Taylor-Reynolds Number Research Articles

Spheres and fibers in turbulent flows at various Reynolds numbers

We perform fully coupled numerical simulations using immersed boundary methods of finite-size spheres and fibers suspended in a turbulent flow for a range of Taylor-Reynolds numbers 12.8<Reλ<442 and solid mass fractions 0≤M≤1. Both spheres and fibers reduce the turbulence intensity with respect to the single-phase flow at all Reynolds numbers, with fibers causing a more significant reduction than the spheres. The particles' effect on the anomalous dissipation tends to vanish as Re→∞. A scale-by-scale analysis shows that both particle shapes provide a “spectral shortcut” to the flow, but the shortcut extends further into the dissipative range in the case of fibers. Multifractal spectra of the near-particle dissipation show that spheres enhance dissipation in two-dimensional sheets, and fibers enhance the dissipation in structures with a dimension greater than one and less than two. In addition, we show that spheres suppress vortical flow structures, whereas fibers produce structures which completely overcome the turbulent vortex stretching behavior in their vicinity. Published by the American Physical Society 2024

Comparison of forcing schemes to sustain homogeneous isotropic turbulence

Studies of forced homogeneous isotropic turbulence (HIT) of multiphase systems rely on a comprehensive understanding of the single-phase HIT flow to quantify any turbulence modifications due to injection of the dispersed phase. Here, we compare external forcing schemes to generate and sustain single-phase HIT. The considered forcing schemes, Lundgren, Arnold–Beltrami–Childress, and Mallouppas, are based on the application of the body force in physical space to inject energy into the flow at large length scales. Direct numerical simulations are performed in cubic periodic domains of 1283 and 2563 size using a lattice Boltzmann method. The range of the Taylor's Reynolds number achieved is ReλT=24.4–75.4. The Lundgren force takes the longest time to generate turbulence and produces significant fluctuations in the turbulence properties in the statistically stationary state. Additionally, this force interacts with the velocity field in the entire range of wavenumbers, which is not the case for the other two forces. However, the scale-by-scale analysis shows that for the considered forces, the behavior of the non-linear energy transfer, dissipation, and energy injection terms differs only within the initial 16% of the wavenumbers that represent large length scales. After that, all terms behave consistently among each other for different forcing schemes. We conclude that the three considered large-scale forcing schemes do not affect the generated turbulent flow fields at small scales and can be used to study turbulence modification by the dispersed phase.

Effect Of Power-Law Fluids Flow Structures On Germicides Disinfection Through Taylor-Couette Configuration

Abstract Fluid disinfection involving ultraviolet rays (UV) is a promising method due to its easy implementation and low cost compared to other methods. In the present work, fluid disinfection in a Taylor-Couette configuration operating with power-law fluids with different absorbance coefficients,and fluence rates were simulated using the Lattice Boltzmann Method. The effects of operating parameters such as Taylor and axial Reynolds numbers, power-law index behavior, and fluence rate were analyzed. Results show that the required UV dose decreases for an increase in absorbance coefficient, while it grows for increasing power-law indexes. For T a = 120 and Re = 3, the disinfection reaches 82.3% for pseudo-plastic fluids and is complete for dilatant fluids. Considering different absorbance coefficients, it was observed that a = 0.4 leads to complete disinfection regardless of the fluid. For a = 0.5, fluid disinfection is complete for the dilatant fluid only. A value of 0.6 leads to partial disinfection (~90%) for all fluids.

An experimental study on the settling velocity of inertial particles in different homogeneous isotropic turbulent flows

We propose an experimental study on the gravitational settling velocity of dense, sub-Kolmogorov inertial particles under different background turbulent flows. We report phase Doppler particle analyser measurements in a low-speed wind tunnel uniformly seeded with micrometre scale water droplets. Turbulence is generated with three different grids (two consisting of different active-grid protocols while the third is a regular static grid), allowing us to cover a very wide range of turbulence conditions in terms of Taylor-scale-based Reynolds numbers ( $Re_\lambda \in [30\unicode{x2013}520]$ ), Rouse numbers ( $Ro \in [0\unicode{x2013}5]$ ) and volume fractions ( $\phi _v \in [0.5\times 10^{-5}\unicode{x2013}2.0\times 10^{-5}]$ ). We find, in agreement with previous works, that enhancement of the settling velocity occurs at low Rouse number, while hindering of the settling occurs at higher Rouse number for decreasing turbulence energy levels. The wide range of flow parameters explored allowed us to observe that enhancement decreases significantly with the Taylor–Reynolds number and is significantly affected by the volume fraction $\phi _v$ . We also studied the effect of large-scale forcing on settling velocity modification. The possibility of changing the inflow conditions by using different grids allowed us to test cases with fixed $Re_\lambda$ and turbulent intensity but with different integral length scale. Finally, we assess the existence of secondary flows in the wind tunnel and their role on particle settling. This is achieved by characterising the settling velocity at two different positions, the centreline and close to the wall, with the same streamwise coordinate.

