Transition to Superfluid Turbulence

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid ³He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction—the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of the dynamics is vortex number conserving, while at low friction and large vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of ³He-A and ³He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin–Helmholtz instability.      

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.     

Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow

The critical velocity v _c for the onset of turbulent drag of small spheres oscillating in superfluid ⁴He is frequency dependent (ω/2π from 100 Hz to 700 Hz) and is described by $v_{c}=2.6\sqrt{\kappa \omega}$ , where κ is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives $v_{c}\approx \sqrt{8\kappa \omega/\beta}$ , where β～1 depends on the coefficients of mutual friction. This agrees well with the data and implies that v _c is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with v _c obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.     

Geometry and Topology of Superfluid Turbulence

Superfluid turbulence consists of a very complex, apparently disordered, tangle of quantized vortex filaments. Until now it has been usual to characterize the vortex tangle mainly in terms of its density (length of vortex line per unit volume). The vortex line density is related to energy, so it has a simple physical interpretation; moreover, it is directly measured in the experiments and is easily computed in the numerical simulations. Unfortunately, the vortex line density does not describe the intrinsic disorder, coiling and linking which occurs within the turbulent vortex tangle due to the combined action of the Biot–Savart law and vortex reconnections. Using ideas borrowed from modern geometry and knot theory, firstly we introduce new measures to describe the geometrical and topological complexity of superfluid turbulence. Secondly, we test these measures on a model problem--the growth of a patch of quantized vorticity--and compare the rate of growth of complexity against the rate of growth of energy and length. Finally, we determine how vortex reconnections depend on the vortex line density.     

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.     

Dynamic Simulation of the Superfluid/Normal Fluid Interface Motion in 4He

No Heading We report on the development of a fully time-dependent computer simulation of the ⁴He normal fluid/superfluid (He-I/He-II) interface dynamics. Both the diverging thermal conductivity and the rapidly changing heat capacity of ⁴He near the lamda point present a challenge to traditional numerical methods for integrating the heat diffusion equation. We use the Dupont-II three-time-level method known for its good convergence properties for strong nonlinear models. Still, this algorithm does not conserve energy precisely, so a supplementary convergence criterion based on absolute enthalpy error is developed. We report on the underlying theoretical model, the numerical algorithm and its implementation, and simulation results. We compare the results with experimental data and discuss the error analysis and the balance between simulation fidelity and convergence.PACS numbers: 64.60.Ht, 66.60.+a, 67.40.Pm     

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.     

Time-of-Flight Measurements of Vortices Emitted from Quantum Turbulence in Superfluid 4He

An oscillating obstacle generates quantum turbulence in superfluids, when vortices remained attached to obstacle surfaces or vortex rings collided with it during oscillation. Turbulence provides a source of vortices; however, the characteristics of these vortices are not clear. In the present work, we report the flight of vortices emitted from quantum turbulence in superfluid ⁴He at low temperatures, using vibrating wires as a generator and a detector of vortices. A vortex-free vibrating wire can detect only the first colliding vortex ring, though it will be refreshed after low vibration and be able to detect a vortex ring again. By measuring a period from the start of turbulence generation to the vortex detection repeatedly, we find an exponential distribution of time-of-flights with a non-detection period t ₀ and a mean detection period t ₁, suggesting a Poisson process. Both periods t ₀ and t ₁ increase with increasing distance between a generator and a detector. A vortex flight velocity estimated from period t ₀ suggests that the sizes of the emitted vortex rings distribute to a range smaller than a generator thickness or a generator vibration amplitude. Vortices are emitted radially from a turbulence region, at least in the direction of oscillator vibration.     

Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation of normal liquid ³He has been studied over a range of temperatures from slightly above the superfluid transition temperature, T _c, to approximately 10mK at the constant pressures of 1 and 5bar. Using longitudinal LiNbO₃ transducers, operating both on and off resonance, the experiment was performed at 15 discrete frequencies located in several broadband frequency windows, including 16–25, 60–70, and 105–111MHz. The results are compared to Landau's prediction for the attenuation of zero sound in the quantum limit, (k _B Tk _B T _F), where ₀(P,T, )= (P) T ²{1+(/2k _B T)²}. Calibration of the received zero sound signals was performed by measuring the temperature dependence of the first sound attenuation from 30 to 800mK at those same frequencies and pressures. The data are compared to previous results.     

