Polarization of superfluid turbulence

We show that normal-fluid eddies in turbulent helium II polarize the tangle of quantized vortex lines present in the flow, thus inducing superfluid vorticity patterns similar to the driving normal-fluid eddies. We also show that the polarization is effective over the entire inertial range. The results help explain the surprising analogies between classical and superfluid turbulence which have been observed recently.     

Measurement of the normal-fluid velocity in superfluids

Numerical calculations of (finite temperature) superfluid vortex ring propagation against a particulate sheet show that the solid particle trajectories collapse to a very good approximation to the normal-fluid path lines. We propose an experiment in which, by measuring the solid particles' velocities, direct information about the instantaneous normal-fluid velocity values could be obtained.     

Classical and quantum regimes of superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q^?1 playing the same role as the Reynolds number Re=UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re?1 in classical hydrodynamics, and q?1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re_s=UR/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.     

On the dynamics of superfluid vorticity in non-dissipative processes

We investigate the consequences of the possible existence of superfluid vorticity on the Landau two-fluid equations. Assuming a conservation law for superfluid circulation, we show that in non-dissipative situations, the superfluid vorticity is swept along by the normal fluid.     

Fractal dimension of superfluid turbulence

Superfluid turbulence consists of a disordered tangle of quantized vortex filaments which interact with each other and with the normal fluid. We develop a kinematic model of normal-fluid turbulence to study superfluid vortex tangles at finite temperatures and show by numerical simulation that the system of filaments has a fractal dimension larger than one. We find that the fractal dimension is directly related to the vortex-line density and is independent of temperature over a wide range.     

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.     

Asymptotics of unit Burger number rotating and stratified flows for small aspect ratio

Rotating and stably stratified Boussinesq flow is investigated for Burger number unity in domain aspect ratio (height/horizontal length) δ<1 and δ=1. To achieve Burger number unity, the non-dimensional rotation and stratification frequencies (Rossby and Froude numbers, respectively) are both set equal to a second small parameter ?<1. Non-dimensionalization of potential vorticity distinguishes contributions proportional to (?δ)⁻¹, δ⁻¹ and O(1). The (?δ)⁻¹ terms are the linear terms associated with the pseudo-potential vorticity of the quasi-geostrophic limit. For fixed δ=1/4 and a series of decreasing ?, numerical simulations are used to assess the importance of the δ⁻¹ contribution of potential vorticity to the potential enstrophy. The change in the energy spectral scalings is studied as ? is decreased. For intermediate values of ?, as the flow transitions to the (δ?)⁻¹ regime in potential vorticity, both the wave and vortical components of the energy spectrum undergo changes in their scaling behavior. For sufficiently small ?, the (δ?)⁻¹ contributions dominate the potential vorticity, and the vortical mode spectrum recovers k⁻³ quasi-geostrophic scaling. However, the wave mode spectrum shows scaling that is very different from the well-known k⁻¹ scaling observed for the same asymptotics at δ=1. Visualization of the wave component of the horizontal velocity at δ=1/4 reveals a tendency toward a layered structure while there is no evidence of layering in the δ=1 case. The investigation makes progress toward quantifying the effects of aspect ratio δ on the ?→0 asymptotics for the wave component of unit Burger number flows. At the lowest value of ?=0.002, it is shown that the horizontal kinetic energy spectral scalings are consistent with phenomenology that explains how linear potential vorticity constrains energy in the limit ?→0 for fixed δ.     

Topological noise scalings in superfluid and classical turbulence

We calculate the topological noise characterizing the direction of line vortices in superfluid and classical turbulence by finding the intersection of line vortices with square surfaces of edge length l_s positioned normal to three orthogonal axes. In the case of homogeneous superfluid turbulence in thermal counterflow, we find that the noise scales as l_s along the two directions normal to the counterflow and as l _s ^3/2 along the direction parallel to it. In homogeneous isotropic superfluid turbulence, at T→0 K, the noise scales as l _s ^7/4 . In homogeneous isotropic classical turbulence, the scaling is l _s ² . We offer possible interpretations of the computed scalings, as well as justification for their differences.     

Vortex locking in direct numerical simulations of quantum turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.     

Two remarks on free precession of neutron stars with superfluid vortices

The presence of superfluidity in neutron stellar interiors modifies free precession frequencies. The effect is particularly large if vortices are pinned to the stellar crust, in which case frequencies are bounded from below by ～ψΩ, where ψ is the ratio of pinned superfluid moment of inertia to stellar moment of inertia, and Ω is half the superfluid vorticity.     

