The determination of the energy barrier for phase slips in superfluid4He

The velocity dependence of the energy barrier for vortex creation in microscopic apertures is determined. When compared to results from other laboratories, the energy barrier seems to be a universal function of velocity. This universality suggests that the vortex nucleation process is independent of the microscopic surface structure of the aperture. In DC flow experiments, the vortices are nucleated at rates up to 700kHz. In single phase slip experiments, the rate of nucleation is on the order of 10 Hz. Each of these types of experiments gives the energy barrier in a different velocity regime. The energy barrier has more curvature, as a function of velocity, than can be accounted for by the half-ring model of vortex nucleation.     

The flow past a spinning sphere in a slowly rotating fluid at small reynolds number

The axisymmetric flow due to a uniform stream at infinity past a slowly rotating sphere in a viscous incompressible rotating fluid is studied and the results are presented mostly in the form of graphs of the streamlines. A region of reversed flow and vortex formation is found to occur near the front or rear stagnation points under certain conditions depending upon the speed of the uniform stream at infinity, the radius of the sphere and the angular velocity of the sphere. The fluid may rotate in the same or opposite directions.     

Dynamics of quantized vortices in rotating superfluid

Dynamics of interactive quantized vortices in rotating superfluid is studied theoretically. This work considers the basic system where superfluid is contained in a cylindrical vessel that rotates about its axis at an angular velocity. Although two-dimensional equilibrium patterns of vortex arrays are understood fairly well at present, there has been only a little amount of information on the dynamical aspects. Thus this work studies some typical dynamical problems, i.e., formation of vortex array and spin-down process. We describe also three-dimensional analysis which is much more troublesome than two-dimensional one.     

Superfluid in the Space Between Rotating Spheres II: The Shape of Vortices and Nonequilibrium States

Vortex dynamics is used to consider the following problems concerning vortices in the space between concentric spheres: the equilibrium shape of vortices (they are almost rectilinear if their number is large), the metastable clusters with nonequilibrium number of vortices, the processes of vortex breaking and connection in the vicinity of the inner sphere equator, the annihilation in the vicinity of the outer sphere equator, and the behavior of an almost freely rotating double-sphere device during the variation of the superfluid angular momentum caused by the changes of vortex configuration (similar phenomena are among the possible reasons of pulsars self-acceleration).     

Vortex Nucleation and the Levitation of Charged Helium II Drops

Intrinsic nucleation of quantized vortices in Helium II can be studied by means of rotating freely suspended superfluid drops at angular velocities above some critical value. The motivation for doing so is described, as well as recent progress in the electrostatic levitation of Helium II drops charged with positive ions. To date, stable levitation has been achieved for drops of order 100–150 micrometers in diameter, with a surface charge density about a factor of ten smaller than Rayleigh limit, and a diameter a similar factor less than the maximum allowed in normal gravity. We discuss the possibility of rotating these drops via the surface charge density and discuss the advantages of a microgravity environment, including the attainment of significantly larger suspended drops. Recent efforts to find optical seed particles for angular velocity measurements are discussed.     

Trapping of Vorticity by Îl-textures in 3He-A

No Heading Using a rotating cryostat, we have observed nucleation, annihilation and strong intrinsic pinning of continuous vortices in a slab of superfluid ³He-A containing stable textural defects. A model of a critical state set by either the critical velocity for vortex nucleation or pinning strength is developed. It predicts a hysteretic dependence of trapped vorticity on the angular velocity of rotation, in agreement with the observations. We argue that the static defects responsible for nucleation and trapping of vorticity are networks of domain walls between regions of opposite orientation of the Îl-vector.PACS numbers: 76.40.11f, 67.40.Bz, 67.40.Pm.     

Dynamics of field dislocations and disclinations in a few-mode fiber. IV. Formation of an optical vortex

The physical mechanisms responsible for the formation of an optical vortex in the field of a few-mode fiber have been investigated experimentally and theoretically. In an optical fiber with a parabolic refractive index profile an optical vortex is formed as a result of interaction between circularly polarized rotating pure edge dislocations of circularly polarized even and odd CP₁₁ modes. In a stepped-index fiber the formation of an optical vortex is also related to the simultaneous propagation of even and odd modes. The fields of these modes alter their structure over the fiber length and are not manifested by rotating edge dislocations. It has been found experimentally that a stable vortex does not alter its degree of polarization of the field at fiber lengths greater than 10 m. An unstable vortex, for which the product of the spin and the topological charge is always less than zero, periodically decays and recovers at a beat length of 0.65 m. It is noted that a stable optical vortex cannot be formed by orthogonally polarized LP₁₁ modes. This is because an optical vortex transfers additional angular momentum like the CP₁₁ modes whereas the LP₁₁ modes do not transfer additional angular momentum of the field. Pis’ma Zh. Tekh. Fiz. 23, 70–75 (March 12, 1997)     

