The Influence of Acoustic Emission on the Onset of Turbulent Flow in He II

An experimental study is carried out on the influence of acoustic emission on the development of turbulent flow in He II at temperature 370 mK and at various pressures, from the saturated vapor pressure to that of ⁴He crystallization. The experimental technique of oscillating quartz tuning fork was applied for simultaneously exciting both superfluid flow, near the oscillating tuning fork prongs, and the acoustic wave emission. The flow rate of He II and the amplitude of the radiated acoustic waves were driven by the fork prongs, excited by voltage oscillations. Furthermore, the power of an acoustic wave depends on the density and sound velocity in He II as ρ/c ⁵, which in turn depends on the pressure. This allowed to measure the influence of the amplitude of acoustic emission on the flow in He II. It has been shown that the occurrence of acoustic radiation by tuning fork leads to an increased flow velocity for the beginning of nonlinear flow regime.     

On the Visualization of Thermal Counterflow of He II Past a Circular Cylinder

Thermal counterflow of superfluid ⁴He is investigated experimentally in the proximity of a 3 mm diameter cylinder by analyzing the motions of micrometer-sized solid particles, focusing especially on the occurrence of macroscopic vortices. The influence of heating an opaque brass cylinder by the light source is studied, as thermal counterflow is generated from its surface, and compared with the case of a transparent plexiglass cylinder of the same size. Additionally, we report our preliminary investigation of vertical counterflow around the transparent cylinder. We find that care should be taken when applying conventional visualization techniques—particle image velocimetry and particle tracking velocimetry—as spurious vortical structures might be identified in quantum flows displaying two-fluid behavior.     

Questions Related to the Oscillatory Flow of He II through a Grid at Low Temperatures

No Heading The flow of pure He II at low temperatures and a range of pressures is probed using an electrostatically-driven oscillating grid. With increasing oscillation amplitude, a (history dependent) first threshold is reached where the initially pure superflow abruptly changes: the resonant frequency decreases and the response becomes strongly nonlinear, attributable to quantized vortices responding to the motion of the grid so as to increase its effective mass without additional damping. On further increase of oscillation amplitude a second threshold is reached, probably marking the onset of superfluid turbulence. The increase in effective mass is believed to be due to a boundary layer of vortex loops that can evolve into turbulent flow at the second threshold. Open questions and problems for future research are formulated.     

Decay of Counterflow Quantum Turbulence in Superfluid 4He

We have simulated the decay of thermal counterflow quantum turbulence from a statistically steady state at T=1.9 K, with the assumption that the normal fluid is at rest during the decay. The results are consistent with the predictions of the Vinen equation (in essence the vortex line density decays as t ^?1). For the statistically steady state, we determine the parameter c ₂, which connects the curvature of the vortex lines and the mean separation of vortices. A formula connecting the parameter χ ₂ of the Vinen equation with c ₂ is shown to agree with the results of the simulations. Disagreement with experiment is discussed briefly.     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Vortex Generation in Superfluid 3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid ³He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

He II flow in a narrow slit

After a brief review of the relevant He II-flow equations, we report results of our investigations of He II counterflow in the presence of net liquid flow, using a narrow-plane parallel slit. Measurements of the liquid temperature inside the flow channel indicate that with counterflow, there is always some supercomponent vorticity present at least along a part of the channel. With higher velocities, a transition from laminar to turbulent normal-component flow was observed.On leave from Shanghai Institute of Technical Physics, Academia Sinica, 420 Zong Shan Bei Ji Road, Shanghai, People's Republic of China.     

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     

Interaction of a macroscopic probe with liquid He II

It is shown that the results of the Pellam Rayleigh disk experiment are accounted for by the thermohydrodynamic equations when the relative velocity between the normal and superfluid components is included and the probe acts as an isothermal boundary.Supported in part by a Themis contract from DoD to the Cryogenics Center.     

The transverse acoustic impedance of He II under pressure

The transverse acoustic impedanceZ of bulk liquid He II has been measured at a frequency of 20.5 MHz at temperatures from 30 mK to 2.2 K, at pressures up to 25 bar. Results at SVP have been published previously. The impedance was found from the temperature dependence of the quality factor and resonant frequency of an AT-cut quartz crystal resonator immersed in the liquid. Below 0.5 K the crystal also acts as a microbalance and a change in frequency associated with a loss peak at 10 bar is interpreted as the localization of a second layer of⁴He atoms. At higher pressures no further growth of solid⁴He on the crystal surfaces was observed. Between 0.6 and 1.6 K we interpretZ as being primarily due to rotons and we have determined the roton relaxation time at all pressures as =(8.5±0.4)×10^–14 T ^–1/3 exp (/kT) sec, using the theory by Roberts and Donnelly, where is the roton energy gap. The transition from hydrodynamic viscous behavior to the nonhydrodynamic regime was investigated in detail. The data were consistent with completely diffuse scattering of the rotons at the gold-plated electrodes on the crystal. Measurements near the -point, forT/T >0.99, were analyzed to determine the superfluid healing length asa(T)=(0.10±0.02)^–2/3 nm, where =1–T/T , at all pressures. An analysis of data for 0.1 gave a slightly larger value, equivalent toa(T)=(0.13±0.02)^–2/3 nm. Below 1.6 K the excess normal fluid density associated with the healing layer is similar to that found in thin films.     

