Abstract
The article presents results obtained based on numerical simulation of two-dimensional vortex points and inertial tracer particles in two-component counterflowing superfluid He-II. In the low temperature limit (no normal fluid, no friction) our model would reduce to Onsager's famous vortex gas. The flow of the nor- mal component of the He-II is assumed uniform, while the superfluid velocity field is induced by vortex points which model three-dimensional quantized vortex lines. Probability density functions of velocity and accelera- tion of tracer particles and superfluid velocity field are obtained. We find that tails of probability distributions follow power-laws with various exponents, except in the case of sufficiently coarse-grained superfluid velocity field, where Gaussian shape is observed. The decay of the number of vortices is also studied, yielding results in agreement with Vinen's phenomenological model of quantum turbulence.
Highlights
Liquid 4He cooled below certain temperature becomes superfluid and is called He-II
The vorticity of the superfluid component cannot be arbitrary, as in classical viscous fluids, but is concentrated to thin topological defects of the size of the order of inter-atomic distance, usually imagined as lines, around which circulation is quantized in units κ ≈ 10−7m2 called quanta of circulation
In the normal component it is assumed that the turbulence is essentially the same as in classical viscous fluids
Summary
Liquid 4He cooled below certain temperature (so-called λpoint, approx. 2.17 K at SVP) becomes superfluid and is called He-II. 2.17 K at SVP) becomes superfluid and is called He-II Properties of this liquid phase are strongly influenced by quantum-mechanical effects and are conveniently, with sufficient accuracy, described by a two-fluid model. This model identifies two components within He-II – the superfluid component with zero viscosity that carries no entropy, and the viscous normal fluid component that carries all the entropy of the liquid. Where B is the mutual friction coefficient and c1, c2 are parameters of order unity The fourth section is dedicated to results, and the fifth concludes the paper
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