Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale . In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution 512 3 (R λ ≈ 185). Following the trajectories of up to 120 million particles with Stokes numbers, St, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: (i) The root-mean-squared acceleration a rms sharply falls off from the fluid tracer value already at quite small Stokes numbers; (ii) At a given St the normalised acceleration a rms /(ǫ 3 /ν) 1/4 increases with R λ consistently with the trend observed for fluid tracers; (iii) The tails of the probability density function of the normalised acceleration a/a rms decrease with St. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small St, and filtering induced by the particle response time, that takes over at larger St.

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism and its merits and limitations are discussed. Understanding the Lagrangian statistics of particles advected by a turbulent velocity field, u(x, t), is important both for its theoretical implications [1] and for applications, such as the development of phenomenological and stochastic models for turbulent mixing [2]. Recently, several authors have attempted to describe Lagrangian statistics such as acceleration by constructing models based on equilibrium statistics (see e.g. [3,4,5], critically reviewed in [6]). In this letter we show how the multifractal formalism offers an alternative approach which is rooted in the phenomenology of turbulence. Here, we derive the Lagrangian statistics from the Eulerian statistics without introducing ad hoc hypotheses.In order to obtain an accurate description of the particle statistics it is necessary to measure the positions, X(t), and velocities, v(t) ≡Ẋ(t) = u(X(t), t), of the particles with very high resolution, ranging from fractions of the Kolmogorov timescale, τ η , to multiples of the Lagrangian integral time scale, T L . The ratio of these timescales, T L /τ η , gives an estimate of the micro-scale Reynolds number, R λ , which may easily reach values of order 10 3 in laboratory experiments. Despite recent advances in experimental techniques for measuring Lagrangian turbulent statistics [7,8,9], direct numerical simulations (DNS) still offer higher accuracy albeit at a slightly lower Reynolds number [10,11,12,13]. In this letter we are concerned with single particle statistics, that is, the statistics of velocity and acceleration fluctuations along individual particle trajectories. Here, we analyse Lagrangian data obtained from a recent DNS of homogeneous isotropic turbulence [14] which was performed on 512 3 and 1024 3 cubic lattices with Reynolds numbers up to R λ ∼ 280. The Navier-Stokes equations were integrated using fully de-aliased pseudo-spectral methods for a total time T ≈ T L . Millions of Lagrangian particles (passive tracers) were released into the flow once a statistically stationary velocity field had been obtained. The positions and velocities of the particles were stored at a sampling rate of 0.07τ η . The Lagrangian velocity was calculated using linear interpolation. Acceleration was calculated both by following the particle and by direct computation from all three forces acting on the particle -the pressure gradients, viscous forces and the large scale forcing. The two measurements were found to be in very good agreement. The flow was forced by keeping the total energy constant in th...

4 pageshe statistical properties of fluid particles transported by a three-dimensional fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics are investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov time scale, , up to one large-eddy turnover time. Our analysis reveals the existence of relatively rare trapping events in vortex filaments which give rise to enhanced intermittency on Lagrangian observables up to 10. Lagrangian velocity structure function attain scaling properties in agreement with the multifractal prediction only for time lags larger than those affected by trappin

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R 2 120:740. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. ParisiFrisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.