Comparison of cavitation flows in He I and He II

This paper describes some of the results of an experimental study on the cavitation phenomena in He II and He I by the visualization and the measurements of the pressure and the temperature. The cavitation flow is generated in liquid helium driven by a bellows pump in the downstream region of the throat in a Venturi channel with a rectangular cross section. It is found that there are some definite differences in the appearance of cavitation between He I and He II flows, and that the λ-phase transition from He I to He II is sometimes induced because of the temperature drop in cavitating He I flow. In addition, the expression for the relation between the amount of the temperature drop induced by cavitation and the void fraction was described, which was found to be qualitatively in good agreement with the experimental result.     

Switching Phenomena between Laminar and Turbulent Flows of Superfluid 4He Generated by a Vibrating Wire

We have investigated the turbulence transition of the superfluid ⁴He flow generated by a vibrating wire. For a 1.2-kHz vibrating wire, we observed intermittent switchings between laminar and turbulent flows. The switching rate decreases with increasing temperature above 100 mK, until no occurrence of the switchings at 350 mK. For a 2.4-kHz vibrating wire, we find that the switching rate is much lower than that of the 1.2-kHz vibrating wire even at low temperatures. This result indicates that a mechanism causing the switchings is influenced by the temperature and the oscillation frequency of the superfluid flow.     

Observation of a new flow state in He II counterflow

We report the observation of a new flow state for He II in thermal counterflow. The new state has been observed only in metal flow tubes, experiments with similar size glass tubes showing no trace of it whatever. Furthermore, the new state exists only over a finite range of heat currents and can be induced from the laminar flow region only by the application of a mechanical shock to the cryostat. For certain temperatures the new state can couple with the Vinen state of mutual friction, producing sustained oscillations in the temperature difference between the tube ends. It is speculated that this new state is due to a type of flow in the normal fluid which has recently been proposed for classical fluids, spiral flow.     

Coalescence of Levitated He II Drops

We describe experiments to study the coalescence of He II drops levitated in a magnetic trap. Using a high speed CCD camera, we have produced movies of drops coalescing at temperatures as low as 0.7 K. We examine some interesting features of the motion during and following coalescence.     

Anomalous Trajectories of H2 Solid Particles Observed Near a Sphere Oscillating in Superfluid Turbulent 4He

Using a relatively low cost apparatus, consisting of a glass dewar and a digital camera capable of taking images at 240 frames per second we have observed trajectories of frozen H₂ particles which follow the flow of liquid helium below 2 K, around a sphere oscillating at 38 Hz. In some of the images the motion is compatible with laminar flow, while at high amplitudes, where we can reach Reynolds numbers of a few thousand in the normal component, the flow is clearly turbulent. In some of the videos taken we find particles being suddenly accelerated to several times the velocity of the oscillating sphere.     

Decay of the Turbulent Cascade of Capillary Waves on the Charged Surface of Liquid Hyrdrogen

No Heading We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that the decay begins from the high frequency spectral domains of the surface oscillations and is of a quasi-adiabatic character. The characteristic relaxation time of the whole turbulent cascade is close to the viscous damping time for capillary waves of frequency equal to the driving frequency.PACS numbers: 47.27.–i, 47.25.+i     

Boiling phenomena in pressurized He II confined to a channel

Results from an experiment to study boiling phenomena in a channel containing pressurized He II are presented as a function of temperature, pressure and orientation with respect to gravity. The experimental apparatus is made of glass to allow visual observations and high-speed motion pictures to be made of boiling events. Visual data are combined with temperature and pressure measurements to characterize the boiling behaviour and to group the phenomena into boiling regimes. Results are presented in the form of heat transfer regime maps, temperature and pressure traces during boiling, and sketches of the helium vapour and liquid in the channel. One unexpected result is the observation of a macroscopic region of He I with He II below and vapour above. The two interfaces are clearly visible. Another unanticipated result is that the boiling phenomena are often characterized by the periodic production, growth and collapse of vapour even though the heat input is constant.     

Frequency Characteristics of a Quartz Tuning Fork Immersed in He II

The effect of dissipation on frequency characteristics of tuning forks was measured, the dissipation being induced by acoustic radiation of different wavelengths, excited by tuning forks. The tuning forks have been immersed in the superfluid helium. The fork resonance frequencies 32, 77 and 99 kHz have been measured at T=370 mK in the pressure range between SVP and 24.9 atm. Most of the tuning forks have been studied in a commercial can. It is found that at wavelength λ>0.6 cm the frequency dependence is determined by the relationship between density and pressure. It is established that a decrease in wavelength enhances influence of the acoustic radiation on the fork oscillation frequency. In the case where the sound wavelength is equal to the can internal diameter an acoustic resonance occurs. The frequency reaches values higher than the fork frequency in vacuum. Further reduction of the sound wavelength leads to the situation when the resonant frequency is similar to the frequency at long wavelengths.