Quasiclassical theory of vortices in3He-B

We report weak-coupling numerical calculations of the order parameter and the free energy of isolated vortices in superfluid³He in the framework of the quasiclassical theory of superfluid Fermi-liquids. Unlike earlier work with the Ginzburg-Landau theory, our results are not restricted to the vicinity ofT _c. We show that Fermi-liquid effects play an important role at lower temperatures. It appears there is a transition from the double core vortex to an A-phase-core vortex at the vapor pressure just above 0.5T_c.     

Quantized vortex ring dynamics and the vortex core radius in He II

Using a newly developed time-of-flight technique, we have determined the temperature dependence of the vortex core radius in the range 0.35 K T 0.60 K by means of precise measurements of vortex ring dynamics. One of us (W.I.G.) has extended this work to a measurement of the pressure dependence of the vortex core radius. Our results are in agreement with the earlier work of Rayfield and Reif atT=0.28 K and zero pressure ¹ and with a model of the vortex core proposed by Glaberson, Strayer, and Donnelly. ^2,3 The precision of our measurements enabled us to observe differences in the dynamics of oppositely charged vortex rings in the same electric field configurations. We were able to quantitively account for these differences in a simple way by incorporating the frictional drag associated with the ion bound on the vortex core into the equations of motion. Our results suggest that the negative ion shape is not greatly distorted by its presence on the vortex core, nor is the negative ion strongly shielded by the vortex velocity field. Some of our results have been previously reported. ^4–6 Research supported in part by the National Science Foundation.During part of the period of this research, M. Steingart held an N.D.E.A. Title IV Fellowship.Alfred P. Sloan Foundation Fellow.     

The Vortex Lability In a Supersaturated Superfluid 3 He-4 He Mixture and the Quantum Phase-Separation Kinetics

The supersaturated superfluid ³ He-⁴ He mixture in the presence of quantized vortices is considered. A specific type of the lability against the vortex core expansion arises from concentrating ³ He atoms onto the vortex core. This affects significantly the region of the ³ He concentrations at which the rate of nucleating stable ³ He-concentrated phase can be noticeable. The most clear case of the vortex structure is a straight-line vortex with the uniformly distributed 3He atoms along the core. Such lability leads to some features in the thermal activation and quantum tunneling nucleation, resulting, in particular, in a relatively small supersaturation of about 1% which can be achieved. The critical value of the supersaturations corresponding to the vortex lability is dispersed because of the finite size of the ³ He-concentrated phase along the vortex core. We analyze this dispersion and its effect on the quantum separation in supersaturated ³ He-⁴ He mixtures. The value of the supersaturation conserves its order of the magnitude, changing only by a numerical factor. We also emphasize an important difference of the coefficient in the term responsible for the lability from the superfluid density s. The supersaturation observed in experiments lies within the range of the vortex lability and, probably, is connected with this lability.     

The orientational phase transition at a vortex in3He-B

The orientational phase transition in the vicinity of a single vortex in³He-B is studied. It is the phase transition from a uniformn-texture withn parallel to the magnetic field and the vortex line to ann-texture that is nonuniform near the vortex. The problem of the instability of the the uniformn-texture is equivalent to the quantum mechanical two-dimensional problem of a bound state in a field with an attractive potential 1/r ². The orientational phase transition at a vortex array is also considered. In the limit of large vortex density the orientational phase transition transforms to the phase transition studied by Gongadze et al. The theoretical results are compared with the observed phase transition at a vortex in³He-B.     

Heat conduction by liquid helium II in capillary tubes. IV. Mutual friction under pressure

We report measurements of supercritical heat conduction in liquid helium II at pressures above the vapor pressure. The measurements were made in glass capillary tubes of diameter 50.5 and 366.8 m in the temperature range from 1.2 to 2.1 K. As in our previous results at the vapor pressure, a clear distinction can be made between two regimes in which the average separation of vortex lines is either comparable with or larger than the size of the flow channel. In the wider tube, at high relative velocities v between the superfluid and normal component, where the vortex spacing is small, a modified form of Gorter-Mellink mutual friction F _sn is observed which varies as F_sn=A_snv(v–v₀)². The coefficient A increases with pressure, and its variation with T/T(p) is in fairly good agreement with Schwarz ' microscopic theory of superfluid turbulence. However, the absolute magnitude of A is in general larger than in Schwarz ' theory and also larger than most other experimental values. In the narrower tube the measurements are all in the regime where the vortex spacing is comparable with the tube size, and they do not agree with the predictions of the Gorter-Mellink law. At present, the data cannot be analyzed quantitatively in the terms of the vortex line density, because B, the vortex line scattering coefficient, is not known at high pressures.Preparation of this paper was supported by a U.S. National Science Foundation grant DMR 7901073 and by a UK Science Research Council Senior Fellowship (DFB).SRC Senior Fellow.     

