Fluid Dynamics Experiments for Planetary Interiors.

Understanding fluid flows in planetary cores and subsurface oceans, as well as their signatures in available observational data (gravity, magnetism, rotation, etc.), is a tremendous interdisciplinary challenge. In particular, it requires understanding the fundamental fluid dynamics involving turbulence and rotation at typical scales well beyond our day-to-day experience. To do so, laboratory experiments are fully complementary to numerical simulations, especially in systematically exploring extreme flow regimes for long duration. In this review article, we present some illustrative examples where experimental approaches, complemented by theoretical and numerical studies, have been key for a better understanding of planetary interior flows driven by some type of mechanical forcing. We successively address the dynamics of flows driven by precession, by libration, by differential rotation, and by boundary topography.

Reconnection scaling in quantum fluids.

Fundamental to classical and quantum vortices, superconductors, magnetic flux tubes, liquid crystals, cosmic strings, and DNA is the phenomenon of reconnection of line-like singularities. We visualize reconnection of quantum vortices in superfluid 4He, using submicrometer frozen air tracers. Compared with previous work, the fluid was almost at rest, leading to fewer, straighter, and slower-moving vortices. For distances that are large compared with vortex diameter but small compared with those from other nonparticipating vortices and solid boundaries (called here the intermediate asymptotic region), we find a robust 1/2-power scaling of the intervortex separation with time and characterize the influence of the intervortex angle on the evolution of the recoiling vortices. The agreement of the experimental data with the analytical and numerical models suggests that the dynamics of reconnection of long straight vortices can be described by self-similar solutions of the local induction approximation or Biot-Savart equations. Reconnection dynamics for straight vortices in the intermediate asymptotic region are substantially different from those in a vortex tangle or on distances of the order of the vortex diameter.

Dynamics of analog logic-gate networks for machine learning.

We describe the continuous-time dynamics of networks implemented on Field Programable Gate Arrays (FPGAs). The networks can perform Boolean operations when the FPGA is in the clocked (digital) mode; however, we run the programed FPGA in the unclocked (analog) mode. Our motivation is to use these FPGA networks as ultrafast machine-learning processors, using the technique of reservoir computing. We study both the undriven dynamics and the input response of these networks as we vary network design parameters, and we relate the dynamics to accuracy on two machine-learning tasks.

Sub-micron solid air tracers for quantum vortices and liquid helium flows.

The dynamics of quantized vortices in superfluids has received increased attention recently because of novel techniques developed to visualize them directly. One of these techniques [G. P. Bewley et al., Nature 441, 588 (2006)] visualized quantized vortices and their reconnections in superfluid flows of (4)He by using solid hydrogen tracers of micron-size or larger. The present work improves upon the previous technique by using substantially smaller particles created by injecting atmospheric air diluted in helium gas. These smaller particles are detectable thanks to the higher index of refraction of nitrogen compared to hydrogen and thanks to an improved visualization setup. The optical counting estimate, which agrees with terminal velocity estimates, suggests that the tracer diameter is typically 400 ± 200 nm and could be as small as 200 nm; being smaller, but not so small as to be influenced by thermal motion, the particles get trapped on the vortices faster, perturb the vortices less, possess smaller Stokes drag, and stay trapped on fast-moving vortices, as also on vortices generated closer to the superfluid transition temperature. Unlike the past, the ability to create particles in the superfluid state directly (instead of creating them above the λ-point and cooling the fluid subsequently), ensures greater temperature stability for longer periods, and enables the tracking of long and isolated vortices. These advantages have also led to the direct visualization of Kelvin waves. The use of other seed gases could lead to the visualization of even smaller tracers for quantized vortices. We discuss the visualization setup and provide suggestions for further improvement.

Nanoparticle dispersion in superfluid helium.

Cryogenic fluid flows including liquid nitrogen and superfluid helium are a rich environment for novel scientific discovery. Flows can be measured optically and dynamically when faithful tracer particles are dispersed in the liquid. We present a reliable technique for dispersing commercially available fluorescent nanoparticles into cryogenic fluids using ultrasound. Five types of fluorescent nanoparticles ranging in size from 5 nm to 1 µm were imaged in liquid nitrogen and superfluid helium, and were tracked at frame rates up to 100 Hz.

Visualization of two-fluid flows of superfluid helium-4.

Cryogenic flow visualization techniques have been proved in recent years to be a very powerful experimental method to study superfluid turbulence. Micron-sized solid particles and metastable helium molecules are specifically being used to investigate in detail the dynamics of quantum flows. These studies belong to a well-established, interdisciplinary line of inquiry that focuses on the deeper understanding of turbulence, one of the open problem of modern physics, relevant to many research fields, ranging from fluid mechanics to cosmology. Progress made to date is discussed, to highlight its relevance to a wider scientific community, and future directions are outlined. The latter include, e.g., detailed studies of normal-fluid turbulence, dissipative mechanisms, and unsteady/oscillatory flows.

