Turbulent Flow Around an Oscillating Body in Superfluid Helium: Dissipation Characteristics of the Nonlinear Regime

By examining the resonance curves of an oscillator submerged in superfluid liquid helium, it is found that their shape is affected by two distinct dissipation regimes when the amplitude is large enough to generate turbulence in the liquid. In a resonance curve, the central part close to resonance, may be in a turbulent regime, but the response is of much lower amplitude away from the resonance frequency, so that the oscillation can still be in the linear regime for frequencies not exactly at resonance. This introduces an ambiguity in estimating the inverse quality factor Q ^?1 of the oscillator. By analyzing experimental data we consider a way of matching the two ways of estimating Q ^?1 and use the information to evaluate the frictional force as a function of velocity in a silicon paddle oscillator generating turbulence in the superfluid.     

Stability of Laminar and Turbulent Flow of Superfluid 4He at mK Temperatures Around an Oscillating Microsphere

The flow of superfluid helium around a vibrating microsphere is investigated at temperatures between 1 K and 25 mK. At small oscillation amplitudes pure potential flow is observed, the linear drag force on the sphere being determined only by ballistic quasiparticle scattering below 0.7 K with phonons contributing exclusively below 0.5 K. At larger oscillation amplitudes a strongly nonlinear drag force gives evidence of stable turbulent flow if at least 0.6 pW are transferred from the sphere to the turbulent superfluid. In an intermediate range of amplitudes (or driving forces) both flow patterns are unstable and intermittent switching between both is observed below 0.5 K. We have recorded time series of this switching phenomenon at constant drives and temperatures lasting up to 36 hours. We have made a statistical analysis of the times series by means of reliability theory. The lifetime of the turbulent phases grows with increasing drive and diverges at a critical value (or at least becomes unmeasurably long). Stability of the laminar phases in the intermediate regime depends on the excess velocity of the sphere above the critical velocity. Metastable laminar phases are observed above the critical velocity having a mean lifetime limited to 25 minutes by natural background radioactivity which occasionally produces local vorticity due to ionization of the liquid. Finally, it is suggested that the breakdown of potential flow belongs to the class of “system failure” experiments which is well known in reliability testing and whose statistical properties are described by extreme-value theory. PACS numbers: 67.40.Vs, 47.27.Cn.     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

Turbulent flow formation in a spherical layer at a variable velocity of rotation of the outer spherical boundary

Transitions to turbulent flow regimes in a layer of a viscous incompressible fluid confined between counterrotating spherical boundaries have been experimentally studied in the case of periodic variations in the outer sphere rotation velocity at a constant velocity of the inner sphere. A periodic flow regime formed during the rotation of spherical boundaries at constant velocities in the opposite direction is under consideration. The effect of the amplitude and frequency of modulation of the velocity of outer sphere on the transition from this regime to chaos has been determined. Based on the results of flow visualization and flow velocity measurements by the laser Doppler anemometry technique, it is shown that turbulent flows with spatiotemporal intermittency can be formed in the spherical layer.     

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

No Heading We have measured responses of vibrating wire resonators in superfluid ⁴He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.PACS numbers: 67.40 Vs, 67.40 Pm     

Measurements of Turbulence Onset and Dissipation in Superfluid Helium with a Silicon Double Paddle Oscillator

We have studied experimentally the response of a silicon single crystal double paddle oscillator submerged in superfluid helium from the lambda point to 1.55 K. Measuring the resonance frequency and dissipation on three modes of this high Q system allows us to study the dissipation at the onset of turbulence in the flow around the paddle. The critical velocity V _c for turbulence onset decreases with temperature. If we use the density of the normal component of the superfluid to obtain a Reynolds number Re associated with V _c we find a value which is largely temperature independent. This result is different from the behavior previously found by other authors below 1 K, where the quantized vorticity (extrinsic nucleation) is observed at velocities more than an order of magnitude greater. In our temperature range, we conclude that the transition is governed by the normal fraction acting as a classical fluid. The laminar regime shows a dissipation that is proportional to the viscous drag calculated by well known formulas for an object oscillating in a liquid. We also find a decrease in resonance frequency in the turbulent regime which is clearly observed but hard to reproduce from run to run.     

Observation of Laminar and Turbulent Flow in Superfluid 4He using a Vibrating Wire

No Heading We have investigated the laminar and the turbulent flow in superfluid ⁴He using a vibrating wire made of thin NbTi ( 2.5 m). The wire velocity as a function of applied force has shown a large hysteresis at the first cooling from normal fluid to the superfluid state. But after a couple of increasing and decreasing wire velocity we have found that the hysteresis vanished and the laminar and the turbulent flow are clearly separated at a critical velocity. The wire moving just after the first cooling must be influenced by remnant vortices nucleated through the superfluid transition. The appearance of the laminar flow below the critical velocity suggests that vortex strings on the wire seem to be selected as suitable sizes by a vibrating flow at higher velocities. We also measured the velocity dependence after immersing the wire directly into the superfluid and found that the laminar region expands up to a velocity much higher than the critical velocity observed above. This result indicates that remnant vortices are considerably reduced by the immersing method.PACS numbers: 67.40.Vs, 47.27.Cn     

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.     

