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...

International audienceThe olfactory system of male moths is exquisitely sensitive to pheromones emitted by females and transported in the environment by atmospheric turbulence. Moths respond to minute amounts of pheromones, and their behavior is sensitive to the fine-scale structure of turbulent plumes where pheromone concentration is detectible. The signal of pheromone whiffs is qualitatively known to be intermittent, yet quantitative characterization of its statistical properties is lacking. This challenging fluid dynamics problem is also relevant for entomology, neurobiology, and the technological design of olfactory stimulators aimed at reproducing physiological odor signals in well-controlled laboratory conditions. Here, we develop a Lagrangian approach to the transport of pheromones by turbulent flows and exploit it to predict the statistics of odor detection during olfactory searches. The theory yields explicit probability distributions for the intensity and the duration of pheromone detections, as well as their spacing in time. Predictions are favorably tested by using numerical simulations, laboratory experiments, and field data for the atmospheric surface layer. The resulting signal of odor detections lends itself to implementation with state-of-the-art technologies and quantifies the amount and the type of information that male moths can exploit during olfactory searches