Alice M. Crawford

Fluid Particle Accelerations in Fully Developed Turbulence

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, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg–Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov. 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, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable—particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

Measurement of particle accelerations in fully developed turbulence

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 70000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 [ges ] R λ [ges ] 970. Particle trajectories exhibiting accelerations up to 16000 m s −2 (40 times the r.m.s. 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 [ges ] 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 .

Experimental Lagrangian acceleration probability density function measurement

Abstract We report experimental results on the acceleration component probability distribution function at Rλ=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 three times the standard deviation and find them to be highly non-Gaussian.

Three-Dimensional Structure of the Lagrangian Acceleration in Turbulent Flows

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.

Conditional and unconditional acceleration statistics in turbulence

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 u6 and show that this is qualitatively consistent with the stretched exponential tails of the unconditional acceleration proba...

On the distribution of Lagrangian accelerations in turbulent flows

Superstatistical Lagrangian stochastic models are shown to predict accurately the distribution of the magnitude of the acceleration vector in three-dimensional high Reynolds-number turbulence. Distributions are closely log-normal having high tails that are nearly coincident with measured distributions of enstrophy. The findings support the view that the dominant contribution to extreme accelerations comes from centripetal accelerations induced by vortex filaments.

A silicon strip detector system for high resolution particle tracking in turbulence

We describe a high speed imaging system that is used to track tracer particles in highly turbulent flows. The system uses silicon strip detectors designed for high energy physics experiments and is capable of reading two detectors at a frame rate of 70 kHz. Each detector contains 512 strips and measures a one-dimensional projection of the light striking it. The position measurements from this system have a dynamic range of 6400:1. Extensions to higher frame rates and more detectors are possible. We describe the detectors, readout system, supporting systems, and give an evaluation of the measurement accuracy.

Fluid acceleration in the bulk of turbulent dilute polymer solutions

We studied the effects of long-chain polymers on the small scales of turbulence by experimental measurements of Lagrangian accelerations in the bulk of turbulent flows of dilute polymer solutions. Lagrangian accelerations were measured by following tracer particles with a high-speed optical tracking system. We observed a significant decrease in the acceleration variance in dilute polymer solutions as compared with in pure water. The shape of the normalized acceleration probability density functions, however, remained the same as in Newtonian water flows. We also observed an increase in the turbulent Lagrangian acceleration autocorrelation time with polymer concentration. The decrease of acceleration variance and the increase of acceleration autocorrelation time are consistent with a suppression of viscous dissipation, and cannot be explained by a mere increase of effective viscosity due to the polymers.