Velocity Probability Density Function Research Articles

Tailoring incoming shear and turbulence profiles for lab‐scale wind turbines

AbstractAn active grid is used to generate a variety of turbulent shear profiles in a wind tunnel. The vertical bars are set to flap through varying angles across the test section producing a variation in the perceived solidity, resulting in a mean shear. The horizontal bars are used in a fully random operational mode to set the background turbulence level. It is demonstrated that mean velocity profiles with approximately the same shear can be produced with different turbulence intensities and local turbulent Reynolds numbers based on the Taylor microscale, λ. Conversely, it is also demonstrated that flows can be produced with similar turbulence intensity profiles but different mean shear. It is confirmed that the length scales and dynamics, the latter being assessed through the velocity spectra and probability density functions, do not vary significantly across the investigation domain. Such flows are of particular relevance for studies investigating the effect of in‐flow conditions on obstacles where these studies wish to decouple the effects of turbulence intensity and mean shear, a feat previously unattainable in experimental facilities. Given that the power output of wind turbines is known to be a function of both mean shear and turbulence intensity, the experimental methodology presented herein is invaluable to the wind turbine model testing community who, at present, cannot exert such control authority over the in‐flow conditions.

Parkinson Disease Detection from Speech Articulation Neuromechanics.

Aim: The research described is intended to give a description of articulation dynamics as a correlate of the kinematic behavior of the jaw-tongue biomechanical system, encoded as a probability distribution of an absolute joint velocity. This distribution may be used in detecting and grading speech from patients affected by neurodegenerative illnesses, as Parkinson Disease.Hypothesis: The work hypothesis is that the probability density function of the absolute joint velocity includes information on the stability of phonation when applied to sustained vowels, as well as on fluency if applied to connected speech.Methods: A dataset of sustained vowels recorded from Parkinson Disease patients is contrasted with similar recordings from normative subjects. The probability distribution of the absolute kinematic velocity of the jaw-tongue system is extracted from each utterance. A Random Least Squares Feed-Forward Network (RLSFN) has been used as a binary classifier working on the pathological and normative datasets in a leave-one-out strategy. Monte Carlo simulations have been conducted to estimate the influence of the stochastic nature of the classifier. Two datasets for each gender were tested (males and females) including 26 normative and 53 pathological subjects in the male set, and 25 normative and 38 pathological in the female set.Results: Male and female data subsets were tested in single runs, yielding equal error rates under 0.6% (Accuracy over 99.4%). Due to the stochastic nature of each experiment, Monte Carlo runs were conducted to test the reliability of the methodology. The average detection results after 200 Montecarlo runs of a 200 hyperplane hidden layer RLSFN are given in terms of Sensitivity (males: 0.9946, females: 0.9942), Specificity (males: 0.9944, females: 0.9941) and Accuracy (males: 0.9945, females: 0.9942). The area under the ROC curve is 0.9947 (males) and 0.9945 (females). The equal error rate is 0.0054 (males) and 0.0057 (females).Conclusions: The proposed methodology avails that the use of highly normalized descriptors as the probability distribution of kinematic variables of vowel articulation stability, which has some interesting properties in terms of information theory, boosts the potential of simple yet powerful classifiers in producing quite acceptable detection results in Parkinson Disease.

Scalings of heat transport and energy spectra of turbulent Rayleigh-Bénard convection in a large-aspect-ratio box

Direct Numerical Simulations of turbulent convection in a large aspect-ratio box are carried out in the range of Rayleigh number 7 × 104 ≤ Ra ≤ 2 × 106 at Prandtl number Pr=0.71. A strong correlation between the vertical velocity and temperature is observed in the turbulent regime at almost all the length scales. Frequency spectra of all the velocities and temperature show a −5/3 law for a wide band of frequencies. The variances of horizontal velocities at different points in the flow yield a single power-law. Probability density functions of velocities and temperature are close to Gaussian only at higher Rayleigh numbers. The mean and variance of temperature clearly show boundary layers, surface layers and a near-homogeneous bulk region. The boundary layer thickness decreases and bulk-homogeneity is enhanced on increasing the Rayleigh numbers. The wave number spectra of the turbulent kinetic energy exhibit Kolmogorov like (E(k)∼k−5/3) and Bolginao-Obukhov like (E(k)∼k−11/5) behaviour respectively in the central and near-wall regions of the container. An approximate balance between the production due to buoyancy and the dissipation is found in the turbulent kinetic energy budget. Taylor’s approximate equation of the production due to turbulent stretching and the dissipation of turbulent enstrophy is modified by the inclusion of buoyancy production in the enstrophy budget. The present results support the previously proposed 2/7 power-law dependence of the average Nusselt number on the Rayleigh number by yielding an exponent of 0.272, but do not necessarily support the proposed classification of “soft” and “hard” turbulence on the basis of this exponent.