A numerical study of mechanisms of accretion for rotating snow sleeves evolving on conductor rods

It is the purpose of this paper to construct a mathematical/computational model for the accretion of snow on rotating snow sleeves attached to conductor rods, and to consider some of the limitations in the use of the assumption of perfect cylindrical-sleeve growth, as currently employed to provide estimates of snow-loading intensity. For purposes of illustration, three rotating snow accretion regimes are considered, in which the direction of the airflow is always taken as perpendicular to the axis of the conductor rod. Firstly, a horizontal conductor rod is free to rotate and is initially bare. Rotation of the system (conductor rod and accreted snow) is initiated by snow torque, due to eccentric snow loading on the windward side of the conductor, and is driven by aerodynamic torque generated by the windflow past the evolving, rotating, asymmetrical sleeve growth. Secondly, a vertical conductor rod is free to rotate and the bare rod is given an initial small angular velocity; the rotation of the accreting system is then driven by aerodynamic torque alone. Thirdly, a horizontal rod is fixed and is initially covered by an annulus of snow, supported by a thin layer of (unfrozen) water existing between the conductor and the snow sleeve. In this case, the rotation of the snow sleeve is due to the combined snow and aerodynamic torques and is now retarded by the viscous torque due to the rotating thin film of water. Asymptotic solutions obtained for small accretion time supplement numerical results derived from the computational models. Numerical results on these rotating non-periodic snow accretion regimes are presented as a function of the wind speed, snow precipitation rate and diameter of the conductor rod.     

On the Statistical Analysis of Single Vortex Nucleation Events in Superfluid 4He

We investigate the statistical properties of single phase slip events observed in vortex nucleation experiments in ⁴He by the groups in Berkeley and Paris. From the cumulative distribution function of the events we calculate the sliprate as a function of flow velocity. The critical velocity is defned as the mean velocity and its statistical width as the standard deviation. From the slip rate and from the observed linear temperature dependence of the critical velocitywe obtain the energy barrier for vortex nucleation which is a quadratic function of the flow velocity. A comparison with the statistical properties of the laminar to turbulent transition in the flow around an oscillating sphere shows strikingly different behaviour.     

Nucleation of water vapors at temperatures above the boiling point in the presence of ion admixtures

The dependences of the Gibbs energy, entropy, and work of formation on the sizes of the centers of nucleation of a condensed phase with the size of up to 533 molecules formed on singly charged sodium cations and chlorine anions in water vapor at the temperature of 400 K have been calculated on the molecular level by the Monte Carlo method. It has been shown that, when the detailed interaction model is used, the effect of pulling the ion from microdroplets is kept at relatively high temperatures, accelerating the loss of the thermodynamic stability of the center of nucleation and the formation of the typical nucleation barrier, the same as in homogeneous microdroplets. When ion admixtures are present, the free energy barrier to the growth of centers of nucleation in strongly supersaturated vapors is considerably lowered. The nucleation velocity and minimum relative contents of the ion admixtures, able to accelerate nucleation, have been estimated in the region of strong supersaturation.     

Slow viscoelastic fluid flow past a rotating sphere

The problem of axially symmetric flow of a particular type of non-Newtonian fluid past a rotating sphere due to a uniform stream at infinity is investigated. The presence of a region of reversed flow is found under certain conditions depending on the angular velocity of the sphere, the speed of the uniform stream and radius of the sphere. This region which is attached to the rear portion of the sphere is found to depend strongly on the viscoelasticity of the fluid. The vortex is seen to move towards the sphere as the viscoelastic parameter increases while the other parameters are kept fixed. As this viscoelastic parameter approaches a critical value, the vortex is found to disappear.     

Spiralling elliptic vortex solitons in nonlocal nonlinear media

We have introduced a class of spiralling elliptic vortex (SEV) solitons in nonlocal nonlinear media. The SEV soliton has more complicated structures both in its amplitude and in its phase compared with conventional vortex solitons. Different from the circularly symmetric amplitude profile of vortex solitons, the SEV solitons exhibit the elliptic optical spots. Furthermore, the SEV solitons have the special modulated helical phase structures, which make the SEV solitons rotate. For different topological charges, all the SEV solitons own the same critical power, critical cross-term phase coefficient and the critical angular velocity for fixed semiaxis of the elliptic spots. The stability of the SEV solitons is confirmed by the direct numerical simulations with random noises.     

