Structure of a quantum vortex tangle in4He counterflow turbulence

Abstract

The main goal of this paper is to present a comprehensive characterization of well developed vortex tangles in a turbulent counterflow in quantum fluids (with a laminar normal fluid component). We analyze extensive numerical simulations using the vortex filament method, solving the full Biot-Savart equations for the vortex dynamics in a wide range of temperatures and counter-flow velocities. In addition to a detailed analysis of traditional characteristics such as vortex line density, anisotropic and curvature parameters of the vortex tangle, we stress other dynamical and statistical characteristics which are either much less studied or even unstudied. The latter include reconnection rates, mean mutual friction forces, drift velocities and the probability distribution functions of various tangle parameters: the loop length, the line curvature, the mean curvature of loops with a given length, etc. During these studies we compare the three main reconnection procedures which are widely used in the literature, and identify which properties are strongly affected by the choice of the reconnection criteria and which of them are practically insensitive to the reconnection procedure. The conclusion is that the vortex filament method in the framework of the Biot-Savart equation sufficiently robust and well suited for the description of the steady state vortex tangle in a quantum counterflow. The Local-Induction Approximation to this equation may be successfully used to analytically establish relationships between mean characteristics of the stochastic vortex tangle.

Dynamics of the density of quantized vortex lines in superfluid turbulence

“…Then the leading term in the expansion of F (x) ∝ x giving: Both options (2) are of course dimensionally correct and they predict the same stationary solution, L st ∝ V 2 ns , which is well supported by both experiments and numerical simulations (see, e.g. 26 and references therein). In principle, one could hope to distinguish between the different forms of this important equation by comparing their prediction for the time evolution from some initial condition toward L st in the presence of counterflow V ns .…”

On the derivation of the HOMFLYPT polynomial invariant for fluid knots

“…Rob Scharein's KnotPlot, for example, can analyse data extracted from fluid flow simulations (by tracking vorticity, magnetic field, low pressure, or density regions), and compute the HOMFLYPT polynomial to any degree of accuracy. Similar analyses made on complex tangles of superfluid vortices (Barenghi et al 2001;Kondaurova et al 2014) proved that this can be done rather efficiently. By relating changes in topology and structural complexity to changes in energy, this process can be iterated in real time, so as to have a time-dependent information on adaptive topology by HOMFLYPT implementation.…”

“…(i) As experiments and direct numerical simulations of superfluid turbulence show (Tsubota, Araki & Nemirovskii 2000;Leadbeater et al 2003;Kondaurova et al 2014), vortex tangles evolve through continuous production and interaction of small(er)-scale unlinked, unknotted vortex loops. Evidence shows that these loops are planar ring-like structures, with almost no writhe and no twist (superfluid vortices are like empty tubes with no internal structure); thus, their internal helicity is either zero or negligible.…”

“…Meanwhile, overwhelming evidence that vorticity and magnetic fields tend to self-organize into coherent flux tubes and bundles of filaments (Douady, Couder & Brachet 1991;Ishihara et al 2007;Mouri, Hori & Kawashimab 2007;Baggaley et al 2012;Cirtain et al 2013), provides further evidence for possible new relationships between geometric and topological properties of complex fluid systems and energy contents (Barenghi, Ricca & Samuels 2001;Moisy & Jiménez 2004;Buck & Simon 2012;Ricca 2013;Kondaurova et al 2014).…”

Numerical Studies of Quantum Turbulence

“…Adachi et al performed the full Biot-Savart simulation and succeeded in obtaining a steady state without the mixing procedure [31]. After the effort expended along this line, the problems of a homogeneous system were settled [32,33].…”