequency channels appears to be similar to that expected from the turbulence correlation function. The analytical estimations and predictions are confirmed by numerical evaluation of the scattering signal amplitude. The analysis performed proves the feasibility of the radial correlation Doppler reflectometry technique for measurements of the correlation length of a modest level turbulence at oblique launching of the probing wave beam.

An attempt to formulate two-point velocity correlation in inhomogeneous turbulence

An attempt to formulate two-point velocity correlation in inhomogeneous turbulence

The MDF technique for the analysis of tokamak edge plasma fluctuations

Tokamak edge plasma was analyzed by applying the multifractal detrend fluctuation analysis (MF-DFA) technique. This method has found wide application in the analysis of correlations and characterization of scaling behavior of the time-series data in physiology, finance, and natural sciences. The time evolution of the ion saturation current (Is), the floating potential fluctuation (Vf), the poloidal electric field (Ep), and the radial particle flux (Γr) has been measured by using a set of Langmuir probes consisting of four tips on the probe head. The generalized Hurst exponents (h(q)), local fluctuation function (Fq(s)), the Rényi exponents (τ(q)) as well as the multifractal spectrum f(αh) have been calculated by applying the MF-DFA method to Is, Vf, and the magnetohydrodynamic (MHD) fluctuation signal. Furthermore, we perform the shuffling and the phase randomization techniques to detect the sources of multifractality. The nonlinearity shape of τ(q) reveals a multifractal behavior of the time-series data. The results show that in the presence of biasing, Is, Vf, Ep, and Γr reduce about 25%, 90%, 70%, and 50%, respectively, compared with the situation with no biasing. Also, they reduce about 15%, 90%, 35%, and 25%, respectively, after resonant helical magnetic field (RHF) application. In the presence of biasing or RHF, the amplitude of the power spectrum of Is, Vf, Γr, and MHD activity reduce remarkably in all the ranges of frequency, while their h(q) increase. The values of h(q) have been restricted between 0.6 and 0.68. These results are evidence of the existence of long-range correlations in the plasma edge turbulence. They also show the self-similar nature of the plasma edge fluctuations. Biasing or RHF reduces the amount of Fq(s). The multifractal spectrum width of Is, Vf, and MHD fluctuation amplitude reduce about 60%, 70%, and 42%, respectively, by applying biasing. In the presence of RHF, their width reduces about 60%, 85%, and 75%, respectively. It means that biasing and RHF reduce the degree of multifractality.

Turbulence correlation properties measured with ultrafast sweeping reflectometry on Tore Supra

The ultrafast sweep reflectometry technique is used to investigate plasma turbulence on Tore Supra. Thanks to the X-mode polarization, the plasma density and fluctuations over the whole tokamak radius, from the far scrape-off layer (SOL) to the core can be measured. Cross-correlation analysis is applied to all the signal components to estimate the fluctuation correlation length radial profile. The correlation length decreases from the plasma centre to the last closed flux surface and grows again into the far SOL.

Experimental investigation of large porous wind fences for infrasonic wind noise reduction

An extensive experimental investigation of large porous wind fences constructed from commercially available materials has recently been completed. Measured changes to the wind noise, turbulence, and wind velocity profile inside the fence resulting from varying the fence’s height, diameter, and porosity have been measured. The effect of other variables, including porous roofs, a bottom gap, and the addition of secondary windscreens were also studied. An empirical model based on measurements of the turbulence correlation length around the outside of the fence and the velocity gradient across the fence's surface has been derived to develop a better understanding of the wind noise reduction mechanisms. The measurements and model are then used to suggest an optimized wind fence design and predict the band width and magnitude of the wind noise reduction curve.

Heat Transfer Measurements for the Horizontal Micro-Tubes Using Liquid Crystal Thermography

In this study, a non-contact liquid crystal thermography (LCT) method was developed for surface temperature measurements on the micro- and micro-tubes with the diameters of 2000µm, 1000µm, 838µm and 686µm. In the single-phase heat transfer experiments, the fully-developed flow heat transfer data from laminar to turbulent regionswere obtained under the uniform wall heat flux boundary condition. The experiment system was verified with the macro-tube of 2000µm diameter tube. The results showed that buoyancy effect was not observed in the laminar region when the tube diameter was less than 1000 µm. In theturbulent region, the heat transfer data trend followed with the classical turbulent correlation. Furthermore, the current LCT results showed the similar trend when compare with the published LCT data of Yang and Lin[1].

