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.     

Acoustic Turbulence in Superfluid 4He

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid ⁴He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.     

Quantum Evaporation from Superfluid 4He

The quantum evaporation experiments of Brown and Wyatt ² have been re-analysed in the light of a recent measurement of the high-energy phonon spectrum created by a pulse-heated thin film ¹⁰ . Two sources of systematic error become significant at the level of the precision required by this new analysis: firstly, in the detector position which is recalibrated by using large-angle roton evaporation; and secondly, in the liquid height due to capillary action affecting the level-detectors. These effects have been included in an improved simulation of the experiment which has brought the angular dependence of the measured and theoretical phonon-atom evaporation results into agreement within the mechanical tolerances of the apparatus. The reanalysis suggests that the roton-atom evaporation probability increases with wave vector.     

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.     

Energy Spectrum of the Superfluid Velocity Made by Quantized Vortices in Two-Dimensional Quantum Turbulence

We discuss the configurations of vortices in two-dimensional quantum turbulence, studying energy spectrum of superfluid velocity and correlation functions with the distance between two vortices. We apply the above method to quantum turbulence described by Gross-Pitaevskii equation in Bose-Einstein condensates. We make two-dimensional quantum turbulence from many dark solitons through the dynamical instability. A dark soliton is unstable and decays into vortices in two- and three-dimensional systems. In our work, we propose a method of discriminating between the uncorrelated turbulence and the correlated turbulence. We decompose the energy spectrum into two terms, namely the self-energy spectrum E _self (k) made by individual vortices and the interactive energy spectrum E _int (k) made by interference of two vortices. The uncorrelated turbulence is defined as turbulence with E _int (k)?E _self (k), while the correlated turbulence is turbulence where E _int (k) is not much smaller than E _self (k). Our simulations show that in the decay of dark solitons, the vortices created consist of correlated pairs of opposite circulation vortices, leading to the correlated turbulence.     

The Wave-Vector Dependence of Quantum Evaporation from Superfluid 4He

Absolute measurements of the probability of quantum evaporation of atoms by rotons from the surface of superfluid ⁴ He are still problematic. However, it is possible to obtain information about the wave-vector dependence of the evaporation process by using a refined simulation ¹⁴ to interpret the experiments of Brown and Wyatt ¹² . Two theories (Guilleumas et al. ⁹ and Sobnack et al. ¹⁰ ) are compared with these experiments by incorporating their predictions for the quantum evaporation probability into a numerical simulation. Both theories over-estimate the probability of phonon-atom evaporation. For roton (R ⁺ –atom) evaporation, compared with a simulation that assumes all kinetically allowed events are equally probable, the theory of Guilleumas et al. does not significantly improve the agreement with experiment, and the theory of Sobnack et al. increases the discrepancy.     

Preliminary Measurements of Andreev Reflection of Quasiparticles by Turbulence in Superfluid 3He

We present preliminary measurements of Andreev scattering of quasiparticles from turbulence in the B-phase of superfluid ³ He-B. The turbulence is generated by a vibrating wire resonator driven above its pair-breaking critical velocity. The vortices intercept a beam of quasiparticles generated by a nearby black-body radiator. A substantial fraction of the incident quasiparticles are retro-reflected back into the radiator by Andreev scattering processes. The resulting temperature rise within the radiator provides a direct measurement of the flux of quasiparticles Andreev reflected. The technique provides a sensitive probe of superfluid turbulence in the ultra-low temperature regime.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

Observation of Remanent Vortices Attached to Rough Boundaries in Superfluid 4He

We report the study on remanent vortices attached to rough boundaries in superfluid ⁴He after the turbulent transition. We used 2.6 µm vibrating wires with smooth surfaces and rough surfaces, a cover box and slow cooling method, in order to investigate the effect of surface roughness on the condition and the number of vortices attached to a wire. The responses of the wire with smooth surfaces show large hysteresis at the turbulent transition. This result indicates that remanent vortices attached between the wire and surrounding boundaries cause turbulence. At first sweep of driving force of the wire with rough surfaces, we also observed hysteresis as large as the case of the smooth wire: at the other sweeps, however, small hysteresis was observed. These results indicate that once turbulence is generated at a wire velocity during first sweep, vortex lines newly attach between rough surfaces of the wire, which easily cause turbulence at a low wire velocity. Therefore, we conclude that a smooth wire can reduce the number of vortices attached to a wire.     

The Energy Dependence of Roton Quantum Evaporation from Superfluid 4He

We have measured the energy dependence of roton quantum evaporation. A transiently heated cavity filled with superfluid ⁴ He generates R⁺ and R^– rotons. The emitted rotons are collimated and arrive at the free liquid surface with a narrow range of incident angles. We detect two beams of evaporated atoms, one due to R⁺ rotons and the other due to R^– rotons. Our numerical simulation of roton and atom trajectories, using an evaporation probability of 1, yields two angular distributions of atom flux which are similar to our experimental results, but do have systematic differences which we attribute to the evaporation probability. The ratio of the observed signal to the computed value at each bolometer position gives the relative roton quantum evaporation probability as a function of roton energy. We find that this probability increases with roton energy, except perhaps for low energy R^– rotons. We compare these results with theoretical predictions.     

Decay of Quantized Vortices in Quantum Turbulence

The decay of quantized vortex line length in quantum turbulence at zero temperature is studied numerically by solving the Gross–Pitaevskii equation with a small-scale dissipation. The obtained decay of the vortex line length L is consistent with the L ∝ t ^−3/2 behavior which supports the Kolmogorov energy spectrum of quantum turbulence. The mechanism of the decay is discussed.     

