We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.

We describe Lagrangian measurements of water droplets in grid generated wind tunnel turbulence at a Taylor Reynolds number of R(lambda)=250 and an average Stokes number (St) of approximately 0.1. The inertial particles are tracked by a high speed camera moving along the side of the tunnel at the mean flow speed. The standardized acceleration probability density functions of the particles have spread exponential tails that are narrower than those of a fluid particles (St approximately 0) and there is a decrease in the acceleration variance with increasing Stokes number. A simple vortex model shows that the inertial particles selectively sample the fluid field and are less likely to experience regions of the fluid undergoing the largest accelerations. Recent direct numerical simulations compare favorably with these first measurements of Lagrangian statistics of inertial particles in highly turbulent flows.

From hot-wire anemometer measurements in active-grid wind-tunnel turbulence we have determined the Reynolds number dependence of the velocity derivative moments, the mean-squared pressure gradient, χ, and the normalized acceleration variance, a 0 , over the Reynolds number range 100 6 R λ 6 900. The values of χ and a 0 were obtained from the fourth-order velocity structure functions. The derivative moments show power-law dependence on Reynolds number and the exponent is the same with or without shear. In particular, we find the derivative kurtosis, K ∂u/∂x ∼ R 0.39 λ , and there is no evidence of the transition that has been observed in this quantity in some recent work. We find that at high Reynolds numbers, χ and a 0 tend to values similar to those obtained by direct particle tracking measurements and by direct numerical simulation. However, at lower Reynolds number our estimates of χ and a 0 appear to be affected by the evaluation technique which imposes strict requirements on local homogeneity and isotropy.

Our objective is to explain recent Lagrangian acceleration measurements of inertial particles in decaying, nearly isotropic turbulence ͓Ayyalasomayajula et al., Phys. Rev. Lett. 97, 144507 ͑2006͔͒. These experiments showed that as particle inertial effects increased, the variance in the particle acceleration fluctuations was reduced, and the tails of the normalized particle acceleration probability density function ͑PDF͒ became systematically attenuated. We model this phenomenon using a base flow that consists of a two-dimensional array of evenly spaced vortices with signs and intensities that vary randomly in time. We simulate a large sample of inertial particles moving through the fluid without disturbing the flow ͑one-way coupling͒. Consistent with Bec et al. ͓J. Fluid Mech. 550, 349 ͑2006͔͒, we find that our model exhibits preferential concentration or clustering of particles in regions located away from the vortex centers. That is, inertial particles selectively sample the flow field, oversampling regions with high strains and undersampling regions with high vorticities. At low Stokes numbers, this biased "sampling" of the flow is responsible for the reduction in the acceleration variance and partially explains the attenuation of the tails of the acceleration PDF. However, contrary to previous findings, we show that the tails of the PDF are also diminished by "filtering" induced by the attenuated response of the inertial particles to temporal variations in the fluid acceleration: Inertial particles do not respond to fluctuations with frequencies much higher than the inverse of the particle stopping time. We show that larger fluid acceleration events have higher frequencies and hence experience greater filtering by particle inertia. We contrast the vortex model with previous Lagrangian acceleration models by Sawford ͓Phys. Fluids A 3, 1577 ͑1991͔͒ and Reynolds ͓Phys. Fluids 15, L1 ͑2003͔͒ and show that although these models capture some aspects of the inertial particle behavior, it is necessary to employ a model of the flow with spatial structure to capture the effect of sampling on the inertial particle dynamics.

We present measurements, over a wide range of Reynolds numbers ($40\leq R_{\lambda} \leq 470$), of grid-generated turbulence subjected to axisymmetric strain, and of the subsequent evolution of the turbulence after the strain is released. The Reynolds number was varied by the use of both passive and active grids and the strain was produced by a 4:1 area-change axisymmetric contraction placed at various distances from the grid. The time scale ratio of the turbulence to that of the mean strain varied from approximately 10 to 30. The results show reasonable agreement with (linear) rapid distortion theory (RDT) for the velocity variances but, contrary to linear theory, the strained longitudinal, $u_{1}$, spectrum peaked at significantly higher wavenumber than the transverse, $u_{2}$, spectrum. The mismatch in peaks increased with increasing $R_{\lambda}$ and at the highest Reynolds number ($R_{\lambda} = 470$) the peak of the strained $u_{1}$-spectrum occurred at a wavenumber 200 times greater than that of the $u_{2}$-spectrum. As the flow relaxed toward isotropy after the contraction, further evidence of the non-locality in the flow field became apparent, with a second peak in the $u_{2}$-spectrum emerging at a similar wavenumber to the high-frequency peak in the $u_{1}$-spectrum. The strain also caused the longitudinal derivative skewness to change sign but as the flow evolved after the contraction the derivative skewness returned to its typical value of ${-}$0.4. We also show that single-point turbulence models are inadequate to describe the relaxation of the turbulence towards an isotropic state in the postcontraction region.