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.

Taylor Microscale and Effective Reynolds Number near the Sun from PSP

The Taylor microscale is a fundamental length scale in turbulent fluids, representing the end of fluid properties and onset of dissipative processes. The Taylor microscale can also be used to evaluate the Reynolds number in classical turbulence theory. Although the solar wind is weakly collisional, it approximately behaves as a magnetohydrodynamic (MHD) fluid at scales larger than the kinetic scale. As a result, classical fluid turbulence theory and formalisms are often used to study turbulence in the MHD range. Therefore, a Taylor microscale can be used to estimate an effective Reynolds number in the solar wind. NASA’s Parker Solar Probe (PSP) has reached progressively closer to the Sun than any other spacecraft before. The collected data have revealed many new findings in the near-Sun solar wind. Here, we use the PSP data to estimate the Taylor microscale and effective Reynolds number near the Sun. We find that the Taylor microscale and Reynolds number are small compared to the corresponding near-Earth values, indicating a solar wind that has been less processed by turbulence, with very small-scale dissipative processes near the Sun.

Characteristic-Based Fluid Flow Modeling between Two Eccentric Cylinders in Laminar and Turbulent Regimes

Determining the flow between eccentric cylinders is crucial in a wide range of industries. The governing equations for the flow between eccentric cylinders cannot be solved analytically. Therefore, three-dimensional incompressible viscous fluid flow between eccentric and concentric cylinders has numerically been simulated in this paper to investigate them using a characteristic-based approach. The first-order characteristic-based scheme is used to calculate convective terms, whereas the second-order averaging technique is used to calculate viscous fluxes. The Taylor number, eccentricity distance, Reynolds number, and radius ratio are considered the controlling parameters of fluid flow between the cylinders. The influence of flow between cylinders on flow patterns is presented in terms of velocity, pressure, and flow contours. It is found that at a constant Taylor number, the asymmetric centrifugal forces produce the Taylor vortices on the right of the internal rotating cylinder as the eccentric distance increases. When the eccentric distance increases, the magnitude of shear stress and its fluctuation on the cylinder wall, as well as the pressure on the cylinder wall, rise. The numerical results obtained were validated by comparing them to previously published experimental results, which showed a high level of agreement.

Reynolds Number Dependence of the Structure Functions in Homogeneous Turbulence

We compare the predictions of stochastic closure theory (SCT) (Birnir in J Nonlinear Sci 23:657–688, 2013a. https://doi.org/10.1007/s00332-012-9164-z) with experimental measurements of homogeneous turbulence made in the variable density turbulence tunnel (Bodenschatz et al. in Rev Sci Instrum 85(9):093908, 2014) at the Max Planck Institute for Dynamics and Self-Organization in Göttingen. While the general form of SCT contains infinitely many free parameters, the data permit us to reduce the number to seven, only three of which are active over the entire range of Taylor–Reynolds numbers. Of these three, one parameter characterizes the variance of the mean-field noise in SCT and another characterizes the rate in the large deviations of the mean. The third parameter is the decay exponent of the Fourier variables in the Fourier expansion of the noise, which characterizes the smoothness of the turbulent velocity. SCT compares favorably with velocity structure functions measured in the experiment. We considered even-order structure functions ranging in order from two to eight as well as the third-order structure functions at five Taylor–Reynolds numbers (\(R_\lambda \)) between 110 and 1450. The comparisons highlight several advantages of the SCT, which include explicit predictions for the structure functions at any scale and for any Reynolds number. We observed that finite-\(R_\lambda \) corrections, for instance, are important even at the highest Reynolds numbers produced in the experiments. SCT gives us the correct basis function to express all the moments of the velocity differences in turbulence in Fourier space. These turn out to be powers of the sine function indexed by the wavenumbers. Here, the power of the sine function is the same as the order of the moment of the velocity differences (structure functions). The SCT produces the coefficients of the series and so determines the statistical quantities that characterize the small scales in turbulence. It also characterizes the random force acting on the fluid in the stochastic Navier–Stokes equation, as described in this paper.

