Correlations Of Velocity Fluctuations Research Articles

STREAMWISE VORTICES AND REYNOLDS STRESSES OF WALL-BOUNDED TURBULENT SHEAR FLOWS

Reynolds Equation is the most commonly used governing equation in turbulence. However, its application in wall-bounded turbulent shear flows may involve a defect. In general, Reynolds averaging should be ensemble averaging and Reynolds stresses are supposed to express all the actions of turbulence on the mean field. In statistically steady three-dimensional flows, Reynolds stresses are usually defined as correlations of temporal velocity fluctuations so that they cannot contain the influences of steady components of streamwise vortices. This is believed to be one of the reasons why many closure models in RANS meet problems in flows where streamwise vortices play significant roles. In this paper, Spatial-Temporal (S-T) averaged Reynolds stresses were defined, which separates the turbulence actions caused by temporal or spatial velocity fluctuations. DNS data for a fully developed channel flow were then used to check balancing of equations. Comparison showed that the balancing errors in the S-T averaged Reynolds equations were obviously smaller than those in the temporal averaged one, in particular, in the near wall region where the streamwise vortices located. Thus, a combination of traditional model with a supplemental model expressing influences of streamwise vortices might be a way out to improve the turbulence modeling.

Dynamical fluctuations in dense granular flows

We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics-such as the probability distribution of force fluctuations, or the mean friction angle-do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.

Mean electromotive force proportional to mean flow in MILD turbulence

AbstractIn mean‐field magnetohydrodynamics the mean electromotive force due to velocity and magnetic‐field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small‐scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the α effect, is important for large‐scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross‐helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Structures in turbulent boundary layers subjected to adverse pressure gradients

The effects of adverse pressure gradients on turbulent structures were investigated by carrying out direct numerical simulations of turbulent boundary layers subjected to adverse and zero pressure gradients. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution U∞ ~ xm. Two-point correlations of velocity fluctuations were used to show that the spanwise spacing between near-wall streaks is affected significantly by a strong adverse pressure gradient. Low-momentum regions are dominant in the middle of the boundary layer as well as in the log layer. Linear stochastic estimation was used to provide evidence for the presence of low-momentum regions and to determine their statistical properties. The mean width of such large-scale structures is closely associated with the size of the hairpin-like vortices in the outer layer. The conditionally averaged flow fields around events producing Reynolds stress show that hairpin-like vortices are the structures associated with the production of outer turbulence. The shapes of the vortices beyond the log layer were found to be similar when their length scales were normalized according to the boundary layer thickness. Estimates of the conditionally averaged velocity fields associated with the spanwise vortical motion were obtained by using linear stochastic estimation. These results confirm that the outer region of the adverse pressure gradient boundary layer is populated with streamwise-aligned vortex organizations, which are similar to those of the vortex packet model proposed by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54). The adverse pressure gradient augments the inclination angles of the packets and the mean streamwise spacing of the vortex heads in the packets.

Anisotropic turbulence decay in a far momentumless wake in a stratified medium

A new numerical model is constructed of turbulent wake dynamics behind bodies of revolution in a stably stratified medium based on a semiempirical third-order turbulence model. The employed differential transport equations of all triple correlations of velocity field oscillations, written with allowance for fourth-order cumulants and improved algebraic representations of joint triple correlations of velocity and density fluctuations, enable the comprehensive description of an anisotropic turbulence decay in a far momentumless wake in a stratified medium

A closed model of fluctuating particle motion in a turbulent flow

Random particle motion in a turbulent and molecular velocity fluctuation field is considered. Using a spectral representation of the carrier-phase Eulerian velocity fluctuation correlations, a closed system of integral equations for calculating the carrier-phase velocity correlation along the particle trajectory and the particle Lagrangian velocity fluctuation correlation is obtained. Based on this system, the fluctuations of the particle parameters are analyzed. In the limiting case of a passive admixture, an estimate is found for the ratio of the integral Lagrangian and Eulerian time scales and the Kolmogorov constant for the Lagrangian structure function of the carrier-phase velocity fluctuations.