Interplay Between Vorticity and Chirality Inside the Vortex Core in Chiral p-Wave Superconductors

The vortex core in chiral p-wave superconductors exhibits various properties owing to the interplay between the vorticity and chirality inside the vortex core. In the chiral p-wave superconductors, the site-selective nuclear spin-lattice relaxation rate T ^–1 ₁ is theoretically studied inside the vortex core within the framework of the quasiclassical theory of superconductivity. T ^–1 ₁ at the vortex center depends on the sense of the chirality relative to the sense of the magnetic field. The effect of a tilt of the magnetic field upon T ^–1 ₁ is investigated. The effect of the anisotropy in the superconducting gap and the Fermi surface is then investigated. The result is expected to be experimentally observed as a sign of the chiral pairing state in a superconducting material Sr₂RuO₄.     

On “A note on the flow in a trailing vortex” by K. K. Tam

Summary In a recent paper in this Journal (7, 1973, 1–6) Tam suggested that early work by Batchelor on the decay of a laminar trailing vortex was in error. Tam's claim was that the decay of axial velocity defect at the center of the vortex went asx ⁻¹ instead ofx ⁻¹ logx. The purpose of this note is to refute Tam's claim. A further term in the asymptotic expansion for the circulation in the vortex is also obtained.     

On unsteady airfoil-vortex interaction

Summary An experimental investigation on unsteady airfoil-vortex interaction has been done. The incident vortex, to interact with a downstream airfoil (NACA 0018, chord lengthc=20 mm), is generated by a square cylinder (side lengthD=20 mm). The square cylinder and airfoil are arranged in tandem and the spacing ratioL/D of the central distance to the side length is set a constant value of 4.625. The free stream Mach numbers are varied between 0.153 and 0.750, whereas the free stream Reynolds numbers (based on the side lengthD) are varied between 0.713×10⁵ and 3.44×10⁵.It is found that as the incident vortex approaches the airfoil, the circulation and scale are decreased until it arrives at a position near the leading edge of the airfoil. During this stage, some circulation of the incident vortex is transferred to the secondary vortex generated on the airfoil opposite to the surface that the incident vortex approaches. Thus, circulation and scale of the secondary vortex are increased. However, after the incident vortex goes further downstream, no circulation of the incident vortex is transferred to the secondary vortex effectively. As the result, both of the incident vortex and secondary vortex decay due to the viscous dissipation through the interaction with the boundary layer of the airfoil. The locus of the incident vortex is deviated in such a way that it goes away from the airfoil. The streamwise position of the secondary vortex is adjusted by the incident vortex, orvice versa, so as to meet each other just behind the trailing edge of the airfoil.With 8 Figures     

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.     

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.     

Superfluid Vorticity and 1/f Noise in Melting of Solid 4He

One of the ways to reach a zero-vorticity state in superfluid ⁴ He is to melt solid helium slowly at temperatures well below T . This method takes advantage of the small density difference between the liquid and solid phases and of the high critical velocities for vortex formation at low T. However, pinning of the liquid-solid interface on the walls, revealed by 1/f-like pressure fluctuations of up to 1-10 bar in our setup, has consistently led to remanent vortex line densities of 4 · 10³ lines per cm ².     

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios ofU _m toU ₀ are ofO(10⁻¹),O(1) andO(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re=10², 10³ and 3×10³ are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Kármán vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method. This study was supported by the National Natural Science Foundation of China and the Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, as well as by the National Basic Research project “Nonlinear Science”.     

Heat transfer enhancement by winglet-type vortex generator arrays in compact plain-fin-and-tube heat exchangers

The potential of winglet type vortex generator (VG) arrays for air-side heat transfer enhancement is experimentally evaluated by full-scale wind-tunnel testing of a compact plain-fin-and-tube heat exchanger. The effectiveness of a 3VG alternate-tube inline array of vortex generators is compared to a single-row vortex generator design and the baseline configuration. The winglets are placed in a common-flow-up orientation for improved tube wake management. The overall heat transfer and pressure drop performance are assessed under dry-surface conditions over a Reynolds number range based on hydraulic diameter of 220 ≤ Re ≤ 960. It is found that the air-side heat transfer coefficient increases from 16.5% to 44% for the single-row winglet arrangement with an increase in pressure drop of less than 12%. For the three-row vortex generator array, the enhancement in heat transfer coefficient increases with Reynolds number from 29.9% to 68.8% with a pressure drop penalty from 26% at Re = 960 to 87.5% at Re = 220. The results indicate that vortex generator arrays can significantly enhance the performance of fin-tube heat exchangers with flow depths and fin densities typical to those used in air-cooling and refrigeration applications.     