Flame speed characteristics of turbulent expanding flames in a rectangular channel

We present results from studies of freely expanding flames in a unique small-scale convective facility for different free-stream initial conditions, characterized by Taylor-Reynolds numbers in the range of Reλg=179−395 (using the streamwise RMS velocity component and the lateral Taylor-microscale) and an inertial subrange over two decades of wavenumbers. The isotropic, decaying turbulence is generated by an active vane grid. Adding natural gas far upstream, the premixed flow is ignited using Laser Induced Breakdown (LIB) ignition. The evolution of the resulting spherically expanding flames is investigated using qualitative OH-Planar Laser Induced Fluorescence (PLIF). It is shown that trends of flame speeds derived from mean flame radius growth agree well with results from different experimental setups, using a recently developed scaling based on a spectral closure of a thin flame model (Chaudhuri et al., Phys. Rev. E (2011)). Reliable computation of the flame surface density and turbulent flame brush thickness is enabled by the large number of ensembles that can be collected in this type of facility. Trends of these instantaneous statistical quantities are presented and used to further assess the results of time-dependent mean quantities.

Influence of coherent vortex structures in subgrid scale motions on particle statistics in homogeneous isotropic turbulence

Subgrid scale (SGS) structures in large eddy simulations (LES) of turbulent particle-laden flows significantly influence particle dynamics, especially those of small inertial particles. In this study, homogenous isotropic turbulence with Taylor's Reynolds number of 102.3 is generated by a direct numerical simulation (DNS) and a wavelet-based coherent vortex extraction method is implemented to extract the coherent SGS structures and then investigate their effects on particle dynamics, including single-particle and particle-pair statistics. Compared to the classical spectral-filtered DNS (FDNS), which cuts off only the high wavenumber components regardless of the turbulence structures in the SGS motions, the wavelet-filtered DNS (WFDNS) can retain more coherent vortex structures in the SGS flow field with the help of the high compression rate characteristics of wavelet transformation. Comparing the results of WFDNS and FDNS at the identical effective grid number, it can be found that the single-particle statistics are mainly controlled by the macro energy-containing structures, and the SGS coherent vortex structures play important roles in the particle-pair dynamics, including the radial distribution function, radial relative velocity, and collision kernel. Therefore, in view of the characteristic of wavelet filtering that preserves the SGS coherent structure, the wavelet-based structural filter should be particularly suitable for LES modeling of particle-laden flow.

Onset criteria for freely decaying isotropic turbulence

From DNS of turbulence decaying from specified initial conditions for the range of initial Taylor-Reynolds numbers 2.58 < R{\lambda}(0) < 358.6, it was found that the shape of the iconic curve of dimensionless dissipation versus Reynolds number depended strongly on the choice of measurement time. For our preferred time, a composite based on peak values in the dissipation and inertial transfer curves, the result was virtually identical to the forced, stationary case. In the course of studying onset criteria, we found that the exponent for the power-law decay of the energy decreased with increasing Reynolds number and lay in the range 1.35 < n < 2.60. An additional run was performed, using the data from a stationary, forced simulation with R{\lambda} = 335 for the initial condition. The results of this suggested that the time taken for energy to pass through the cascade was about one half of an initial eddy turnover time.

Effect of bubble on the pressure spectra of oscillating grid turbulent flow at low Taylor-Reynolds number

For many engineering applications, measurements of velocity and pressure distributions in the system are of fundamental importance to provide insights into the flow characteristics. In the present study, the experiments were carried out in an oscillating grid system in absence and presence of two different bubble diameters (Db = 2.70 and 3.52 mm) rise using the non-intrusive two-dimensional (2D) particle image velocimetry (PIV) at the low Taylor-Reynolds number (Reλ) ranging from 12 to 60. Using the measured PIV velocity data, the instantaneous pressure fluctuations were estimated by integrating the full viscous form of the Navier-Stokes (N-S) equation. The obtained pressure field was compared with three dimensional (3D) computational fluid dynamics (CFD) simulation which was found to be in good agreement. The pressure spectra of single and two phase flow cases were evaluated by taking Fast Fourier transformation (FFT) of the computed pressure fluctuations. A spectral slope of −7/3 was found in the inertial subrange of the single-phase pressure spectrum. In contrast, the two-phase pressure spectrum exhibited a slope less steep than −7/3 in the inertial subrange because of the extra production of turbulence in the presence of bubble. For single-phase flow, the ratio of pressure integral length scale to the velocity integral length scale (Lp/L) was found to be ∼0.67, and the pressure Taylor microscale (λp) was approximately 0.79 ± 0.03 of the velocity Taylor microscale (λ) within the Taylor-Reynolds number range studied. The scaling ratios based on the single-phase experimental results were compared with existing theory and DNS results and found to accord well; however, these ratios deviate from the theoretical values for two-phase flow. Also, the energy dissipation rate was evaluated based on the pressure spectrum and found to be over-predicted (∼32%) compared those calculated from the velocity spectrum.