Stochastic response analysis of suspension bridge under gusty wind with time-dependent mean velocity

The paper presents a general outline of the method of stochastic response analysis of suspension bridge subjected to randomly fluctuated wind with time-dependent mean velocity. The proposed method is aimed to examine how the repeatable wind gusts affect bridge vibrations and to investigate amplified bridge response in resonant regimes. First, a non-homogeneous wind velocity model and associated buffeting forces are developed. The buffeting forces are derived under the general assumption that their span-wise correlation is the same as that of incoming wind fluctuations. Next, a bridge deck is divided into sections along span, and the dynamic bridge response is obtained with neglecting structure nonlinearities, by summing up component responses due to sectional buffeting forces. For the correlation response analysis an analytical time-domain approach based on stochastic calculus is suggested. The mean function and covariance function of bridge response are derived in the general case where in-time correlation of wind velocity fluctuations results from a given wind spectrum. Additionally, for a tentative estimation, two approximate formulas for variance of bridge response are obtained using two opposing mathematical idealizations of wind correlation in time. In the last part, numerical application of the proposed procedure is presented and advantages in bridge engineering are discussed.

Studies of turbulent angular momentum transport in Taylor-Couette flow via 2D LDV

The turbulent (i.e., fluctuation-driven) transport of angular momentum in Taylor-Couette flow may be observed locally and directly with second order velocity fluctuation correlations obtained by dual beam (2D) Laser Doppler Velocimetry (LDV). This method is complementary to torque measurements, and initial results are commensurate with earlier torque studies performed in turbulent regimes. Other results utilizing this technique with centrifugally-stable high Reynolds number (Re) flows indicate that the fluid is quiescent and devoid of significant angular momentum transport, even up to Re ∼ 106. This latter result is thought to bear upon the hydrodynamic properties of cool astrophysical accretion disks.

Model of the Long Island Sound outflow: Comparison with year-long HF radar and Doppler current observations

A three-dimensional primitive-equation model is used to simulate the Long Island Sound (LIS) outflow for a 1-year (2001) period. The model domain includes LIS and New York Bight (NYB). Tidal and wind forcing are included, and seasonal salinity and temperature variations are assimilated. The model results are validated with the HF radar, moored acoustic Doppler current profiler (ADCP), and ferry-based ADCP observations. The agreement between simulated and observed flow patterns generally is very good. The difference in seasonal mean currents between the model and moored ADCP is about 0.01 m/s; the correlation of dominant velocity fluctuations between the model and HF radar is 0.83; and the difference in mean LIS transport between the model and shipboard ADCP is about 5%. However, the model predicts a prominent tidally generated headland eddy not supported by the HF radar observation. The model sensitivity study indicates that the tides, winds, and ambient coastal front all have important impact on the buoyant outflow. The tides and winds cause stronger vertical mixing, which reduces the surface plume strength. The ambient coastal front, on the other hand, tends to enhance the plume.

Universal Model of Finite Reynolds Number Turbulent Flow in Channels and Pipes

In this Letter, we suggest a simple and physically transparent analytical model of pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model provides an accurate quantitative description of the profiles of the mean-velocity and Reynolds stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe, for a wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

Collective diffusion in sheared colloidal suspensions

Collective diffusivity in a suspension of rigid particles in steady linear viscous flows is evaluated by investigating the dynamics of the time correlation of long-wavelength density fluctuations. In the absence of hydrodynamic interactions between suspended particles in a dilute suspension of identical hard spheres, closed-form asymptotic expressions for the collective diffusivity are derived in the limits of low and high Péclet numbers, where the Péclet number ${\it Pe}\,{=}\,\gamdot a^2/D_0$ with $\gamdot$ being the shear rate and D0 = kBT/6πη a is the Stokes–Einstein diffusion coefficient of an isolated sphere of radius a in a fluid of viscosity η. The effect of hydrodynamic interactions is studied in the analytically tractable case of weakly sheared (Pe ≪ 1) suspensions.For strongly sheared suspensions, i.e. at high Pe, in the absence of hydrodynamics the collective diffusivity Dc = 6 Ds∞, where Ds∞ is the long-time self-diffusivity and both scale as $\phi \gamdot a^2$, where φ is the particle volume fraction. For weakly sheared suspensions it is shown that the leading dependence of collective diffusivity on the imposed flow is proportional to D0 φPeÊ, where Ê is the rate-of-strain tensor scaled by $\gamdot$, regardless of whether particles interact hydrodynamically. When hydrodynamic interactions are considered, however, correlations of hydrodynamic velocity fluctuations yield a weakly singular logarithmic dependence of the cross-gradient-diffusivity on k at leading order as ak → 0 with k being the wavenumber of the density fluctuation. The diagonal components of the collective diffusivity tensor, both with and without hydrodynamic interactions, are of O(φPe2), quadratic in the imposed flow, and finite at k = 0.At moderate particle volume fractions, 0.10 ≤ φ ≤ 0.35, Brownian Dynamics (BD) numerical simulations in which there are no hydrodynamic interactions are performed and the transverse collective diffusivity in simple shear flow is determined via time evolution of the dynamic structure factor. The BD simulation results compare well with the derived asymptotic estimates. A comparison of the high-Pe BD simulation results with available experimental data on collective diffusivity in non-Brownian sheared suspensions shows a good qualitative agreement, though hydrodynamic interactions prove to be important at moderate concentrations.

