Douglas H. Kelley

Emergent dynamics of laboratory insect swarms

Collective animal behaviour occurs at nearly every biological size scale, from single-celled organisms to the largest animals on earth. It has long been known that models with simple interaction rules can reproduce qualitative features of this complex behaviour. But determining whether these models accurately capture the biology requires data from real animals, which has historically been difficult to obtain. Here, we report three-dimensional, time-resolved measurements of the positions, velocities, and accelerations of individual insects in laboratory swarms of the midge Chironomus riparius. Even though the swarms do not show an overall polarisation, we find statistical evidence for local clusters of correlated motion. We also show that the swarms display an effective large-scale potential that keeps individuals bound together, and we characterize the shape of this potential. Our results provide quantitative data against which the emergent characteristics of animal aggregation models can be benchmarked.

Inertial waves driven by differential rotation in a planetary geometry

Dynamics occurring in the Earths outer core involve convection, dynamo action, geomagnetic reversals, and the effects of rapid rotation, among other processes. Inertial waves are known to arise in rotating fluids, and their presence in the core has been previously argued using seismological data (Aldridge and Lumb 1987). They may also be involved in flows affecting the geodynamo. We report experimental observations of inertial wave modes in an Earth-like geometry: laboratory spherical Couette flow with an aspect ratio 0.33, using liquid sodium as the working fluid. Inertial modes are detected via magnetic induction and show good agreement with theoretical predictions in frequency, wavenumber, and magnetic induction structure. Our findings imply that linear wave behavior can dominate the dynamics even in turbulent flows with large Reynolds number Re, where nonlinear behaviors might be expected (here Re ∼ 107). We present evidence that strong differential rotation excites the modes via over-reflection. Earths inner core may also super-rotate and thereby excite inertial modes in the same way. Zonal flows in the core, likely to have higher speeds than the super-rotation, may be a stronger source for exciting inertial modes in the Earth.

Searching for effective forces in laboratory insect swarms

Collective animal behaviour is often modeled by systems of agents that interact via effective social forces, including short-range repulsion and long-range attraction. We search for evidence of such effective forces by studying laboratory swarms of the flying midge Chironomus riparius. Using multi-camera stereoimaging and particle-tracking techniques, we record three-dimensional trajectories for all the individuals in the swarm. Acceleration measurements show a clear short-range repulsion, which we confirm by considering the spatial statistics of the midges, but no conclusive long-range interactions. Measurements of the mean free path of the insects also suggest that individuals are on average very weakly coupled, but that they are also tightly bound to the swarm itself. Our results therefore suggest that some attractive interaction maintains cohesion of the swarms, but that this interaction is not as simple as an attraction to nearest neighbours.

Onset of three-dimensionality in electromagnetically driven thin-layer flows

Two-dimensional fluid flow is often approximated in the laboratory with thin electromagnetically forced fluid layers. The faithfulness of such an experimental model must be considered carefully, however, because the physical world is inherently three-dimensional. By adapting an analysis technique developed for oceanographic data, we divide velocity measurements from a thin-layer flow into two components: one that is purely two-dimensional and another that accounts for all out-of-plane flow. We examine the two- and three-dimensional components separately, finding that motion in thin-layer flows is nearly two-dimensional at low Reynolds numbers, but that out-of-plane flow grows quickly above a critical Reynolds number. This onset is likely due to a shear instability.

Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment

Much of the drama and complexity of fluid flow occurs because its governing equations lack unique solutions. The observed behavior depends on the stability of the multitude of solutions, which can change with the experimental parameters. Instabilities cause sudden global shifts in behavior. We have developed a low-cost experiment to study a classical fluid instability. By using an electromagnetic technique, students drive Kolmogorov flow in a thin fluid layer and measure it quantitatively with a webcam. They extract positions and velocities from movies of the flow using Lagrangian particle tracking and compare their measurements to several theoretical predictions, including the effect of the drive current, the spatial structure of the flow, and the parameters at which instability occurs. The experiment can be tailored to undergraduates at any level or to graduate students by appropriate emphasis on the physical phenomena and the sophisticated mathematics that govern them.

Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence

Using a recently developed filtering technique, we study the spatiotemporal properties of the scale-to-scale fluxes of energy and enstrophy in a weakly turbulent experimental quasi-two-dimensional flow. Although these spectral properties vary in time and space, we show that they persist along the Lagrangian trajectories of fluid elements for times that can be nearly as long as the correlation time of the velocity field itself. Additionally, we show that at small scales, the spectral energy flux persists longest for fluid elements in strongly hyperbolic regions of the flow, whereas at large scales it persists in strongly elliptic regions.