Annular swirling liquid layer with a hollow core

A thick turbulent annular liquid layer that swirls inside a fixed pipe is studied by means of surface observations and stereoscopic particle image velocimetry in an index-matched nozzle facility. This flow combines the complexities of swirling and free-surface turbulence. The free surface of the layer changes the boundary condition compared to filled swirling pipes and introduces the equivalent of a hollow core. The liquid layer shares similarities with turbulent open-channel flows, with the high centrifugal force across the layer having a similar effect to that of gravity in channel flows. At the surface, the restoring forces are surface tension and centrifugal acceleration. The particular nozzle under study has been envisioned for inertial confinement fusion, but the flow has relevance to systems such as compact separators or liquid rocket fuel injectors. Data are acquired at five downstream locations from the nozzle exit for four Reynolds numbers for subcritical flows. Injection flow rate and fluid kinematic viscosity are controlled independently, which allows adjusting independently the Reynolds and Taylor–Reynolds numbers. This also enables control of the centrifugal force at the free surface to test the effects of turbulence intensity on the free surface in regimes where air entrainment and droplet ejection occur. The swirl number is fixed by the design of the nozzle. From velocimetry data, mean velocity and turbulence statistics are extracted. For all the conditions tested, three flow regimes are identified: developing, developed, and transitional. The developed regime appears self-similar on the mean; the swirl creates a favourable pressure gradient that sustains the axial flow and confines the boundary layer near the wall. Large coherent vortex structures are identified in the layer. A simple model is proposed to describe the layer thickness and the velocity distribution in it. In the transitional regime, helical varicose waves generated by centrifugal instability are observed on the surface. Additionally, wall effects are visible in the bulk of the flow, and the main flow features are large overturning motions.

Turbulence strength in ultimate Taylor–Couette turbulence

We provide experimental measurements for the effective scaling of the Taylor–Reynolds number within the bulk $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number $\mathit{Ta}$), in the ultimate regime of Taylor–Couette flow. We define $Re_{\unicode[STIX]{x1D706},bulk}=(\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}}))^{2}(15/(\unicode[STIX]{x1D708}\unicode[STIX]{x1D716}_{bulk}))^{1/2}$, where $\unicode[STIX]{x1D70E}_{bulk}(u_{\unicode[STIX]{x1D703}})$ is the bulk-averaged standard deviation of the azimuthal velocity, $\unicode[STIX]{x1D716}_{bulk}$ is the bulk-averaged local dissipation rate and $\unicode[STIX]{x1D708}$ is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate $\unicode[STIX]{x1D716}(r)$ using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range – without invoking Taylor’s hypothesis. We find an effective scaling of $\unicode[STIX]{x1D716}_{\mathit{bulk}}/(\unicode[STIX]{x1D708}^{3}d^{-4})\sim \mathit{Ta}^{1.40}$, (corresponding to $\mathit{Nu}_{\unicode[STIX]{x1D714},\mathit{bulk}}\sim \mathit{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.40}$) and direct numerical simulations ($\mathit{Nu}_{\unicode[STIX]{x1D714}}\sim \mathit{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\unicode[STIX]{x1D702}_{\mathit{bulk}}/d\sim \mathit{Ta}^{-0.35}$ and the turbulence intensity as $I_{\unicode[STIX]{x1D703},\mathit{bulk}}\sim \mathit{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor–Reynolds number effectively scales as $\mathit{Re}_{\unicode[STIX]{x1D706},\mathit{bulk}}\sim \mathit{Ta}^{0.18}$ in the present parameter regime of $4.0\times 10^{8}&lt;\mathit{Ta}&lt;9.0\times 10^{10}$.

Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence.

The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζ_{n} from the structure functions S_{n}(r), is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio |S_{n}(r)/S_{3}(r)| against the separation r in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots S_{n}(r) against S_{3}(r), with the assumption S_{3}(r)∼r. Using our method for the particular case of S_{2}(r) we obtain the result that the exponent ζ_{2} decreases as the Taylor-Reynolds number increases, with ζ_{2}→0.679±0.013 as R_{λ}→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S_{2}, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.