Direct observation of Kelvin waves excited by quantized vortex reconnection.

Quantized vortices are key features of quantum fluids such as superfluid helium and Bose-Einstein condensates. The reconnection of quantized vortices and subsequent emission of Kelvin waves along the vortices are thought to be central to dissipation in such systems. By visualizing the motion of submicron particles dispersed in superfluid (4)He, we have directly observed the emission of Kelvin waves from quantized vortex reconnection. We characterize one event in detail, using dimensionless similarity coordinates, and compare it with several theories. Finally, we give evidence for other examples of wavelike behavior in our system.

Liquid nitrogen in fluid dynamics: visualization and velocimetry using frozen particles.

High-Reynolds-number flows are common both in nature and industrial applications, but are difficult to attain in laboratory settings using standard test fluids such as air and water. To extend the Reynolds number range, water and air have been replaced at times by low-viscosity fluids such as pressurized air, sulfur hexafluoride, and cryogenic nitrogen gas, as well as liquid and gaseous helium. With a few exceptions, liquid nitrogen has been neglected despite the fact that it has a kinematic viscosity of about a fifth of that of water at room temperature. We explore the use of liquid nitrogen here. In particular, we study the use of frozen particles for flow visualization and velocimetry in liquid nitrogen. We create particles in situ by injecting a gaseous mixture of room-temperature nitrogen and an additional seeding gas into the flow. We present a systematic study of potential seeding gases to determine which create particles with the best fidelity and optical properties. The technique has proven capable of producing sub-micrometer sized tracers that allow particle tracking and particle image velocimetry. We review possible high-Reynolds-number experiments using this technique, and discuss the merits and challenges of using liquid nitrogen as a test fluid.

Excitation of inertial modes in an experimental spherical Couette flow.

Spherical Couette flow (flow between concentric rotating spheres) is one of flows under consideration for the laboratory magnetic dynamos. Recent experiments have shown that such flows may excite Coriolis restored inertial modes. The present work aims to better understand the properties of the observed modes and the nature of their excitation. Using numerical solutions describing forced inertial modes of a uniformly rotating fluid inside a spherical shell, we first identify the observed oscillations of the Couette flow with nonaxisymmetric, retrograde, equatorially antisymmetric inertial modes, confirming first attempts using a full sphere model. Although the model has no differential rotation, identification is possible because a large fraction of the fluid in a spherical Couette flow rotates rigidly. From the observed sequence of the excited modes appearing when the inner sphere is slowed down by step, we identify a critical Rossby number associated with a given mode, below which it is excited. The matching between this critical number and the one derived from the phase velocity of the numerically computed modes shows that these modes are excited by an instability likely driven by the critical layer that develops in the shear layer, staying along the tangent cylinder of the inner sphere.

The Twente turbulent Taylor-Couette (T3C) facility: strongly turbulent (multiphase) flow between two independently rotating cylinders.

A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 × 10(6) with water as working fluid. With this Taylor-Couette system, the parameter space (Re(i), Re(o), η) extends to (2.0 × 10(6), ±1.4 × 10(6), 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.

Selection of inertial modes in spherical Couette flow.

Spherical Couette flow involves fluid sheared between concentric coaxially rotating spheres. Its scientific relevance lies not only in the simplicity of the system but also in its applicability to astrophysical objects such as atmospheres, oceans, and planetary cores. One common behavior in all rotating flows, including spherical Couette flow, is the presence of inertial modes, which are linear wave modes restored by the Coriolis force. Building on a previous identification of inertial modes in a laboratory spherical Couette cell, here we propose selection mechanisms to explain the presence of the particular modes we have observed. Mode selection depends on both amplification and damping. Our experimental observations are consistent with amplification and selection by over-reflection at a shear layer, and we would expect other spherical Couette devices to behave similarly. Damping effects, due in part to the presence of an inner sphere, add further constraints which are likely to play a role in mode selection in planetary atmospheres and cores, including the core of earth.

Boolean chaos.

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultrawide band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultrawide-band source of radio waves.

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 1/2, consistent with the self-similar evolution of the vortices.

Bubbly turbulent drag reduction is a boundary layer effect.

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4 x 10(5), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effect.

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.

Drag reduction in bubbly Taylor-Couette turbulence.

In Taylor-Couette flow the total energy dissipation rate and therefore the drag can be determined by measuring the torque on the system. We do so for Reynolds numbers between Re=7 x 10(4) and Re=10(6) after having injected (i) small bubbles (R=1 mm) up to a volume concentration of alpha=5% and (ii) buoyant particles (rhop/rhol=0.14) of comparable volume concentration. In case (i) we observe a crossover from little drag reduction at smaller Re to strong drag reduction up to 20% at Re=10(6). In case (ii) we observe at most little drag reduction throughout. Several theoretical models for bubbly drag reduction are discussed in view of our findings.