Folding Dynamics and Its Intermittency in Turbulence.

Fluid elements deform in turbulence by stretching and folding. In this Letter, by projecting the material deformation tensor onto the largest stretching direction, we depict the dynamics of folding through the evolution of the material curvature. Results from direct numerical simulation (DNS) show that the curvature growth exhibits two regimes: first, a linear stage dominated by folding fluid elements through a persistent velocity Hessian that then transition to an exponential-growth stage driven by the stretching of already strongly bent fluid elements. This transition leads to strong curvature intermittency at later stages, which can be explained by a proposed curvature-evolution model. The link between velocity Hessian to folding provides a new way to understand the crucial steps in energy cascade and mixing in turbulence beyond the classical linear description of stretching dynamics.

Preferential Rotation of Chiral Dipoles in Isotropic Turbulence.

We introduce a new particle shape which shows preferential rotation in three dimensional homogeneous isotropic turbulence. We call these particles chiral dipoles because they consist of a rod with two helices of opposite handedness, one at each end. 3D printing is used to fabricate these particles with a length in the inertial range and their rotations are tracked in a turbulent flow between oscillating grids. High aspect ratio chiral dipoles preferentially align with their long axis along the extensional eigenvectors of the strain rate tensor, and the helical ends respond to the extensional strain rate with a mean spinning rate that is nonzero. We use Stokesian dynamics simulations of chiral dipoles in pure strain flow to quantify the dependence of spinning on particle shape. Based on the known response to pure strain, we build a model that gives the spinning rate of small chiral dipoles using velocity gradients along Lagrangian trajectories from high resolution direct numerical simulations. The statistics of chiral dipole spinning determined with this model show surprisingly good agreement with the measured spinning of much larger chiral dipoles in the experiments.

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence.

Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D printing technology is used to fabricate particles with slender arms connected at a common center. Shapes explored are crosses (two perpendicular rods), jacks (three perpendicular rods), triads (three rods in triangular planar symmetry), and tetrads (four arms in tetrahedral symmetry). Methods for producing on the order of 10,000 fluorescently dyed particles are described. Time-resolved measurements of their orientation and solid-body rotation rate are obtained from four synchronized videos of their motion in a turbulent flow between oscillating grids with Rλ = 91. In this relatively low-Reynolds number flow, the advected particles are small enough that they approximate ellipsoidal tracer particles. We present results of time-resolved 3D trajectories of position and orientation of the particles as well as measurements of their rotation rates.

Inertial range scaling in rotations of long rods in turbulence.

We derive a scaling relationship for the mean square rotation rate of rods with lengths in the inertial range in turbulence: ∝ l(-4/3). We present experimental measurements of the rotational statistics of neutrally buoyant rods with lengths 2.8

Simulations of granular gravitational collapse.

A freely cooling granular gas in a gravitational field undergoes a collapse to a multicontact state in a finite time. Previous theoretical [D. Volfson et al., Phys. Rev. E 73, 061305 (2006)] and experimental work [R. Son et al., Phys. Rev. E 78, 041302 (2008)] have obtained contradictory results about the rate of energy loss before the gravitational collapse. Here we use a molecular dynamics simulation in an attempt to recreate the experimental and theoretical results to resolve the discrepancy. We are able to nearly match the experimental results, and find that to reproduce the power law predicted in the theory we need a nearly elastic system with a constant coefficient of restitution greater than 0.993. For the more realistic velocity-dependent coefficient of restitution, there does not appear to be a power-law decay and the transition from granular gas to granular solid is smooth, making it difficult to define a time of collapse.

Rotation rate of rods in turbulent fluid flow.

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Acceleration statistics of neutrally buoyant spherical particles in intense turbulence.