NMR Measurement of Nonlocal Dispersion in Complex Flows

The flow and diffusion driven separation of initially adjacent liquid molecules is known as dispersion. The primary physical quantity describing this process, the nonlocal dispersion tensor, provides insight regarding both the spatial and temporal correlations of molecular velocity fluctuations in complex flows. We here propose and demonstrate a nuclear magnetic resonance method for the measurement of this tensor, validating its implementation for the case of cylindrical Couette flow, and demonstrating its application to the study of fluid dispersion in a random bead pack.

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.

Low-frequency wind noise reduction by spherical windscreens

Spherical windscreens are surprisingly effective at reducing wind noise at frequencies for which the turbulence scale is much larger than the windscreen. In the 1930s, Phelps postulated that the low-frequency reduction of windscreens could be explained by assuming that the dc flow pressure distribution around a sphere also applied to low-frequency fluctuations and wind noise. The area average of the dc pressure distribution was then calculated and shown to be smaller than the stagnation pressure. Morgan extended this idea by measuring the pressure distribution around a porous foam windscreen. Recent measurements [Webster et al., J. Acoust. Soc. Am. 118, 2009 (2005)] have shown that the pressure fluctuations at low frequency do not follow the dc distribution and that the velocity and pressure fluctuation correlations are drastically reduced by the presence of the windscreen. A simple calculation demonstrates that the decorrelation of the pressure fluctuations is sufficient to explain the observed low-frequency reduction afforded by the 9.0 cm diameter windscreen. [Research supported by the U.S. Army TACOM-ARDEC at Picatinny Arsenal, NJ.]

1659 一様流中に置いたワッシャーまわり流れの基本構造(G05-10 物体周りの流れ,G05 流体工学)

The present aim is to clarify the combination effect of curvature and streamwise thickness of a ring with rectangular cross sections, which is immersed perpendicularly to uniform flow. In a wind tunnel, the authors carried out the measurements using a deadweight gauge and hot-wire anemometers, and the flow visualisations by a smoke-wire method, for wide rages of Re, d/w and t/w, where Re, d, w and t are the Reynolds number, mean diameter, cross-section width and cross-section thickness of the ring, respectively. Consequently, the Strouhal number St, which is a reduced frequency of regular vortex shedding from the ring, is independent of d/w, t/w and Re. On the other hand, base suction depends not on Re, but on d/w and t/w. Considering d/w and t/w as governing parameters, and regarding to base suction, flow visualisation, velocity fluctuation, mean-velocity profile, turbulence-intensity profile and four-points velocity correlation, we can classify the flow into four flow modes; viz., an over-critical axisymmetrical mode, a sub-critical axisymmetrical mode, a sub-critical non-axisymmetrical mode and a sub-critical less-correlation mode.

Dynamics of bidisperse suspensions under Stokes flows: Linear shear flow and sedimentation

Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multibody hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and nonhydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and self-diffusion. The velocity fluctuation tensor scales linearly up to 15% concentration. Multibody interactions weaken the correlation of velocity fluctuations and lead to a diffusion-like motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio λ varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced self-diffusion coefficient. Thus, for a fixed λ and total concentration, increasing the respective volume fraction of large particles can double the velocity fluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuation levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangian velocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zig-zag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on the concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model.