Hysteresis,Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

We have been studying the behaviour of commercial quartz tuning forks immersed in superfluid ⁴He and driven at resonance. For one of the forks we have observed hysteresis and switching between linear and non-linear damping regimes at temperatures below 10 mK. We associate linear damping with pure potential flow around the prongs of the fork, and non-linear damping with the production of vortex lines in a turbulent regime. At appropriate prong velocities, we have observed metastability of both the linear and the turbulent flow states, and a region of intermittency where the flow switched back and forth between each state. For the same fork, we have also observed anomalous behaviour in the linear regime, with large excursions in both damping, resonant frequency, and the tip velocity as a function of driving force.     

History Dependence of Turbulence Generated by a Vibrating Wire in Superfluid 4He at 1.5 K

We report on the onset of turbulence in normal and superfluid ⁴He using several 13.5 μm diameter vibrating wire resonators placed in a cell, filtered from the surrounding helium bath. We measured the force-velocity characteristics of the wires in normal and superfluid helium over a velocity range up to several meters per second. The transition from laminar to turbulent behavior can be clearly identified. Surprisingly we find that, depending on the cooling history, turbulence in the superfluid does not always develop fully.     

Interaction of Weakly Nonlinear Second Sound Waves with a Vortex Tangle in Helium II

We generalize the analysis of second sound nonlinear waves to include the case in which a turbulent tangle of superfluid vortices is present in the flow. In the limit of weakly nonlinear perturbations the analysis reduces to examining the effect of friction arising from a given vortex tangle on a propagating wave, so that the considered model describes temperature waves propagating in a background of constant quantized vorticity. The obtained analytical solution yields a simple criterion showing that a localized disturbance develops into the temperature discontinuity provided the gradient of the initial disturbance exceeds a critical value; the latter is found as a function of temperature and superfluid vortex line density.     

Can Superfluid Vortex Lines Excite Normal Fluid Turbulence in 4He?

When helium II is made turbulent the superfluid component forms a dense tangle of quantized vortex lines which can be easily detected experimentally using the second sound technique. On the contrary little is known about the normal fluid component: on the experimental side progress has been hindered by the lack of simple flow visualization, and on the theoretical side attention has been concentrated on the effect that a given normal flow has on the superfluid vortices, not vice-versa. Attempting to fill this gap, we discuss results of recent calculations in which we find that normal fluid vorticity structures can be generated by superfluid vortices. In particular we address the issue of whether the superfluid vortices can make the normal fluid turbulent.     

Scattering properties of an impedance-matched, ideal, homogeneous, causal "left-handed" sphere

The plane-wave scattering properties of a sphere of material having an ideal, homogeneous, and causal permittivity epsilon(f), and permeability mu(f) were investigated through detailed three-dimensional finite-difference time-domain, method-of-moments, and series-solution simulations. A Lorentzian functional form was chosen for epsilon(f) and mu( f), as it yields causal responses and allows us to study the physics of the left-handed-medium (LHM) regime. Our interest lies mainly in the frequency range where negative refraction [Re(n) < 0] is observed. We found that when operating in the LHM regime, an impedance-matched sphere responds with scattering features strikingly different from those found in ordinary materials. In particular, we found zero back-scattering and forward scattering that exceeds that of a metal sphere of similar size. The equality of E- and H-plane patterns was proved analytically and numerically, and the possibility of internal subwavelength focusing with a zero index sphere is also reported.     

Experimental investigation of heat transfer through porous media in superfluid helium

An experimental investigation of heat transfer through porous media in superfluid helium has been conducted in the framework of the development of porous electrical insulations for superconducting magnet cables cooled by superfluid helium. Several types of porous media with different characteristics were tested and, in particular, samples with pore size diameters of 0.1 μm, 1 μm, 2 μm, 10 μm and 20 μm. Temperature and pressure were measured between an insulating inner bath and the cryostat bath, communicating only through the porous medium. The cryostat bath is held constant all along the measurement and, for each sample, the tests are performed for bath temperature from 1.4 K to 2.1 K with 0.1 K increment. Depending on the porous medium average pore size diameter, different flow regimes are observed: for porous media with a pore diameter of 0.1 and 1 μm, only the Landau regime is observed whereas for porous media with a pore diameter of 2 μm, we observed the Landau regime and the Gorter-Mellink regime. For samples with a pore diameter of 10 and 20 μm, measurements only permitted to detect the Gorter-Mellink regime. In the laminar regime, the permeability of the samples was determined and it was found that the permeability is constant for bath temperature above 1.9 K whereas it increases as the bath temperature decreases from 1.8 K to 1.4 K. For samples with a pore size diameter of 10 and 20 μm, measurement permits only to observe the turbulent regime and the analysis exhibits a constant average tortuosity for each samples, independently of the bath temperature.     