Non-local generalization of Darcy’s law based on empirically extracted conductivity kernels

In the context of flow and transport in porous and fractured media, Darcy-based continuum models, while computationally inexpensive, are of limited use when the scale of interest is of similar size or smaller than the characteristic network connection length. Recently, we have outlined a non-local Darcy model that bridges the gap between network and Darcy-based descriptions. This formulation is able to account for non-local pressure effects that are not accounted for in a classical Darcy description. At the heart of this non-local flow formulation is a conductivity distribution or kernel that is related to the scalar permeability in the classical Darcy law. In this paper, ensembles of flow networks are considered, of which the necessary statistical information is assumed to be known. In order to relate the conductivity distribution with the flow statistics, a stochastic transport model for fluid particles, termed generalized continuous time random walk (g-CTRW), which is a generalization of correlated continuous time random walk, is introduced. Note that similar assumptions as for correlated CTRW are made, i.e., that lengths and velocities of connections between successive nodes along the trajectories can be described by Markov processes. In order to proceed with a theoretical analysis, a Boltzmann equation is presented, which is consistent with the particle time marching algorithm based on g-CTRW. An important outcome of the analysis is an expression relating the joint probability density function of velocity and connection length in the networks with the conductivity kernel. A numerical, stationary flow example demonstrates how the kernel can be extracted. Further, an algorithm is proposed to compute consistent velocity statistics, mean pressure distribution, and spatially varying conductivity kernel in the case of non-stationary flow. This coupled iterative approach is an attempt to consistently compute stochastic flow and transport in large network ensembles.

Critical Role of Preferential Flow in Field‐Scale Pathogen Transport and Retention

Core Ideas A stochastic stream tube model was extended to simulate field‐scale pathogen transport and fate. Single‐ or dual‐permeability versions of the model were developed that included filtration theory. Pathogen transport and fate are highly dependent on the field‐scale velocity distribution. Physical nonequilibrium effects are coupled with retention, the velocity PDF, and exchange. A stream tube model was applied to simulate pathogen transport and fate in the subsurface at the field scale. Local‐scale transport within each stream tube was described deterministically using analytic solutions for pathogen transport and fate in a uniform or dual‐permeability porous medium. Important pathogen transport and fate processes that were accounted for in an individual stream tube included: advection, dispersion, reversible and irreversible retention, and decay in the liquid and solid phases. The velocity in a stream tube was related to a median grain size using the Kozeny–Carman equation, and filtration theory was used to predict the dependence of retention on physicochemical factors. The field‐scale velocity distribution was described using a unimodal or bimodal lognormal probability density function (PDF). The bimodal lognormal PDF was used in conjunction with the dual‐permeability model to account for exchange between slow and fast velocity domains. The mean and variance of the field‐scale concentrations were calculated from local‐scale stream tube information. The setback distance to achieve a selected risk of infection was determined from the modeled concentrations and a simplified risk assessment approach. Simulation results demonstrate that field‐scale pathogen transport and setback distance were very sensitive to velocity distribution characteristics. Early breakthrough, higher peak concentrations, and larger setback distances were associated with faster stream tubes that had little retention, whereas the opposite trends were associated with slower stream tubes. The relative importance of faster stream tubes increased under physicochemical conditions that enhanced retention.

