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arXiv:0905.4797 · Physical Review B

Motion of vortex ring with tracer particles in superfluid helium

Carlo F. Barenghi, Yu. A. Sergeev

Published Jul 23, 2009• 15 citations
arXivHTMLPDF

Abstract

Recent experiments on quantum turbulence in superfluid helium made use of small tracer particles to track the motion of quantized vortices, determine velocity statistics and visualize vortex reconnections. A problem with this visualization technique is that it may change the turbulent flow which it visualizes. To address this problem, we derive and solve the equations of motion of a quantized vortex ring which contains a given number of particles trapped on the vortex core, hence derive a quantitative criterion to determine in which measure small particles trapped in quantized vortices affect vortex motion. Finally we apply the criterion to a recent experiment.

DOI
10.1103/physrevb.80.024514

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Recent experiments on quantum turbulence in superfluid helium made use of small tracer particles to track the motion of quantized vortices, determine velocity statistics and visualize vortex reconnections. A problem with this visualization technique is that it may change the turbulent flow which it visualizes. To address this problem, we derive and solve the equations of motion of a quantized vortex ring which contains a given number of particles trapped on the vortex core, hence derive a quantitative criterion to determine in which measure small particles trapped in quantized vortices affect vortex motion. Finally we apply the criterion to a recent experiment.
We capture the decay of a quantized vortex ring in superfluid helium-4 by imaging particles trapped on the vortex core. The ring shrinks in time, providing direct evidence for the dissipation of energy in the superfluid. The ring with trapped particles collapses more slowly than predicted by an available theory, but the collapse rate can be predicted correctly if the trapping of the particles on the core is taken into account. We theoretically explore the conditions under which particles may be considered passive tracers of quantized vortices and estimate, in particular, that their dynamics on the large-scale is largely unaffected by the burden of trapped particles if the latter are spaced by more than ten particle diameters along the vortex core, at temperatures between 1.5 K and 2.1 K.
Recent experiments have shown that micron-size particles can be trapped in quantized vortices in superfluid helium. We present results of a dynamically self-consistent calculation of the nonlinear interaction of a sphere and a vortex. We find that, depending on the regime, the sphere can be trapped in the vortex or break free from it. We also find that, if trapped, the sphere can travel along the vortex. We analyze the role played by the various forces acting on the sphere during the interaction.
Superfluids are inviscid flows in which vorticity is supported on filaments with quantized circulation. Such objects, known as quantum vortices, exhibit a hydrodynamical behavior. Experimentally, the dynamics of superfluids has been studied by using particles, which nowadays have become the main tool for visualizing quantum vortices. In this Thesis, we study numerically and analytically the dynamics of active and finite-size particles in superfluids. The superfluid is modeled with the Gross–Pitaevskii equation, while the particles are implemented as moving repulsive potentials coupled with the macroscopic wave function describing the superfluid. Firstly, the model is used to investigate the interaction between particles and quantum vortices at very low temperatures. This part aims to give a theoretical background to the current experiments in which macroscopic particles are used to sample superfluid vortices and quantum turbulence. Specifically, we address the following problems: the capture of a particle by a quantum vortex, the reconnections of vortex filaments and the propagation of Kelvin waves in presence trapped particles and the dynamics of particles in decaying quantum turbulence. In the last part of the manuscript, finite temperature effects are studied in the Fourier-truncated Gross–Pitaevskii model. The goal is to characterize the dynamics of impurities immersed in a thermal bath and how their presence modifies the statistical properties of the fluid. In particular, the random motion of the impurities and the temperature dependence of the friction coefficient are studied. Finally, the clustering of impurities and its effect on the phase transitions of the condensate are investigated.
The motion of quantized vortices is responsible for many intriguing phenomena in diverse quantum-fluid systems. Having a theoretical model to reliably predict the vortex motion therefore promises a broad significance. But a grand challenge in developing such a model is to evaluate the dissipative force caused by thermal quasiparticles in the quantum fluids scattering off the vortex cores. Various models have been proposed, but it remains unclear which model describes reality due to the lack of comparative experimental data. Here we report a visualization study of quantized vortex rings propagating in superfluid helium. By examining how the vortex rings spontaneously decay, we provide decisive data to identify the model that best reproduces observations. This study helps to eliminate ambiguities about the dissipative force acting on vortices, which could have implications for research in various quantum-fluid systems that also involve similar forces, such as superfluid neutron stars and gravity-mapped holographic superfluids.