Ultrasound Velocity Measurement in a Liquid Metal Electrode

A growing number of electrochemical technologies depend on fluid flow, and often that fluid is opaque. Measuring the flow of an opaque fluid is inherently more difficult than measuring the flow of a transparent fluid, since optical methods are not applicable. Ultrasound can be used to measure the velocity of an opaque fluid, not only at isolated points, but at hundreds or thousands of points arrayed along lines, with good temporal resolution. When applied to a liquid metal electrode, ultrasound velocimetry involves additional challenges: high temperature, chemical activity, and electrical conductivity. Here we describe the experimental apparatus and methods that overcome these challenges and allow the measurement of flow in a liquid metal electrode, as it conducts current, at operating temperature. Temperature is regulated within ±2 °C using a Proportional-Integral-Derivative (PID) controller that powers a custom-built furnace. Chemical activity is managed by choosing vessel materials carefully and enclosing the experimental setup in an argon-filled glovebox. Finally, unintended electrical paths are carefully prevented. An automated system logs control settings and experimental measurements, using hardware trigger signals to synchronize devices. This apparatus and these methods can produce measurements that are impossible with other techniques, and allow optimization and control of electrochemical technologies like liquid metal batteries.

Mechanisms driving shape distortion in two-dimensional flow

In order to elucidate the physical processes governing the evolution of material areas in complex flow, we study the shape dynamics of three-point Lagrangian clusters in an experimental quasi–two-dimensional flow. By comparing our measurements with simulations of triangles evolving purely diffusively, we show that the path taken by the mean triangle shape through a suitably defined phase space is indicative of the underlying flow dynamics. We demonstrate the existence of organizing curves in shape space for the evolution of triangles with different initial shapes. Our results suggest a detailed, multi-step process governing the shape dynamics of clusters in complex flow.

Driven inertial waves in spherical Couette flow

Dynamo action in the cores of planets and stars gives rise to their magnetic fields. We explore spherical Couette flows in liquid sodium as a laboratory model of the Earth’s core. Below, we image various spatiotemporal magnetic-field modes present in spherical Couette flows. Our apparatus is comprised of two independently driven rotating spheres, radii 20 and 60 cm, with sodium filling the gap between them Fig. 1 . We apply a B0=50 G axial magnetic field from external magnets and image the resulting induced magnetic field. As the Lundquist number S= B0l * 2 0 −1/2 where l is a characteristic length scale, is the magnetic diffusivity, and is the density is small S=0.7 , the magnetic field is a passive probe of the internal flows. Data from an array of 21 Hall probes along a meridian M1. . .M21 , plus four more distributed along the equator E1. . .E4 , are used to characterize the induced magnetic field exiting the outer sphere. We have projected the resulting data onto a basis of spherical harmonics and used that projection to produce the magneticfield images shown Fig. 2 . Patterns of Coriolis-restored inertial waves are present when the Ekman number, E = / 2 ol where is the kinematic viscosity and o is the angular frequency of the outer sphere , is small, and they depend on the rotation rate ratio of the inner and outer spheres i / o. All data shown here are for fixed o =30 Hz E=1.2 10−8 . The spectrogram at the left of Fig. 2 shows the frequency content of a time series of a single equatorial probe. These wave modes are likely to occur in the Earth’s outer core, but would largely be masked from view by the mantle. FIG. 1. Experimental setup.

Competing forces in liquid metal electrodes and batteries

Abstract Liquid metal batteries are proposed for low-cost grid scale energy storage. During their operation, solid intermetallic phases often form in the cathode and are known to limit the capacity of the cell. Fluid flow in the liquid electrodes can enhance mass transfer and reduce the formation of localized intermetallics, and fluid flow can be promoted by careful choice of the locations and topology of a batterys electrical connections. In this context we study four phenomena that drive flow: Rayleigh-Benard convection, internally heated convection, electro-vortex flow, and swirl flow, in both experiment and simulation. In experiments, we use ultrasound Doppler velocimetry (UDV) to measure the flow in a eutectic PbBi electrode at 160 °C and subject to all four phenomena. In numerical simulations, we isolate the phenomena and simulate each separately using OpenFOAM. Comparing simulated velocities to experiments via a UDV beam model, we find that all four phenomena can enhance mass transfer in LMBs. We explain the flow direction, describe how the phenomena interact, and propose dimensionless numbers for estimating their mutual relevance. A brief discussion of electrical connections summarizes the engineering implications of our work.