A PDF-Based Parameterization of Subgrid-Scale Hydrometeor Transport in Deep Convection

Abstract A parameterization scheme is proposed for the subgrid-scale transport of hydrometeors in an assumed probability density function (PDF) scheme. Joint distributions of vertical velocity and hydrometeor mixing ratios are typically unknown, but marginal (1D) PDFs of these variables are available. The parameterization is developed using high-resolution simulations of continental and tropical deep convection. A 3D cloud-resolving model (CRM) providing benchmark solutions has a horizontal grid spacing of 250 m and employs the Morrison microphysics scheme, which treats prognostically mass and number mixing ratios for four types of precipitating hydrometeors (rain, graupel, snow, and ice) as well as cloud droplet number mixing ratio. The subgrid-scale hydrometeor transport scheme assumes input given in the form of marginal PDFs of vertical velocity and hydrometeor mixing ratios; in this study, these marginal distributions are provided by the cloud-resolving model. Conditional sampling and scaling are then applied to the marginal distributions to account for subplume correlations. The parameterized fluxes tested for four episodes of deep convection show good agreement with benchmark fluxes computed directly from the CRM output. The results demonstrate the potential use of the subgrid-scale hydrometeor transport scheme in an assumed PDF scheme to parameterize the covariances of vertical velocity and hydrometeor mixing ratios.

Probabilistic solution of non-linear vibration energy harvesters driven by Poisson impulses

This paper develops a new solution procedure for obtaining the joint probability density function (PDF) of non-linear energy harvesters under Poisson impulses using the state-space-split method and the exponential-polynomial closure method. In the beginning, a generic electromechanical energy harvester is introduced and its governing equations are transformed into non-dimensional ones. According to the non-dimensional governing equations, a Duffing-type oscillator with piezoelectric conversion mechanism is further considered in this study. The proposed solution procedure includes three steps. First the joint PDF of this system is governed by the generalized Fokker-Plank-Kolmogorov (FPK) equation. The state-space-split method is used to reduce this generalized FPK equation to a low-dimensional one only about displacement and velocity. After that, the exponential-polynomial closure method is further adopted to solve the reduced FPK equation. Finally, the joint PDF of displacement, velocity and voltage can be approximated by the product of the obtained PDF and the conditional Gaussian PDF of voltage. Four cases are investigated considering the effects of non-linearity coefficient, impulse arrival rate and a bistable Duffing oscillator. The PDFs of these state variables and the harvested power are compared with the simulation results, respectively. The good agreement between the obtained PDFs and the simulated results is achieved. Compared with the results of the equivalent linearization method, the strong non-linearity in displacement and lower impulse rate lead the tail PDF of the harvested power to exhibiting hardening and softening behaviors, respectively. For the bistable Duffing oscillator, the PDF of the harvested power differs significantly from the result of the equivalent linearization method in the tail region.

Lie symmetry analysis of the Lundgren–Monin–Novikov equations for multi-point probability density functions of turbulent flow

The problem of turbulence statistics described by the Lundgren–Monin–Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integro-differential equations for the multi-point probability density functions (pdf’s) of velocity. A complete set of point transformations is derived for the one-point pdf’s and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie–Bäcklund operator. Due to the one-way coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

We consider super-diffusive Lévy walks in dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d > 1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

The non‐local character of turbulence asymmetry in the convective atmospheric boundary layer

The inadequacy of conventional gradient diffusion in closure modelling of turbulent heat fluxes within the convective atmospheric boundary layer is often alleviated by accounting for non‐local transport effects, such as Deardorff's counter‐gradient models, Wyngaard's transport asymmetry closures or mass‐flux parametrization. This concept of large‐eddy flux transport is examined here with the principal aim of unifying these seemingly different models. Using large‐eddy simulation (LES) runs for the atmospheric boundary layer, spanning weakly to strongly convective conditions, a generic diagnostic framework that encodes the role of third‐order moments in non‐local transport is developed and tested. The premise is that these non‐local effects are responsible for the inherent asymmetry in vertical transport and hence the necessary non‐Gaussian nature of the joint probability density function (JPDF) of vertical velocity and potential temperature must account for these effects. Conditional sampling (quadrant analysis) of this JPDF and the imbalance between the flow mechanisms of ejections and sweeps are used to characterize this asymmetry, which is then linked to the third‐order moments using a cumulant‐discard method for the Gram–Charlier expansion of the JPDF. While the concept of ejection‐sweep events used here is not a simple extension of that commonly used in the surface layer, their connection to third‐order moments shows that the concepts of bottom‐up/top‐down diffusion or updraught/downdraught models are accounted for by various quadrants of the JPDF. An analogy between mass‐flux models and the relaxed eddy accumulation method reveals that there is a seemingly implicit assumption of a Gaussian JPDF in the former.