Spatially-Resolved NMR Study on Antiferromagnetic Vortex Core in HTSC

Magnetism in the vortex core of nearly-optimal doped Tl₂Ba₂CuO₆₊ (T _c=85 K) is investigated by a spatially-resolved NMR. The NMR relaxation rate T ^–1 ₁ at ²⁰⁵Tl site provides a direct evidence of the significant enhancement of the AF spin correlations in the vortex core region and shows clearly a local AF ordering of the core region Cu spins at T _N=20 K. Above T _N the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T ^*–120 K), indicating that the pseudogap disappears within the vortex core.     

Angular momentum of the fields of a few-mode fiber: I. A perturbed optical vortex

This paper presents the results of studies of the physical nature of the electrodynamic angular momentum of a stable CV ₊₁ ⁺ vortex in a few-mode fiber. It shows that the angular momentum of a CV ₊₁ ⁺ vortex can be conventionally divided into orbital and spin angular momenta. The longitudinal component of the fundamental HE ₁₁ ⁺ mode on the axis of the fiber has a pure screw dislocation with a topological charge of e=+1. The longitudinal component of a CV ₊₁ ⁺ vortex also has a pure screw dislocation on the axis of the fiber with a topological charge of e=+2. Therefore, perturbation of a CV ₊₁ ⁺ vortex by the field of the fundamental HE ₁₁ ⁺ mode removes the degeneracy of the pure screw dislocations of the longitudinal and transverse components of the field and breaks down the structural stability of the CV ₊₁ ⁺ vortex. As a result, an additional azimuthal flux of energy with an angular momentum opposite to that of the fundamental flux is induced. An analogy is drawn between the stream lines of a perturbed CV vortex and the stream lines of an inviscid liquid flowing around a rotating cylinder. Studies of the evolution of a CV vortex in a parabolic fiber show that they are structurally stable when acted on by the perturbing field of the HE ₁₁ ⁺ mode. However, perturbing a CV ₊₁ ⁺ 1 vortex of a stepped fiber with the field of the HE ₁₁ ⁺ mode destroys the structural stability of the vortex. It is found that the propagation of a circularly polarized CV vortex can be represented as a helical wavefront screwing into the medium of the fiber. The propagation of a linearly polarized vortex in free space is characterized by the translational displacement (without rotation) of a helical wavefront. Pis’ma Zh. Tekh. Fiz. 23, 74–81 (November 12, 1997)     

Explosion of Electron Bubbles Trapped on Vortices in He-II

Electrons injected into liquid helium become trapped in a spherical cavity from which the liquid is almost completely excluded. When a negative pressure is applied to the liquid the size of the electron bubble increases, and at a critical negative pressure P _c the bubble explodes. We have observed these explosions and have measured P _c as a function of temperature. At low temperatures an electron bubble can become bound to a quantized vortex. The flow of the helium around the quantized vortex leads to a reduction in the magnitude of P _c. We will report measurements of this reduction in P _c and will make a comparison of the results with theoretical predictions.     

Splitting of a Quadruply Quantized Vortex in the Rb Bose-Einstein Condensate

We observed the sudden deformation of a quadruply quantized vortex into a linear shape in a ⁸⁷Rb (F=2,m _F =2) Bose-Einstein condensate (BEC). Multiply quantized vortex is predicted to split into singly quantized vortices and the observed deformation is considered to be the onset of the splitting. The displacement of the vortex with respect to the center of the BEC would induce the observed splitting. Our theoretical simulation qualitatively supports these arguments.     

Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.     

Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B

We report on the first comprehensive measurements of critical superflow velocities in³He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ω_c(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with³He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps. NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity v_c(T, P)=Ω_c(T, P), whereR is the radius of the container. We findv _c (T, P) to be related to the calculated intrinsic stability limitv _ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.     

Quantized Vortices Beside the Superfluid-Normal Interface

We consider a quantized vortex line parallel to the interface between the concentrated (c) and dilute (d) phases of a liquid ³ He- ⁴ He mixture. The vortex produces a groove-like distortion of the interface deflected into the d-phase. As a vortex approaches the interface, the bending flexure increases, reaching a maximum of 0.65m at a critical distance of 1.3m. Closer positions become absolutely unstable. Distortion of the interface leads to strong reduction of the threshold (6.3cm/s) for the Helmholtz-Kelvin tangential instability.