By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid 4He are strongly non-Gaussian with 1/v(3) power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the (Ω1, Ω2) parameter space at high Reynolds numbers, where Ω1 (Ω2) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = (Ω1 - Ω2)/Ω2 fully determines the state and torque G as compared to G(Ro = ∞) ≡ G∞. The ratio G/G∞ is a linear function of Ro(-1) in four sections of the parameter space. For flows with radially increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji et al., Nature (London), 444, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys. 347, 734 (1999)].

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical and superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micrometersized solid hydrogen particles trapped on quantized vortex cores and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show that the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately 1 ⁄2, consistent with the self-similar evolution of the vortices. reconnection V orticity in superfluid helium is confined to filaments that are only angstroms in diameter. These filaments are the cores of vortices, around which the fluid circulates with quantized angular momentum (1). The reconnection of two such quantized vortices can occur when their cores come into contact, as illustrated in Fig. 1. When reconnection occurs, each core breaks at one point into two parts and exchanges part of itself for part of the other. After reconnection, the vortices draw away from each other. Although this process is thought to be an essential feature of superfluid turbulence (2, 25) and of other systems mentioned below, it has never been observed in helium until now. This article is a first report of such observations. Quantized vortices can be considered theoretically as phase singularities and as topological defects in the order parameter describing the superfluid. In that sense, analogs to the vortices exist in a wide range of systems where reconnection is also an essential feature and where our work has possible implications. These systems include superconductors (3), liquid crystals (4), and heart tissue (5). In addition, reconnection is thought to play an important role in the dynamics of magnetic field lines in magnetized plasmas (6) where it affects solar convection and space weather. Whereas reconnection is difficult to observe in many of these systems, it has been observed directly in a Newtonian fluid (7,8) and in liquid crystals (4). In superfluid helium, the phenomenon has been studied by using numerical simulations of the nonlinear Schrödinger equations (9, 10), and this study provided evidence that the picture of superfluid turbulence as consisting of reconnecting vortices (2) is essentially correct. The evolution of vortices after reconnection has also been explored by using line-vortex models (11, 12), and described analytically (13,14).Although we cannot directly observe quantized vortex lines, we infer their locations by observing the motions of micrometersized solid hydrogen particles. We observe the particles as they pass through a thin sheet, which itself lies within a much larger volume of fluid, as described below. Some of the particles may be trapped on quantized vortex cores, as we demonstrat...

By analyzing trajectories of solid hydrogen tracers in superfluid 4 He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t) ≈ A (κ|t − t0|) 1/2 , where κ = h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t) = B|t−t0| α and (b) a correction-factor expressionThe measured frequency distribution of α is peaked at the predicted value α = 0.5, although the half-height values are α = 0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24 ± 0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c = 0 with a half-height range of −0.9 s −1 to 1.5 s −1 . In light of possible physical interpretations we regard the correctionfactor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤ 0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.

We discuss an experimental technique to visualize motion in the bulk of superfluid 4 He by tracking micron-sized solid hydrogen tracers. The behavior of the tracers is complex since they may be trapped by the quantized vortices while also interacting with the normal fluid via Stokes drag. We discuss the mechanism by which tracers may be trapped by quantized vortices as well as the dependencies on hydrogen volume fraction, temperature, and flow properties. We apply this technique to study the dynamics of a thermal counterflow. Our observations serve as a direct confirmation of the two-fluid model as well as a quantitative test of the normal fluid velocity dependence on the applied heat flux.