On Measuring the Terms of the Turbulent Kinetic Energy Budget from an AUV

Abstract The terms of the steady-state, homogeneous turbulent kinetic energy budgets are obtained from measurements of turbulence and fine structure from the small autonomous underwater vehicle (AUV) Remote Environmental Measuring Units (REMUS). The transverse component of Reynolds stress and the vertical flux of heat are obtained from the correlation of vertical and transverse horizontal velocity, and the correlation of vertical velocity and temperature fluctuations, respectively. The data were obtained using a turbulence package, with two shear probes, a fast-response thermistor, and three accelerometers. To obtain the vector horizontal Reynolds stress, a generalized eddy viscosity formulation is invoked. This allows the downstream component of the Reynolds stress to be related to the transverse component by the direction of the finescale vector vertical shear. The Reynolds stress and the vector vertical shear then allow an estimate of the rate of production of turbulent kinetic energy (TKE). Heat flux is obtained by correlating the vertical velocity with temperature fluctuations obtained from the FP-07 thermistor. The buoyancy flux term is estimated from the vertical flux of heat with the assumption of a constant temperature–salinity (T–S) relationship. Turbulent dissipation is obtained directly from the usage of shear probes. A multivariate correction procedure is developed to remove vehicle motion and vibration contamination from the estimates of the TKE terms. A technique is also developed to estimate the statistical uncertainty of using this estimation technique for the TKE budget terms. Within the statistical uncertainty of the estimates herein, the TKE budget on average closes for measurements taken in the weakly stratified waters at the entrance to Long Island Sound. In the strongly stratified waters of Narragansett Bay, the TKE budget closes when the buoyancy Reynolds number exceeds 20, an indicator and threshold for the initiation of turbulence in stratified conditions. A discussion is made regarding the role of the turbulent kinetic energy length scale relative to the length of the AUV in obtaining these estimates, and in the TKE budget closure.

Large-scale motions in a supersonic turbulent boundary layer

Wide-field particle image velocimetry measurements were performed in a Mach 2 turbulent boundary layer to study the characteristics of large-scale coherence at two wall-normal locations ($y/\delta\,{=}\,0.16$ and 0.45). Instantaneous velocity fields at both locations indicate the presence of elongated streamwise strips of uniform low- and high-speed fluid (length$\,{>}\,8\delta$). These long coherent structures exhibit strong similarities to those that have been found in incompressible boundary layers, which suggests an underlying similarity between the incompressible and supersonic regimes. Two-point correlations of streamwise velocity fluctuations show coherence over a longer streamwise distance at $y/\delta\,{=}\,0.45$ than at $y/\delta\,{=}\,0.16$, which indicates an increasing trend in the streamwise length scale with wall-normal location. The spanwise scale of these uniform-velocity strips increases with increasing wall-normal distance as found in subsonic boundary layers. The large-scale coherence observed is consistent with the very large-scale motion (VLSM) model proposed by Kim & Adrian (Phys. Fluids, vol. 11, 1999, p. 417) for incompressible boundary layers

Examination of large-scale structures in turbulent microchannel flow

Microscopic particle image velocimetry was performed on turbulent flow in microchannels of various diameters and aspect ratios to evaluate the characteristics of large-scale turbulent structures. Spatial correlations of velocity fluctuations were measured along the channel centerlines and at four other locations, and characteristic turbulent length scales were defined. For square microchannels, excellent agreement was observed between the measured length scales and results for macro-scale duct flow. Along the centerline of the square microchannels the normalized longitudinal length scale, 2Lxuu/W, ranged from 0.30 to 0.37, the lateral length scale, 2Lyuu/W, ranged from 0.16 to 0.18, and the ratio between the two length scales, Lxuu/Lyuu ranged from 1.88 to 2.00, results which agree well with macroscale results. Results for non-square microchannels indicate that as aspect ratio increases, the ratio Lxuu/Lyuu also increases, ranging from 2.29 for an aspect ratio of 2.09 up to 3.75 for an aspect ratio of 5.68. Measurements were repeated at various distances from the side walls of the microchannels. For the square microchannels the turbulent structures are smaller near the side walls than near the center of the microchannel with 2Lxuu/W ranging from 0.30 to 0.38 along the centerline, but dropping to 0.04–0.06 at y/(W/2)=0.94. Similar results were observed for the rectangular microchannels. For the rectangular microchannels 2Lxuu/W ranged from 0.32 to 0.42, compared to 0.30–0.38 for the square microchannels.

A stochastic analysis of a nonlinear flow response

In this article a stochastic analysis of velocity fluctuations from a nonlinear flow response is presented. The statistical analysis is based on probability averages of the flow quantities evaluated over several realizations of the examined turbulent flow. In order to define the realizations, a long-time record of a turbulent velocity signal is cut up into pieces of length T , where T is much longer than the characteristic velocity fluctuation correlation time occurring in the flow. These pieces are then treated as observations of different responses in an ensemble of similarly simulated flows. The ergodic assumption is investigated, and it is shown that in some regions of the flow the standard statistical approach of time average fails to capture the nonlinear response of the flow. The ergodicity deviations based on samples from three-dimensional numerical simulations are compared with theoretical predictions given by scaling arguments and also with data from experimental observations. A very good agreement is observed. Calculations of the normalized auto-correlation functions and power spectra are also performed.