A First Order Normal to Superfluid Transition: Prewetting in the 4He-Rich Film below Liquid 3He

We summarize our earlier work on the prewetting transition in the ⁴He-rich film in contact with liquid ³He at low temperatures. We make a new fit to the experimental data using a simpler assumption than previously. The strong pressure dependence of the jump in film thickness at the transition D^s _min(P) is quantitatively explained. It is due to the depletion of the ³He concentration in the superfluid film. This is caused by the van der Waals field of the wall. As a result of the pressure dependence, the prewetting line begins at a quantum (T=0) critical point at 13.2 atm. The T=0 dewetting pressure is predicted to be 32.5 atm. The low temperature phase diagrams for the system are drawn in the D^s vs pressure plane and in the plane (₄–₃) vs ₃, where ₄ and ₃ are the chemical potentials. We predict that the prewetting line is metastable above an applied pressure of 25.75 atm. Above this pressure, bulk hcp ⁴He crystals should appear.     

Thermodynamic Magnetization of Normal and Superfluid 3He

We have measured the thermodynamic magnetization in the various phases of normal and superfluid ³ He. The A-B discontinuity differs from that inferred from nuclear-specific (NMR) experiments. We offer reasons why this apparent disagreement can be consistent with our current picture of super-fluid ³ He. One consequence of this measurement is an improved set of values for the phenomenological Landau-Ginzburg free energy -parameters.     

Broadband Frequency Study of the Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation, ₀(,T, P), of normal liquid ³ He has been studied over a broad range of frequency (/2 = 8 – 50 MHz). Data has been collected at a constant temperature (T 1.1 mK) which is just above the superfluid transition temperature, T _c , when the liquid is near a pressure, P, of 1 bar. The results are compared to Landau's prediction in the quantum limit, k _B T k _B T _F , where ₀(,T,P) = (P) T ²[l + (/2k _B T)²]. Deviations from Landau's prediction are compared to the results of other workers and are discussed with respect to additional (unidentified) extrinsic background effects and (possible) intrinsic scattering mechanisms due to fluctuations in the liquid.     

Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

We demonstrate that in a wide range of heat fluxes the dynamics of heat transfer in superfluid helium is determined by the existence of remanent quantized vortices. The vortex density dynamics determines the rise of temperature near the heater and the boiling-up of superfluid helium. It permits to understand the results of the experiments of several groups.     

哈特曼装置上均方根湍流速度的测量及研究

对哈特曼装置上的粉尘粒子速度及均方根（ｒｏｏｔ－ｍｅａｎ－ｓｑｕａｒｅ,ＲＭＳ）湍流速度进行了测量及研究,获得了哈特曼装置上不同位置粉尘粒子速度、ＲＭＳ湍流速度随时间的变化曲线。粉尘粒子速度采用激光多谱勒测速仪进行测量。文中还对激光测速法及数据处理中ＲＭＳ计算窗口的选取进行了讨论。     

Excitation and Detection of Surface Waves on Normal and Superfluid 3He

We describe the measurement principles to excite and detect surface waves on liquid helium at very low temperatures. We excited the waves mechanically by rocking the whole cryostat with frequencies of few hertz. The waves were detected capacitively with an interdigital capacitor on a vertical wall of the cuboid experimental volume. In superfluid ³He at around 0.2 mK at least eleven surface resonances were observed below 11 Hz whereas in normal fluid only a few resonances were observable above 50 mK.     

Mid-Gap State Formed Inside Mott Gap of 1T-TaS2 Single Crystals and Metal-Insulator Transition

We have measured electrical resistivity, Hall coefficient, thermoelectric power, and magnetization for charge-density wave (CDW) material 1T-TaS₂ single crystals grown by varying the excess sulfur content x _es. We have revealed that a small mid-gap state is formed inside the Mott gap and that anomalous low temperature transport is not governed by the Mott gap state itself but by the mid-gap state. The electric properties of the mid-gap state are modified by increasing x _es (or hole doping), and we have found the insulator-metal transition occurs by hole doping below 60K.     

Superfluid State of 4He Films Adsorbed on 27 Å Pores in HMM-2

We have measured the superfluid density ρ _s of ⁴He films adsorbed on the porous material HMM-2 by a torsional oscillator. The substrate has pores of 27 Å in diameter with ordered three-dimensional connectivity. ρ _s increases as T decreases, without any feature of the universal jump and the associated dissipation peak characteristic of the two-dimensional Kosterlitz–Thouless transition. We also observed resonances of the standing wave modes, from which we can estimate the sound velocity. Assuming linear dependence on (ρ _s/ρ _s(0))^1/2 and ignoring refractions, the sound velocities are extrapolated to about 20 m/s at T=0.