Rheological behavior of castor oil mixed with different pyromellitic esters

The paper presents the rheological behavior study of castor oil mixed with different pyromellitic esters. The pyromellitic tetraesters used were obtained through the esterification of pyromellitic anhydride with a special alcohol of a complex alkyl-aryl structure (2-phenoxy-ethanol) in conjunction with a linear aliphatic alcohol with variable length (n-butanol, n-decanol). The influence of pyromellitic esters? structure and concentration was determined, as well as that of temperature, on the rheological behavior, by setting the dependence between the shear stress ? and the shear rate ?. The analysis of dependence between ? and ? demonstrates that the studied solutions have Newtonian behavior. The evolution of samples' viscosity with temperature was characterized by Arrhenius type equations, being established the values of viscous flow activation energy, Ea. This constant can be correlated with the effect of reducing friction in the presence of additives. It was also realized a characterization of annulus fluids flow under the effect of rotational motion, calculating the values of Taylor-Reynolds number (TaRe).

Lagrangian statistics of light particles in turbulence

We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter db = 340 μm and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Reλ) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry. It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23 to 30. The acceleration flatness values show an increasing trend with Reλ, consistent with previous experiments [G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, “Measurement of particle accelerations in fully developed turbulence,” J. Fluid Mech. 469, 121 (2002)]10.1017/S0022112002001842 and numerics [T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, “Small-scale statistics in highresolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics,” J. Fluid Mech. 592, 335 (2007)]10.1017/S0022112007008531. These acceleration PDFs show a higher intermittency compared to tracers [S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, “Modeling inertial particle acceleration statistics in isotropic turbulence,” Phys. Fluids. 20, 095104 (2008)]10.1063/1.2976174 and heavy particles [S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, “Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence,” Phys. Rev. Lett. 97, 144507 (2006)]10.1103/PhysRevLett.97.144507 in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Reλ. We also compare our results with experiments in von Kármán flows and point-particle direct numerical simulations with periodic boundary conditions.

Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence

AbstractThree-dimensional Voronoï analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data sets from numerics in the point particle limit and one experimental data set. We study the clustering behaviour at different density ratios, particle response times (i.e. Stokes numbers $\mathit{St}$) and two Taylor–Reynolds numbers (${\mathit{Re}}_{\lambda } = 75$ and 180). The probability density functions (p.d.f.s) of the Voronoï cell volumes of light and heavy particles show different behaviour from that of randomly distributed particles, i.e. fluid tracers, implying that clustering is present. The standard deviation of the p.d.f. normalized by that of randomly distributed particles is used to quantify the clustering. The clustering for both light and heavy particles is stronger for higher ${\mathit{Re}}_{\lambda } $. Light particles show maximum clustering for $\mathit{St}$ around 1–2 for both Taylor–Reynolds numbers. The experimental data set shows reasonable agreement with the numerical results. The results are consistent with previous investigations employing other approaches to quantify the clustering. We also present the joint p.d.f.s of enstrophy and Voronoï volumes and their Lagrangian autocorrelations. The small Voronoï volumes of light particles correspond to regions of higher enstrophy than those of heavy particles, indicating that light particles cluster in higher vorticity regions. The Lagrangian temporal autocorrelation function of Voronoï volumes shows that the clustering of light particles lasts much longer than that of heavy or neutrally buoyant particles. Due to inertial effects arising from the density contrast with the surrounding liquid, light and heavy particles remain clustered for much longer times than the flow structures which cause the clustering.

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian–Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force–known as Basset–Boussinesq history force–and the non-Stokesian drag based on Schiller–Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor–Reynolds number, R e λ ≃ 31 , for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81–91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.

The bottleneck effect and the Kolmogorov constant in isotropic turbulence

A large database from direct numerical simulations of isotropic turbulence, including recent simulations for box sizes up to 40963 and the Taylor–Reynolds number Rλ ≈ 1000, is used to investigate the bottleneck effect in the three-dimensional energy spectrum and second-order structure functions, and to determine the Kolmogorov constant, CK. The difficulties in estimating CK at any finite Reynolds number, introduced by intermittency and the bottleneck, are assessed. The data conclusively show that the bottleneck effect decreases with the Reynolds number. On this basis, an alternative to the usual procedure for determining CK is suggested; this proposal does not depend on the particular choices of fitting ranges or power-law behaviour in the inertial range. Within the resolution of the numerical data, CK thus determined is a Reynolds-number-independent constant of ≈1.58 in the three-dimensional spectrum. A simple model including non-local transfer is proposed to reproduce the observed scaling features of the bottleneck.