We measure acceleration statistics of neutrally buoyant spherical particles with a diameter 0.4 < d/eta < 27 in intense turbulence (400 < R(lambda) < 815). High speed cameras image polystyrene tracer particles in a flow between counterrotating disks. The measurements of acceleration variance clearly resolve the transition from the tracer like behavior of small particles to the much smaller accelerations of large particles. Two models of this transition from small to large particle behavior are critically examined. For d > 5eta, decreases with the diameter as d(-2/3), in agreement with inertial range scaling arguments. Consistent with earlier work, we find that the scaled acceleration probability density function shows very little dependence on particle size.

Experimental measurements of the collapse of a two-dimensional granular gas under gravity.

We experimentally measure the decay of a quasi-two-dimensional granular gas under gravity. A granular gas is created by vibrofluidization, after which the energy input is halted, and the time-dependent statistical properties of the decaying gas are measured with video particle tracking. There are two distinct cooling stages separated by a high temperature settling shock. In the final stage, the temperature of a fluid packet decreases as a power law T proportional, variant(t{c}-t);{alpha} just before the system collapses to a static state. The measured value of alpha ranges from 3.3 to 6.1 depending on the height, significantly higher than the exponent of 2 found in theoretical work on this problem [D. Volfson, B. Meerson, and L. S. Tsimring, Phys Rev. E 73, 61305 (2006)]. We also address the question of whether the collapse occurs simultaneously at different heights in the system.

Visualization of collisional substructure in granular shock waves.

We study shock wave formation and propagation in an experimental vertically driven quasi-two-dimensional granular gas. We measure the moments of the single particle velocity distribution as a function of space and time. The space-time fields of the velocity moments show acoustic waves with a serrated substructure on the scale of a particle diameter. We show that this substructure is the result of collisional transport in which sequential collisions each transport momentum and energy by one particle diameter.

Real-time image compression for high-speed particle tracking.

High-speed particle tracking with digital video creates very large data rates and as a result experimenters are forced to make compromises between spatial resolution, temporal resolution, and the duration over which data is acquired. The images produced in particle tracking experiments typically contain a large amount of black space with relatively few bright pixels and this suggests the possibility of image compression. This paper describes a system for real-time compression of high-speed video. A digital circuit placed between the camera (500 Hz, 1280 x 1024 pixels) and frame grabber compresses data in real-time by comparing input pixels with a threshold value and outputs a vector containing the brightness and position of the bright pixels. In a typical experiment, the compression ratio for an image ranges from 100 to 1000 and varies dynamically depending on the number of filtered pixels. The reduced data rate makes it possible to write directly to the hard disk. While previously data could only be acquired for 6.5 s into 4 GB of dedicated video RAM, the new system could acquire full resolution data continuously for up to a week into a 600 GB hard drive.

Failure and strengthening of granular slopes under horizontal vibration.

We present experimental measurements of a granular slope under horizontal vibration. We use optical particle tracking to measure the motion of surface beads as the slope fails. We find that for all but the largest inclination angles, initial bead motion leads to strengthening rather than an avalanche. The initial motion of the beads is usually intermittent and evolves differently for different preparations, slope angles, and rates of increase in the vibration amplitude. When a specific criterion is chosen to define failure, the Coulomb friction model adequately describes the average acceleration required to produce failure, as long as slope preparation and experimental protocol are constant. However, the observed intermittent motion and rate dependence indicate that strengthening microrearrangements are important features that affect failure of slopes under external perturbations.

Experimental measurements of stretching fields in fluid mixing.

Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching field. This quantity, previously available only numerically, attains local maxima along lines that coincide with the stable and unstable manifolds of hyperbolic fixed points of Poincaré maps. Contours of a passive impurity field are found at each instant to be oriented parallel to the lines that have recently experienced large stretching. The local stretching varies by 12 orders of magnitude.

Ordered clusters and dynamical states of particles in a vibrated fluid.

Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered microcrystallites, time-periodic structures, and chaotic fluctuating patterns with complex dynamics. A model based on streaming flow gives a good quantitative account of the attractive part of the interaction.