Nonlinear Second Sound Waves and Acoustic Turbulence in Superfluid 4He

The preliminary results of an investigation of nonlinear second sound waves in a high quality resonator filled with superfluid ⁴He are presented and discussed. It is found that, for a sufficiently strong periodic driving force, a cascade of second sound waves is formed at multiple harmonics of the driving frequency over the extremely wide frequency range 1–100 kHz. It can be described by a power law A _ω =const.×ω ^−m , where the scaling index m≈1. These observation can be attributed to the formation of a Kolmogorov-like turbulent cascade in the system of second sound waves, accompanied by directed energy flux through the frequency scales. It manifests itself as a limiting of the amplitude of a standing wave, a distortion of the shape of the initially harmonic waves, and a reduction of the effective quality factor Q of the resonator.     

Propagation of Quantized Vortices Driven by an Oscillating Sphere in Superfluid 4He

We performed numerical simulation of quantum turbulence at 0 K generated from remnant vortices attached to an oscillating sphere. The remnant vortices are extended by the sphere motion and form a tangle with emitting vortex loops. As time passes, the length of vortices in a computational volume becomes statistically steady. We investigate in the statistical steady state the distribution of the length of vortex loops and anisotropy of their propagation direction caused by the sphere oscillation. The propagation direction of the emitted vortex loops is anisotropic along the oscillation direction of the sphere. The obtained results are consistent with results obtained in the experimental study using vibrating wires in superfluid ⁴He.     

Quantum Statistics of Three-Dimensional Vortex Filament in Superfluid 4He

The quantum statistics of three-dimensional vortex filament in superfluid ⁴ He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is in quantitative agreement with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the damped harmonic oscillator approximation.     

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.     

The Effect of Roton Backflow on Quantum Evaporation from Superfluid 4He

We investigate the effect of roton backflow on the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He at T=0 K by including backflow semi-phenomenologically in the form of a backflow potential in the theory of Sobnack et al. [M. B. Sobnack, J. C. Inkson, and J. C. H. Fung, Phys. Rev. B 60, 3465 (1999)]. We assume that all the surface scattering processes are elastic and that the quasiparticles and atoms are incident obliquely to the free surface. We calculate probabilities for the various one-to-one surface scattering processes allowed for a range of energies and compare the scattering rates with those obtained when backflow is neglected.     

AC Thermal Conductivity Measurements in Dilute Mixtures of 3He in Superfluid 4He

In Part III of a three-part study, we report measurements of the thermal response, T(), of ³ He-superfluid- ⁴ He mixtures to an ac heat flux, Q(t)=Q₀e^it. These data are for dilute concentrations, X, and they show the presence of three separate thermal resistances. One of these is the bulk-fluid resistance predicted by Khalatnikov and associated with the effective conductivity, _eff . Results for this component of the resistance are in quantitative agreement with the Khalatnikov predictions. With parallel work by Murphy and Meyer, these experiments resolve a long-standing conflict between theory and experiment. One of the remaining resistances is the ordinary boundary resistance R_b. The third resistance, R ₀ , is independent of the fluid layer height, d. This resistance is presumably the same as that seen in earlier dc measurements. Both the temperature and concentration dependences of this anomalous resistance differ from that of either R _fluid or R_b. It has been ascribed recently by Murphy and Meyer to effects associated with the narrow gaps usually present in cryogenic thermal conductivity experiments. We use an ad hoc model as a convenient way to parameterize the extra thermal resistance. The present studies have been carried out with an apparatus which permits us to vary d continuously and in situ from zero to 3 mm. This feature and the ac technique are important for separating the various components of the thermal resistance. In two preceeding studies, we considered related aspects of the ac thermal response of liquid helium. Part I addresses the response of normal liquid helium. Part II, provides the theoretical backdrop for the present experimental study.     

Experiments on the Dynamics of Vortices in Superfluid 4He with No Normal Component

Negative ions, probe particles of radius ~ 10–20 ?, can be injected into helium, manipulated and detected. They can be trapped by quantized vortices and hence used as vortex detectors. We show that by observing the change of the ion current caused by rotation of helium one can learn about the presence and dynamics of vortices even at very low-temperatures.     

Producing Towed Grid Quantum Turbulence in Liquid 4He

To produce turbulence in a pure quantum liquid, a superconducting linear motor has been built to tow a grid through a channel of superfluid helium at 20 mK. The design was developed using a computer simulation which considered the critical aspects of the cryogenic and electrical environment. This resulted in a single superconducting solenoid motor with an armature moving through its center. This light insulating armature is constructed of 3 phenolic tubes separated by two hollow cylindrical niobium cans placed 26 mm apart, with the turbulence-producing grid attached to one end. A conducting section on the armature, composed of one of the Nb cylinders and silver paint coating part of the phenolic rod, is inside a closely fitting capacitor made of two semi-cylindrical copper sheets. This capacitor, coupled to a bridge circuit, measures the armature position. When driven with the properly shaped current pulse (also determined by simulation), a magnetic field is produced that accelerates the rod (and grid) quickly, moves the rod and grid at near constant speed for at least 10 mm, and then quickly decelerates it. With LabView, complex pulse shapes are applied to the superconducting solenoid to produce the desired motion. The decay of turbulence is detected by the calorimetry technique in the isolated cell after the grid is pulled. Results of tests at 4.2 K (normal, classical liquid) and in superfluid down to 1.3 K, show that the motor preforms adequately in this temperature regime.