Reduced particle settling speed in turbulence

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).

Response and Reliability of a Giant Magnetostrictive Film Actuator Subject to Axial Random Excitation

A giant magnetostrictive thin film (GMF) actuator designed as a simply supported beam under axial white noise excitation is studied. Firstly, a non-dimensional stochastic difference equation governing the motion is simplified by the modified stochastic averaging method. Subsequently, the stationary probability density function of amplitude and the joint probability density function of displacement and velocity were obtained respectively. Finally, the reliability was studied by the backward Kolmogorov (BK) equation to guarantee the safety of the actuator. Numerical simulations are carried out to verify the theoretical analysis.

Structural organization of the quiescent core region in a turbulent channel flow

The structural organization of the quiescent core region in a turbulent channel flow was explored using direct numerical simulation data at Reτ=930. The quiescent core region is the uniform momentum zone located at the center of the channel, and contains the highest momentum with a low level of turbulence. The boundary of the quiescent core region can be identified from the probability density function of the streamwise modal velocity. The streamwise velocity changes abruptly near the boundary of the core region. The abrupt jump leads the increase of the velocity gradient, which is similar to the vorticity thickness of the laminar superlayer at the turbulent/non-turbulent interface. The strong shear induced from the abrupt change is originated from the vortical structure lying on the boundary of the core region. The spanwise population densities of the prograde and retrograde vortices have a local maximum near the boundary of the core region. The prograde vortex dominantly contributes to the total mean shear near the core boundary and the contribution to the total mean shear rapidly decreases within the core region. The prograde and retrograde vortices form a counter-rotating vortex pair at the boundary of the core region associated with the nibbling mechanism. The boundary of the core region contains large-scale concave and convex features. The concave (convex) core interface is organized by the negative-u (positive-u) regions which induce the ejections (sweeps) around the core boundary.

Large eddy simulation of the near-field vortex dynamics in starting square jet transitioning into steady state

Large eddy simulation (LES) is carried out to study the vortex dynamics in the near-field of a starting turbulent square jet as well as its evolution into a developed steady jet. Simulations are conducted at Reynolds numbers (Re = UjD/υ) of 8000 and 45 000 based on the nozzle hydraulic diameter D and jet velocity (Uj). A Reynolds stress model was used to simulate the internal flow in the nozzle which provided the inlet conditions for the LES of the jet. To validate the simulations, turbulence statistics are compared with experimental results available for a steady square jet. Evaluation of the probability density function, skewness, and flatness of the centerline streamwise velocity (Uc) shows deviation from the Gaussian distribution in the near-field. Evolution of the self-induced deformation of the leading vortex ring is investigated to further clarify the role of axis-switching. The axis-switching is initiated earlier at low Reynolds number while the completion of the axis-switching process occurred at the same dimensionless time for both Reynolds numbers. The role of pressure distribution on vortex ring deformation is investigated. It is shown that the influence of pressure-induced azimuthal instability tends to deform a two-dimensional vortex ring topology into a three-dimensional one and revert back to a two-dimensional character again. The break-down and diffusion of the tip of the vortex are also studied. Evolution of the shear layer from a starting jet to a developed jet is studied in terms of the vorticity field. For a starting jet, entrainment is shown to occur in the presence of corner hairpin vortices.

On coherent structures and mixing characteristics in the near field of a rotating-pipe jet

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.

Probability characteristics of nonlinear dynamical systems driven by δ-pulse noise.

For a nonlinear dynamical system described by the first-order differential equation with Poisson white noise having exponentially distributed amplitudes of δ pulses, some exact results for the stationary probability density function are derived from the Kolmogorov-Feller equation using the inverse differential operator. Specifically, we examine the "effect of normalization" of non-Gaussian noise by a linear system and the steady-state probability density function of particle velocity in the medium with Coulomb friction. Next, the general formulas for the probability distribution of the system perturbed by a non-Poisson δ-pulse train are derived using an analysis of system trajectories between stimuli. As an example, overdamped particle motion in the bistable quadratic-cubic potential under the action of the periodic δ-pulse train is analyzed in detail. The probability density function and the mean value of the particle position together with average characteristics of the first switching time from one stable state to another are found in the framework of the fast relaxation approximation.