Transition to Quantum Turbulence Generated by Thin Vibrating Wires in Superfluid 4He

We report the turbulent transition in superfluid ⁴He generated by a vibrating wire as a function of its thickness. The response of a vibrating wire with a 3 μm diameter in superfluid ⁴He at 1.2 K reveals a hysteresis at the turbulent transition between an up sweep and a down sweep of driving force, while no hysteresis appears for wires with a thickness larger than 4.7 μm diameter. These results indicate that the 3 μm wire is efficient for reducing the number of vortex lines attached to it. A cover box and slow cooling also prevent vortex lines from attaching to a wire, resulting in a vortex-free vibrating wire. The effective mass of the vortex-free vibrating wire is almost constant in a wide range of velocities up to 400 mm/s; however, the wire density estimated from the resonance frequency is a half of the expected value of wire material, suggesting that a wire mass becomes lighter or a wire diameter becomes larger in the superfluid effectively.     

Propagation of a Turbulent Fronts in Quantum Fluids

This paper is part of our series of studies on the dynamics of inhomogeneous vortex tangles. We consider here the motion of turbulent fronts. There are a number of experiments in which the authors observed the development of superfluid turbulence in quantum fluids in the form of propagating fronts. There are also experiments in which the authors observed the appearance of the moving structures (“plugs”), regions with the high vortex line density in the counterflowing superfluid helium. These phenomena have both scientific and applied interest. For example, the possibility of spontaneous formation of “plugs” can radically affect heat transfer in channels with superfluid helium, which is used as a refrigerant for cooling superconducting devices. There are a number of hypotheses for how the fronts and “plugs” appear and what their dynamics are, in particular, how to evaluate the velocity of propagations. In the present work we elaborate the approach of the combustion-like propagation of the superfluid turbulent domain. A key assumption is that propagation of the front occurs in diffusion manner of diffusion with the source of the vortices behind the front, just like the combustion process. Additionally, there is a drift motion of the vortex tangles due to polarization of the vortex loops. Interplay of these effects determines the speed of the turbulent front propagation. We performed a comparison with the experimental data.     

Properties of slowly rotating helium II and the superfluidity of pulsars

Results of an experimental study of superfluid He II properties in the non-stationary rotation regime are presented. On the basis of an analysis of the experimental data it is shown that the behavior of pulsar rotation (sudden jumps in speed, long relaxation processes) can be explained on the basis of the assumption of a neutron superfluid in pulsars.Institute of Physics of the Academy of Sciences of the Georgian SSR     

The Dynamic Texture of Superfluid 3He-B at Very Low Temperatures and in High Magnetic Fields

No Heading We report experiments using a pair of crossed vibrating wire resonators (VWRs) in the B phase of superfluid ³He in the zero temperature ballistic limit and in magnetic fields up to the B to A phase transition field of 340 mT. The VWRs are sensitive mechanical probes of energy gaps, textures and turbulent flow. In high magnetic fields the energy gap is no longer isotropic but significantly distorted, and the damping measured by the VWRs increases. With the crossed pair, we find that we can reduce the damping measured by one VWR when we increase the drive on the other one. We suggest that the reduction arises from the orientation of the surrounding texture by superflow and the screening of quasiparticles by the creation of superfluid turbulence.PACS numbers: 67.57.Fg, 67.57.Hi.     

Time-of-Flight Experiments of Vortex Rings Propagating from Turbulent Region of Superfluid 4He at High Temperature

We report the time-of-flight of quantized vortex rings generated by a vibrating wire in superfluid ⁴He which contains normal fluid component. A cover box of vibrating wires and slow cooling of superfluid reduce the number of vortices attached to wire surfaces, enabling us to study vortex rings propagating from a turbulent region. Using two vibrating wires as a generator and a detector of vortices, the time-of-flight of vortices propagating a distance of 0.88 mm was measured at 1.25 K. We find that the time-of-flights distribute from 0.06 s to 27.4 s, much larger than the lifetimes of circular vortex rings limited in the size of a generator amplitude. These results imply that large vortex rings with non-circular shape or vortex tangles are created by the generator, propagating slowly and colliding with the detector before complete disappearance.