Structure of the surface vortex sheet between two rotating 3He superfluids

We study a two-phase sample of superfluid 3He where vorticity exists in one phase (3He-A) but cannot penetrate across the interfacial boundary to a second coherent phase (3He-B). We calculate the bending of the vorticity into a surface vortex sheet on the interface and solve the internal structure of this new type of vortex sheet. The compression of the vorticity from three to two dimensions enforces a structure which is made up of 1 / 2-quantum units, independently of the structure of the source vorticity in the bulk. These results are consistent with our NMR measurements.     

Transition to ballistic regime for heat transport in helium II

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter–Mellinck regime of turbulent superfluids, is extended to describe the transition to ballistic regime in narrow channels wherein the radius R is comparable to (or smaller than) the phonon mean-free path ?   in superfluid helium. To do so, we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to R²$R^2$ (Landau regime) to another one proportional to R? (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.     

Fermi gases in slowly rotating traps: superfluid versus collisional hydrodynamics

The dynamic behavior of a Fermi gas confined in a deformed trap rotating at low angular velocity is investigated in the framework of hydrodynamic theory. The differences exhibited by a normal gas in the collisional regime and a superfluid are discussed. Special emphasis is given to the collective oscillations excited when the deformation of the rotating trap is suddenly removed or when the rotation is suddenly stopped. The presence of vorticity in the normal phase is shown to give rise to precession and beating phenomena which are absent in the superfluid phase.     

Superfluid bosons and flux liquids: disorder,thermal fluctuations,and finite-size effects

The influence of different types of disorder (both uncorrelated and correlated) on the superfluid properties of a weakly interacting or dilute Bose gas, as well as on the corresponding quantities for flux line liquids in high-temperature superconductors at low magnetic fields are reviewed, investigated and compared. We exploit the formal analogy between superfluid bosons and the statistical mechanics of directed lines, and explore the influence of the different “imaginary time” boundary conditions appropriate for a flux line liquid. For superfluids, we discuss the density and momentum correlations, the condensate fraction, and the normal-fluid density as function of temperature for two- and three-dimensional systems subject to a space- and time-dependent random potential as well as conventional point-, line-, and plane-like defects. In the case of vortex liquids subject to point disorder, twin boundaries, screw dislocations, and various configurations of columnar damage tracks, we calculate the corresponding quantities, namely, density and tilt correlations, the “boson” order parameter, and the tilt modulus. The finite-size corrections due to periodic vs. open “imaginary time” boundary conditions differ in interesting and important ways. Experimental implications for vortex lines are described briefly.     

Emission of discrete vortex rings by a vibrating grid in superfluid 3He-B: a precursor to quantum turbulence

We report a transition in the vorticity generated by a grid moving in the B phase of superfluid 3He at T相似文献   

Vorticity generated near a field emitter in superfluid helium

We estimate the density of vorticity near a field emitter in superfluid helium, and discuss the implications for experiments which employ field emission characteristics to detect the appearance of a single nearly vortex in a rotating vessel.     

Mutual friction in the laminar flow of superfluid helium II through capillary tubes

The Hall-Vinen-Bekarevich-Khalatnikov theory is applied to the laminar flow of superfluid helium through capillary tubes. Velocity profiles obtained for the superfluid are interpreted in terms of the motion of vortex rings. The thermodynamic potential gradient as a function of the average superfluid and normal fluid velocities compares favourably with recent experimental results. It is concluded that the vortex rings originate at the wall and disappear at the tube axis.     

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.     

Alignment of anisotropic superfluids by flow

We discuss some features of one dimensional superflow in a p-state superfluid. The direction l of the orbital momentum is anchored at the walls, but l tends to become aligned along the flow lines, when the superfluid velocity exceeds a certain threshold.     

Introduction to the vortex sheet of superfluid He-A

It is well known that superfluids respond to rotation by forming vortex lines. It has been recently discovered that a different type of state consisting of a vortex sheet, instead of lines, can be created in the A phase of superfluid ³He. This paper presents an introduction to the vortex sheet. We first discuss ⁴He, where a vortex sheet is unstable. The way to realize a stable sheet in ³He-A is called a vortex soliton. It consists of a topologically stable domain wall to which nonsingular vorticity is bound. The vortex soliton has been observed by nuclear magnetic resonance, and its most prominent experimental properties are explained. The macroscopic shape of the sheet and the superfluid flow in a rotating container are discussed.