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.      

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.     

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.     

Superfluid Spin-down with Random Unpinning of the Vortices

The so-called creeping motion of the pinned vortices in a rotating superfluid involves random unpinning and vortex motion as two physically separate processes. We argue that such a creeping motion of the vortices need not be (biased) in the direction of an existing radial Magnus force, nor should a constant microscopic radial velocity be assigned to the vortex motion, in contradiction with the basic assumptions of the vortex creep model. We point out internal inconsistencies in the predictions of this model which arise due to this unjustified foundation that ignores the role of the actual torque on the superfluid. The proper spin-down rate of a pinned superfluid is then calculated and turns out to be much less than that suggested in the vortex creep model, hence being of even less observational significance for its possible application in explaining the post-glitch relaxations of the radio pulsars.     

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.     

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.     

Experimental studies on fourth sound in superfluid helium

In a superfluid liquid-helium cavity packed with a fine powder, only the supercomponent is free to move and pressure waves transmitted by the supercomponent are called fourth sound. We have observed that the resonance frequency of the powder-filled chamber may be shifted by introducing vortices. Both static and dynamic measurements were made on the resonance frequency and signal height in order to explore the effect of exceeding the critical velocity of the superfluid in the powder-filled chamber.Supported by the Robert A. Welch Foundation, Houston, Texas.     

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.     

Quantised vortex visualisation

No Heading If superfluid helium-4 is rotated, a triangular array of singly quantised vortices is created. The vortices have core diameters of approximately five angstroms and are pinned at the cell upper and lower boundaries. If the fluid has a free surface, the upper ends of the vortices splay out into large (0.5 mm) shallow dishes which should be visible to an optical probe under certain conditions. The vortex array is very unstable to mechanical noise but can be held stationary with the addition of helium-3 which can lie along the vortex cores or form bubbles in the surface dimples.We report investigations on free surface superfluid helium under rotation, using a cooled 77K optical CCD. We describe the difficulties encountered and how we have overcome them.PACS numbers: 67.40.Vs; 68.03.Cd; 47.37.+q.     

Numerical studies of heat transfer characteristics by using jet discharge at downstream of a backward-facing step

Summary This study presents the numerical predictions of the fluid flow and heat transfer characteristics for a backward-facing step by discharging a jet perpendicularly to the main flow. The turbulent governing equations are solved by a control-volume-based finite-difference method with power-law scheme and the well known K– model and its associate wall function to describe the turbulent behavior. The interesting parameters include entrance Reynolds number (Re _h ), dimensionless jet location (X _j/H) and the ratio of jet velocity (U _j/U₀) with channel expansion ratio ER=1.67. The predicted attachment point is in good agreement with the experiment. It is found that the optimum position is atX _j/H=2.1 (X _j: location of jet measured from the step position, H: the step height).Notation B nozzle width - C ₁,C ₂,C turbulent constant - D channel height - ER expansion ratio, - G generation rate of turbulent kinetic energy - H step height - h _x local heat transfer coefficient - J velocity ratio,U _j/U ₀ - K turbulent kinetic energy - q heat flux - Re _h Reynolds number based on step height,U ₀ H/ - S source term - T temperature - U ₀ inlet velocity - U _j jet velocity - U friction velocity - U, V x, y component velocity - X _j position of discharging jet - X _R reattachment length of the main flow - X _jR reattachment length of the upper discharging jet flow - y ⁺ dimensionless distance from the wall - dependent variables - turbulent diffusion coefficient - _e , _l , _T effective, laminar, turbulent viscosity - density - Von Kármán constant - turbulent Prandtl number - _w wall shear stress - turbulent energy dissipation rate     

Intrinsic critical velocities in superfluid4He flow through 12-μm diameter orifices near Tλ: Experiments on the effect of geometry

We report super fluid⁴He flow measurements at temperatures from 1.2 K up to T — 3 mK in three orifices of different mesoscopic geometry. Under conditions of our experiments, the flow usually reaches a temperature-dependent intrinsic critical velocity, where dissipation is believed to occur by thermal (or quantum) nucleation of individual quantized vortex rings or loops. The nucleation rate should be sensitive to the wall geometry of the flow channel and to any local velocity enhancement at the most favorable nucleation site. According to the Iordanskii-Langer-Fisher (ILF) theory, the radius of the critical vortex ring, the threshold size which can grow freely by extracting energy from the flow, increases inversely as the superfluid density on approach to the superfluid onset temperature, T. Thus sufficiently near T the critical ring should be large enough that the geometry relevant to the nucleation process and local velocity enhancement can be studied by scanning electron microscope (SEM). We examined our three orifices by SEM. One, a standard optical pinhole, has a relatively smooth taper on one side and a sharp lip on the other. The second is similar, but contains a 1-m flake perpendicular to the flow, which should provide additional velocity enhancement at its edge. In the third, the sharp lip is beveled to reduce the velocity enhancement at that site. Contrary to expectation, the intrinsic critical velocities are the same, within a relative calibration error of 10%, in all three cases. Thus, local sites of enhanced velocity do not appear to be active in nucleating vortices. This raises a question whether the classical two-fluid model which underlies the ILF calculation is adequate to describe the superfluid hydro-dynamics near walls, as it affects the vortex nucleation process.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

Superfluid density in the presence of persistent current in superfluid4He

The superfluid density _s in the presence of persistent current(v _n –v _s 0) is investigated using the Doppler-shifted fourth-sound technique. In the vortex-free Landau state, _s remains constant within our experimental resolution of two parts in 10 ⁵ . This is not inconsistent with a theoretical prediction by Khalatnikov. Where vortices are present outside the Landau region, a fractional change in _s becomes as large as 1.2%, depending on rotation velocity and temperature, and shows a relatively complex hysteresis behavior.This research is supported by NSF and ONR.     

