Gregory P. Bewley

Superfluid helium: visualization of quantized vortices.

When liquid helium is cooled to below its phase transition at 2.172 K, vortices appear with cores that are only ångströms in diameter, about which the fluid circulates with quantized angular momentum. Here we generate small particles of solid hydrogen that can be used to image the cores of quantized vortices in their three-dimensional environment of liquid helium. This technique enables the geometry and interactions of these vortices to be observed directly.

Characterization of reconnecting vortices in superfluid helium

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical and superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micrometer-sized solid hydrogen particles trapped on quantized vortex cores and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show that the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately ½, consistent with the self-similar evolution of the vortices.

Inertial waves in rotating grid turbulence

Using liquid helium, liquid nitrogen, and water as test fluids, we attempt to generate homogeneous turbulence in a steadily rotating system. We create turbulence by pulling a grid in rotating channels with both square and round cross sections, and observe large-scale inertial waves in the flow. These inertial waves quickly sense the boundaries, and resonate at frequencies characteristic of the container. We describe some of their properties and argue that the resultant inhomogeneity is a feature of any real system.

DECAY OF TURBULENCE AT HIGH REYNOLDS NUMBERS

Turbulent motions in a fluid decay at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the decay rate is not generally known. This Letter concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reaches higher Reynolds numbers than ever before and covers a wide range of them (10^{4}<Re=UM/ν<5×10^{6}), we measure the decay rate with the unprecedented precision of about 2%. Here U is the mean speed of the flow, M is the forcing scale, and ν is the kinematic viscosity of the fluid. We observe that the decay rate is Reynolds-number independent, which contradicts some models and supports others.

Observation of the sling effect

When cloud particles are small enough, they move with the turbulent air in the cloud. On the other hand, as particles become larger their inertia affects their motions, and they move differently than the air. These inertial dynamics impact cloud evolution and ultimately climate prediction, since clouds govern the Earths energy balances. However, we lack a simple description of the dynamics. Falkovich et al?describe theoretically a new dynamical mechanism called the ?sling effect? by which extreme events in the turbulent air cause idealized inertial cloud particles to break free from the airflow (Falkovich et al 2002 Nature 419 151). The sling effect thereafter causes particle trajectories to cross each other within isolated pockets in the flow, which increases the chance of collisions that forms larger particles. We combined experimental techniques that allow for precise control of a turbulent flow with three-dimensional tracking of multiple particles at unprecedented resolution. In this way, we could observe both the sling effect and crossing trajectories between real particles. We isolated the inertial sling dynamics from those caused by turbulent advection by conditionally averaging the data. We found the dynamics to be universal in terms of a local Stokes number that quantifies the local particle velocity gradients. We measured the probability density of this quantity, which shows that sharp gradients became more frequent as the global Stokes number increased. We observed that sharp compressive gradients in the airflow initiated the sling effect, and that thereafter gradients in the particle flow ran away and steepened in a way that produced singularities in the flow in finite time. During this process both the fluid motions and gravity became unimportant. The results underpin a framework for describing a crucial aspect of inertial particle dynamics and predicting collisions between particles.

Signatures of non-universal large scales in conditional structure functions from various turbulent flows

We present a systematic comparison of conditional structure functions in nine turbulent flows. The flows studied include forced isotropic turbulence simulated on a periodic domain, passive grid wind tunnel turbulence in air and in pressurized SF6, active grid wind tunnel turbulence (in both synchronous and random driving modes), the flow between counter-rotating

Extreme fluctuations of the relative velocities between droplets in turbulent airflow

We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St < 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, which suggests that the Stokes drag model misses important dynamics. Nevertheless, the scaling behavior of the extreme events in both the experiments and the simulations can be captured by the same multi-fractal model.

On integral length scales in anisotropic turbulence

We found experimentally a dependence of the integral length scales of correlation functions measured in different directions in a turbulent flow on the velocity fluctuation anisotropy in those same directions. We derive invariants for anisotropic turbulence that is locally isotropic, and so a relationship between the velocity and length scales. The results emphasize the importance of defining the Reynolds number, which was about 480, in terms of scalar quantities instead of these scales. We also find that the normalized energy dissipation rate was approximately independent of the anisotropy.

Variable density turbulence tunnel facility

The Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, produces very high turbulence levels at moderate flow velocities, low power consumption, and adjustable kinematic viscosity between 10(-4) m(2)/s and 10(-7) m(2)/s. The Reynolds number can be varied by changing the pressure or flow rate of the gas or by using different non-flammable gases including air. The highest kinematic viscosities, and hence lowest Reynolds numbers, are reached with air or nitrogen at 0.1 bar. To reach the highest Reynolds numbers the tunnel is pressurized to 15 bars with the dense gas sulfur hexafluoride (SF6). Turbulence is generated at the upstream ends of two measurement sections with grids, and the evolution of this turbulence is observed as it moves down the length of the sections. We describe the instrumentation presently in operation, which consists of the tunnel itself, classical grid turbulence generators, and state-of-the-art nano-fabricated hot-wire anemometers provided by Princeton University [M. Vallikivi, M. Hultmark, S. C. C. Bailey, and A. J. Smits, Exp. Fluids 51, 1521 (2011)]. We report measurements of the characteristic scales of the flow and of turbulent spectra up to Taylor Reynolds number R(λ) ≈ 1600, higher than any other grid-turbulence experiment. We also describe instrumentation under development, which includes an active grid and a Lagrangian particle tracking system that moves down the length of the tunnel with the mean flow. In this configuration, the properties of the turbulence are adjustable and its structure is resolvable up to R(λ) ≈ 8000.

The journey of hydrogen to quantized vortex cores

Nanoscale hydrogen particles in superfluid helium track the motions of quantized vortices. This provides a way to visualize turbulence in the superfluid. Here, we trace the evolution of the hydrogen from a gas to frozen particles migrating toward the cores of quantized vortices. Not only are the intervening processes interesting in their own right, but understanding them better leads to more revealing experiments.