Experiments on low-Reynolds-number turbulent flow through a square duct

Previous experimental studies on turbulent square duct flow have focused mainly on high Reynolds numbers for which a turbulence-induced eight-vortex secondary flow pattern exists in the cross-sectional plane. More recently, direct numerical simulations (DNS) have revealed that the flow field at Reynolds numbers close to transition can be very different; the flow in this ‘marginally turbulent’ regime alternating between two states characterised by four vortices. In this study, we experimentally investigate the onset criteria for transition to turbulence in square ducts. In so doing, we highlight the potential importance of Coriolis effects on this process for low-Ekman-number flows. We also present experimental data on the mean flow properties and turbulence statistics in both marginally and fully turbulent flow at relatively low Reynolds numbers using laser Doppler velocimetry. Results for both flow categories show good agreement with DNS. The switching of the flow field between two flow states at marginally turbulent Reynolds numbers is confirmed by bimodal probability density functions of streamwise velocity at certain distances from the wall as well as joint probability density functions of streamwise and wall normal velocities which feature two peaks highlighting the two states.

Probabilistic solution of non-linear random ship roll motion by path integration

This paper investigates the probability density function (PDF) of non-linear random ship roll motion using a previously developed path integration method. The mathematical model of ship rolling motion consists of a linear-plus-cubic damping and a non-linear restoring moment in the form of odd-order polynomials up to fifth-order terms. In the path integration method, the interpolation scheme is based on the Gauss–Legendre quadrature integration rule and the short-time transition probability density function is formulated by short-time Gaussian approximation. The present work extends the path integration method to the case of non-linear random ship roll motion. Different values of non-linearity coefficient and excitation intensity are used to examine the effectiveness of the path integration method. Numerical analysis shows that the results of the path integration method agree well with the simulation results, even in the tail region. The path integration method is effective and it is simply implemented in the examined cases. Due to the presence of non-linear damping terms and non-linear restoring moment terms, the PDFs of roll angle and angular velocity exhibit highly non-Gaussian behaviors.

Evaluation of PBL Parameterizations in WRF at Subkilometer Grid Spacings: Turbulence Statistics in the Dry Convective Boundary Layer

Abstract Planetary boundary layer (PBL) parameterizations in mesoscale models have been developed for horizontal resolutions that cannot resolve any turbulence in the PBL, and evaluation of these parameterizations has been focused on profiles of mean and parameterized flux. Meanwhile, the recent increase in computing power has been allowing numerical weather prediction (NWP) at horizontal grid spacings finer than 1 km, at which kilometer-scale large eddies in the convective PBL are partly resolvable. This study evaluates the performance of convective PBL parameterizations in the Weather Research and Forecasting (WRF) Model at subkilometer grid spacings. The evaluation focuses on resolved turbulence statistics, considering expectations for improvement in the resolved fields by using the fine meshes. The parameterizations include four nonlocal schemes—Yonsei University (YSU), asymmetric convective model 2 (ACM2), eddy diffusivity mass flux (EDMF), and total energy mass flux (TEMF)—and one local scheme, the Mellor–Yamada–Nakanishi–Niino (MYNN) level-2.5 model. Key findings are as follows: 1) None of the PBL schemes is scale-aware. Instead, each has its own best performing resolution in parameterizing subgrid-scale (SGS) vertical transport and resolving eddies, and the resolution appears to be different between heat and momentum. 2) All the selected schemes reproduce total vertical heat transport well, as resolved transport compensates differences of the parameterized SGS transport from the reference SGS transport. This interaction between the resolved and SGS parts is not found in momentum. 3) Those schemes that more accurately reproduce one feature (e.g., thermodynamic transport, momentum transport, energy spectrum, or probability density function of resolved vertical velocity) do not necessarily perform well for other aspects.

Sedimentation of finite-size spheres in quiescent and turbulent environments

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.