Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles. These two competing effects can either increase or decrease the geometrical collision rates between same-size particles and are crucial for realistic modeling of coalescing particles.Many industrial, atmospheric, and astrophysical phenomena ranging from the microphysics of cloud formation, to planet formation in a dusty circumstellar disk of gas, involves the modeling of the interactions between small solid particles suspended in a turbulent carrier flow. Two main effects are typically at play: a viscous drag that particles experience with the agitated fluid and an external force, such as gravity, that acts because of their density contrast with the fluid. While drag is predominant for small particles, gravity takes over the dynamics of large particles and most studies treat these two asymptotics independently. However it is usually at this critical transition that standard modeling fails, as is evident when estimating for instance the rate at which rain is triggered in warm clouds [1,2]. Most models are unable to circumvent a bottleneck in the droplet growth for diameters around 20-40µm. A key improvement might be to combine turbulent and gravitational effects.In this Letter we understand the intriguing interplay between turbulence, gravity, and particle sizes. This question is of fundamental importance in fluid dynamics, in particular, and in non-equilibrium statistical physics, in general, as it is central to modeling coalescences in natural or laboratory droplet suspensions. The most noticeable effect of turbulence on the settling of heavy particles is the increase of their terminal velocity induced by a preferential sweeping along the downward fluid flow [3][4][5]. This phenomenon is mostly understood on qualitative grounds and has been quantified only in model flows [6]. Furthermore very little is known on the effect of gravitational settling on two-particle statistics. Fundamental theoretical and numerical studies of the clustering of particle pairs [7,8] and of the enhancement of collisions due to inertia [9, 10] usually neglect gravity. We present here, by combining state-of-the-art direct numerical simulations with theoretical results based on our asymptotic analysis, a systematic study of the dynamical and statistical properties of particles as a function of (i) the level of turbulence of the carrier flow (Reynolds number), (ii) the inertia of the particles (Stokes number), and (iii) the ratio between the turbulent accelerations and gravity (Froude numb...

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.

The dynamics of neutrally buoyant particles transported by a turbulent flow is investigated for spherical particles with radii of the order of the Kolmogorov dissipative scale or larger. The pseudo-penalization spectral method that has been proposed by Pasquetti et al. (Appl. Numer. Math., vol. 58, 2008, pp. 946-954) is adapted to integrate numerically the simultaneous dynamics of the particle and of the fluid. Such a method gives a unique handle on the limit of validity of pointparticle approximations, which are generally used in applicative situations. Analytical predictions based on such models are compared to result of very well-resolved direct numerical simulations. Evidence is obtained that Faxén corrections reproduce dominant finite-size effects on velocity and acceleration fluctuations for particle diameters up to four times the Kolmogorov scale. The dynamics of particles with larger diameters is consistent with predictions obtained from dimensional analysis.