Mean free path effects in superfluid4He

The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from T down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.     

The existence of Taylor vortices and wide-gap instabilities in spherical Couette flow

Summary The flow of a viscous incompressible fluid in the gap between two concentric spheres was investigated for the case where only the inner sphere rotates and the outer one is stationary. Flow visualization studies were carried out for a wide range of Reynolds numbers (Re2·10⁵) and aspect ratios (0.080.5) to determine the instabilities during the laminar-turbulent transition and the corresponding critical Reynolds numbers as a function of the aspect ratio. It was found that the laminar basic flow loses its stability at the stability threshold in different ways. The instabilities occurring depend strongly on the aspect ratio and the initial conditions. For small and medium aspect ratios (0.080.25), experiments were carried out as a function of the Reynolds number to determine the regions of existence for basic flow, Taylor vortex flow, supercritical basic flow and furthermore, to give the best fit for the maximum number of pairs of Taylor vortices as a function of aspect ratio. For wide gaps (0.330.5), however, Taylor vortices could not be detected. The first instability manifests itself as a break of the spatial symmetry and non-axisymmetric secondary waves with spiral arms appear depending on the Reynolds number. For =0.33, secondary waves with an azimuthal wave numbern=six, five and four were found, while in the gap with an aspect ratio of =0.5 secondary waves withn=five, four and three spiral arms exist. Frequencies of these secondary waves were measured, the corresponding critical Reynolds numbers and the transition Reynolds numbers during the transition to turbulence were found. The flow modes occurring at the poles look very similar to those found in the flow between two rotating disks. Effects of non-uniqueness and hysteresis were determined as a function of the acceleration rate.     

Superfluid transition in4He in gravity and heat flow

When⁴He in a normal fluid state near the superfluid transition is cooled from the bottom below the transition, a superfluid region appears at the bottom and slowly expands in the upward direction. We performed simulations for this case in one dimension fixing the temperature T_b at the bottom and the heat flux at the top Q. We find densely distributed phase slip centers rapidly oscillating in time in the expanding superfluid region. Their role is to produce a temperature gradient compensating the transition temperature gradient (dT(p)/dp) pg in gravity and to produce a constant negative reduced temperature T-T(p) with small fluctuations superposed. The superfluid velocity multiplied by the correlation length is found to be violently fluctuating around /3m.     

Studying the effect of the temperature factor on the transition from a laminar to a turbulent regime of flow in a boundary layer

Based on the generalization of experimental data, we propose a formula for the calculation of the effect of the temperature factor and the transition from a laminar flow regime to one that is turbulent in the boundary layer of a plate; this formula has been confirmed by experiments performed in the following range of parameter variation: 0.5 2.6; 0.2 M 3.6; 0.1 9%.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 2, pp.218–224, February, 1969.     

Some expectation on the mechanism of cross-flow instability in a swept wing flow

Summary Three-dimensional boundary layer transition on axisymmetric rotating bodies is the subject of a comprehensive experimental study. Based on this study, hypotheses are made on the mechanism of cross-flow instability for swept wing flow. These new results are combined with past explanations to provide a rough sketch for the entire flow field over the swept wing. From this new viewpoint there appears the mechanism of traveling waves, being induced by a stationary disturbance. Some uncertainties appearing in recent papers concerning this flow field are discussed. Among these uncertainties for which an explanation is provided, is the discrepancy of frequencies between the hot wire signal and the visualized flow pattern.Nomenclature x direction along a potential flow stream line - y direction normal to a potential flow stream line - z direction normal to bothx andy directions - U mean velocity inx-direction - V mean velocity iny-direction - x direction along a disturbance - y direction normal tox direction - u, v, w fluctuating velocity components inx, y, z directions - U velocity inx-direction with wall fixed coordinate - U _e velocity of outer edge of boundary-layer - U uniform flow velocity normal to leading edge - V uniform flow velocity parallel to leading edge - Q upstream velocity - N rotation speed of an axisymmetric body - P arbitrary point on a disk surface - r radius to a pointP - R ₀ radius of a disk or a cylinder - U _p phase velocity of ring like vortices - T position where wall streaks appear in the case of oil flow visualization - Re _c,t critical and transitional Reynolds numbers - angle of the spiral disturbance - boundary-layer thickness - angular velocity - sweep angle of a body - wave length of disturbance - kinematic viscosity of a fluid With 11 Figures     

The Superfluid Transition and Vortex Dynamics in Submonolayer Superfluid 4He Films in Porous Glass Under Rotation

A combination of a rotating dilution refrigerator and high-Q torsional oscillator technique has been used to study dynamics of vortices in thin ⁴ He films adsorbed on the porous glass (d=1m pore size). Under rotation an additional dissipation peak with the amplitude proportional to the angular velocity is seen at the middle of the superfluid transition, on the low temperature side of the stationary peak which is present even at =0. We attribute this peak to the 3D Type vortices created in multiply connected ⁴ He film by the rotation. Peak shape of the rotation-induced dissipation could be interpreted as a freezing of the 3D vortices well below T _c