Off-Centered Vortices in Cylindrically Confined Condensates

We consider noncentered vortices and their arrays in a large cylindrically trapped Bose-Einstein condensate at zero temperature. Using the Thomas-Fermi approximation, we investigate the dependence of the kinetic energy and the angular momentum on the distance of an off-centered vortex with respect to the symmetry axis. We generalize the results to vortex arrays and give a physical insight of the smooth behavior of the angular momentum found experimentally.     

Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential

We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of the rotating lattice potential.     

涡旋光束轨道角动量在大气湍流传输下的特性分析

从拉盖尔-高斯涡旋光束表达式出发,基于瑞利衍射理论,通过研究涡旋光束在大气湍流中传输时的旋转相干函数的变化规律,总结了涡旋光束在大气湍流中传输时各轨道角动量之间的串扰情况,使用了拓扑荷数探测概率描述串扰规律,并推导了拓扑荷数探测概率的解析表达式。研究了涡旋光束通过湍流后的拓扑荷数的分布情况,并将结果与涡旋光束通过大气随机相位屏的数值仿真结果进行了对比,给出了理论与仿真的拓扑荷数的探测概率随湍流强度以及初始涡旋光束拓扑荷数大小的关系图对比,验证了推导的拓扑荷数探测概率解析表达式的正确性。通过该表达式可进一步研究大气湍流与涡旋光束相互作用从而影响涡旋光束轨道角动量散射的本质,为涡旋光束的空间光通信中选择合适的拓扑荷数间隔,以及在不同湍流强度下选择合适束腰大小以减少串扰带来的误码率提供了理论依据。     

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.     

Transfer of discrete inclusions by fluxes with concentrated vorticity

Problems related to modeling of the motion of discrete inclusions (solid particles, drops or bubbles) in flows with concentrated vorticity are considered. A comparative evaluation of the force factors in the equation of motion of a test particle is made. The results of numerical modeling of the motion of discrete inclusions in the gap between concentric rotating cylinders and a vortex flow formed by the liquid rotating with a constant angular velocity over a fixed base are discussed. The coordinates of the points of equilibrium of the test particle in the vortex flow are found. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 36–45, March–April, 2007.     

Free convection boundary layer flow of a micropolar fluid past slender bodies

The transverse curvature effects on axisymmetric free convection boundary layer flow of a micropolar fluid past vertical cylinders are investigated using the theory of micropolar fluids formulated by Eringen. The governing equations for momentum, angular momentum and energy have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters, transverse curvature parameter and Prandtl number of the fluid. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced surface heat transfer rate as compared with Newtonian fluids.     

Non-unique solutions of the boundary layer equations for the flow near the equator of a rotating sphere in a rotating fluid

Summary In this paper it is shown, using a numerical technique, that axially-symmetric solutions of the boundary layer equations which describe the rotating flow near the equator of a rotating sphere are not unique. In certain regimes it is found that at least three possible solutions are possible. When the sphere and fluid rotate with almost the same angular velocity it is shown that the approach to solid body rotation is a non linear process.With 5 Figures     

Dynamics of Quantized Vortices in a Rotating Cylindrical Vessel

Recently Finne et al. found a transition to the turbulent state in rotating superfluid ³He-B which is insensitive to the fluid velocity, but rather controlled by temperature. They reported that at low temperatures a few seed vortices, injected into a vortex-free region, developed through a transient turbulent state to a vortex array. The experimental observations were consistent with the numerical simulation of dynamics of quantized vortices. However, we do not understand well how the seed vortex follows the above scenario and, especially, how the turbulent vortices change to a vortex array. Although the previous numerical simulation was done for a rotating cubic vessel, we study here the vortex dynamics in a rotating cylindrical vessel which is more suitable for the comparison with the experiments. We developed a numerical method for calculating the vortex dynamics in a cylindrical vessel and investigated the vortex dynamics after a vortex seed loop was injected into a vortex-free region. The numerical result shows that the seed vortex becomes unstable, especially near the cylindrical side wall, and develops into turbulent vortices. After that a vortex array appears in the central region, collecting the vortices from the surrounding tangle. PACS numbers: 67.40.Vs, 47.32.Cc, 47.37.+q.