Simulation of isotropic turbulence degeneration based on the large-eddy method

In this paper, the simulation of isotropic turbulence degeneration is studied. The turbulent process is modeled based on filtered three-dimensional unsteady Navier-Stokes equations. For the closure of the main equations, a viscous model of turbulence is used. The problem is solved numerically, i.e., in solving the equation of motion the modified method of fractional steps using compact schemes is employed and the equation for pressure is solved by the Fourier method in combination with matrix factorization. Temporal variations in the kinetic energy of turbulence and changes in the micro scale of turbulence and longitudinal-transverse correlation functions have been obtained. Longitudinal and transverse one-dimensional spectra have been found.

Comparison of edge turbulence imaging at two different poloidal locations in the scrape-off layer of Alcator C-Mod

This paper describes 2D imaging measurements of plasma turbulence made in the scrape-off layer of the Alcator C-Mod tokamak simultaneously at two different poloidal locations, one near the outer midplane and the other near the divertor X-point region. These images were made with radial and poloidal resolution using two gas puff imaging diagnostics not directly connected along a B field line. The turbulence correlation structure has a significantly different tilt angle with respect to the local flux surfaces for the midplane and X-regions, and a slightly different ellipticity and size. The time-averaged turbulence velocities can be different in the midplane and X-regions, even within the same flux surface in the same shot. The structures are partially consistent with a magnetic flux tube mapping model, and the velocities are compared with various models for turbulence flow.

Isotope Effect and Multiscale Physics in Fusion Plasmas

The mechanism governing the impact of the mass isotope on plasma confinement is still one of the main scientific conundrums facing the magnetic fusion community after more than thirty years of intense research. We have investigated the properties of local turbulence and long-range correlations in hydrogen and deuterium plasmas in the TEXTOR tokamak. Experimental findings have shown a systematic increasing in the amplitude of long-range correlations during the transition from hydrogen to deuterium dominated plasmas. These results provide the first direct experimental evidence of the importance of multiscale physics for unraveling the physics of the isotope effect in fusion plasmas.

Galactic spiral patterns and dynamo action – II. Asymptotic solutions

The exploration of mean-field galactic dynamos affected by a galactic spiral pattern, begun in Chamandy et al. (2013, hereafter Paper I) with numerical simulations, is continued here with an asymptotic solution. The mean-field dynamo model used generalizes the standard theory to include the delayed response of the mean electromotive force to variations of the mean magnetic field and turbulence parameters (the temporal non-locality, or {\tau} effect). The effect of the spiral pattern on the dynamo considered is the enhancement of the {\alpha}-effect in spiral-shaped regions (which may overlap the gaseous spiral arms or be located in the interarm regions). The axisymmetric and enslaved non-axisymmetric modes of the mean magnetic field are studied semi-analytically to clarify and strengthen the numerical results. Good qualitative agreement is obtained between the asymptotic solution and numerical solutions of Paper I for a global, rigidly rotating material spiral (density wave). At all galactocentric distances except for the co-rotation radius, we find magnetic arms displaced in azimuth from the {\alpha}-arms, so that the ridges of magnetic field strength are more tightly wound than the {\alpha}-arms. Moreover, the effect of a finite dynamo relaxation time {\tau} (related to the turbulence correlation time) is to phase-shift the magnetic arms in the direction opposite to the galactic rotation even at the co-rotation radius. This mechanism can be used to explain the phase shifts between magnetic and material arms observed in some spiral galaxies.

Kinetic theory of weak turbulence in plasmas

From the nonlinear Vlasov equation, a nonlinear turbulence scattering term is found to describe stochastic dissipation on a time scale longer than the turbulence correlation time. The evolution of the plasma distribution is determined by the well-understood unperturbed motion of charged particles, with the effects of the fluctuating part of fields described by the turbulence scattering term. In the present framework, one can identify various important physics, from the linear and quasilinear regimes to the nonlinear regime, in particular, the connections between the widely used Kadomtsev-Pogutse equation [B. B. Kadomtsev and O. P. Pogutse, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1970), pp. 368-387] and the Frieman-Chen equation [Frieman and Chen, Phys. Fluids 25, 502 (1982)]. The nonlinear scattering term indicates the Onsager symmetry relation of turbulent transport and a nonlinear frequency or k spectrum shift of a resonantly excited wave.