We use silicon strip detectors (originally developed for the CLEO III high energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70,000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 ≥ R λ ≥ 970. Particle trajectories exhibiting accelerations up to 16,000 m s −2 (40 times the rms value) are routinely observed. The probability density function of the acceleration is found to have Reynolds number dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low Reynolds number direct numerical simulations, and with the K41 based Heisenberg-Yaglom prediction for R λ ≥ 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at R λ = 970. The coupling of the acceleration to the large scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τ η .

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport[1, 2], processes in stirred chemical reactors and combustion systems [3], and in the industrial production of nanoparticles[4]. The perspective of particle trajectories has been used successfully to describe mixing and transport in turbulence[3, 5], but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations [6,7], based on the 1941 scaling theory of Kolmogorov[8, 9] (K41). Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that universal K41 scaling of the acceleration variance is attained at high Reynolds numbers. Our data show strong intermittency-particles are observed with accelerations of up to 1,500 times the acceleration of gravity (40 times the root mean square value). Finally, we find that accelerations manifest the anisotropy of the large scale flow at all Reynolds numbers studied.In principle, fluid particle trajectories are easily measured by seeding a turbulent flow with minute tracer particles and following their motions with an imaging system. In practice this can be a very challenging task since we must fully resolve particle motions which take place on times scales of the order of the Kolmogorov time, τ η = (ν/ǫ) 1/2 where ν is the kinematic viscosity and ǫ is the turbulent energy dissipation. This is exemplified in Fig. 1, which shows a measured three-dimensional, time resolved trajectory of a tracer particle undergoing violent accelerations in our turbulent water flow, for which τ η = 0.3 ms. The particle enters the detection volume on the upper right, is pushed to the left by a burst of acceleration and comes nearly to a stop before being rapidly accelerated (1200 times the acceleration of gravity) upward in a cork-screw motion. This trajectory illustrates the difficulty in following tracer particles-a particle's acceleration can go from zero to 30 times its rms value and back to zero in fractions of a millisecond and within distances of hundreds of micrometers.Conventional detector technologies are effective for low Reynolds number flows[10, 11], but do not provide adequate temporal resolution at high Reynolds numbers. However, the requirements are met by the use of silicon strip detectors as optical imaging elements in a particle tracking system. The strip detectors employed in our experiment (See Fig. 2a) were developed to measure particle tracks in the vertex detector of the CLEO III experiment operating at the Cornell Electron Positron Collider [12]. When applied to particle tracking in turbulence (See Fig. 2b) each detector measures a one-dimensional projection of the image of the tracer particles. Using a data acquisition system designed for the turbulence expe...

We report experimental results on the acceleration component probability distribution function at R λ = 690 to probabilities of less than 10 −7 . This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several models inspired by non-extensive statistical mechanics. We also look at acceleration component probability distributions conditioned on a velocity component for conditioning velocities as high as 3 times the standard deviation and find them to be highly non-Gaussian.

We report experimental results on the three-dimensional Lagrangian acceleration in highly turbulent flows. Tracer particles are tracked optically using four silicon strip detectors from high energy physics that provide high temporal and spatial resolution. The components of the acceleration are shown to be statistically dependent. The probability density function of the acceleration magnitude is comparable to a log-normal distribution. Assuming isotropy, a log-normal distribution of the magnitude can account for the observed dependency of the components. The time dynamics of the acceleration components is found to be typical of the dissipation scales, whereas the magnitude evolves over longer times, possibly close to the integral time scale.

In this paper we study acceleration statistics from laboratory measurements and direct numerical simulations in three-dimensional turbulence at Taylor-scale Reynolds numbers ranging from 38 to 1000. Using existing data, we show that at present it is not possible to infer the precise behavior of the unconditional acceleration variance in the large Reynolds number limit, since empirical functions satisfying both the Kolmogorov and refined Kolmogorov theories appear to fit the data equally well. We also present entirely new data for the acceleration covariance conditioned on the velocity, showing that these conditional statistics are strong functions of velocity, but that when scaled by the unconditional variance they are only weakly dependent on Reynolds number. For large values of the magnitude u of the conditioning velocity we speculate that the conditional covariance behaves like u 6 and show that this is qualitatively consistent with the stretched exponential tails of the unconditional acceleration probability density function ͑pdf͒. The conditional pdf is almost identical in shape to the unconditional pdf. From these conditional covariance data, we are able to calculate the conditional mean rate of change of the acceleration, and show that it is consistent with the drift term in second-order Lagrangian stochastic models of turbulent transport. We also calculate the correlation between the square of the acceleration and the square of the velocity, showing that it is small but not negligible.