Luiza P. Kondaurova

Structure of a quantum vortex tangle in 4 He counterflow turbulence

dynamics in a wide range of temperatures and counterflow velocities. We start with the analysis of the macroscopic characteristics of the quantum vortex tangle such as vortex line density, its mean anisotropic and curvature parameters, the mean friction force between normal and superfluid components, the drift velocity of the vortex tangle, etc. Next we proceed to the main goal of the paper and move from the traditional macroscopic approach in terms of mean characteristics of the vortex tangle to the microscopic statistical and kinetic levels of description of quantum turbulence. These include objects that are much less studied or even totally neglected such as the vortex reconnection rates, the correlations and probability distribution functions (PDFs) of the vortex loop lengths, of the line curvature, of the mean curvatures of individual loops, the cross-correlation function between the loop length and its mean curvature, and the autocorrelation function of the vortex-line orientations. This detailed statistical information is required for a deeper understanding of quantum turbulence and for the development of its advanced theoretical description. In addition, we identify which of the studied properties are strongly affected by the choice of the reconnection criteria that are traditionally used in the vortex filament method and which of them are practically insensitive to the reconnection procedure. We conclude that the vortex filament method is sufficiently robust and well-suited for the description of the steady-state vortex tangle in the quantum counterflow.

Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence

Institute of Thermophysics, Novosibirsk, RussiaThe quantization of vortex lines in superfluids requires the introduction of their density L(r,t) inthe description of quantum turbulence. The space homogeneous balance equation for L(t), proposedby Vinen on the basis of dimensional and physical considerations, allows a number of competingforms for the production term P. Attempts to choose the correct one on the basis of time-dependenthomogeneous experiments ended inconclusively. To overcome this difficulty we announce here anapproach that employs an inhomogeneous channel flow which is excellently suitable to distinguishthe implications of the various possible forms of the desired equation. We demonstrate that theoriginally selected form which was extensively used in the literature is in strong contradiction withour data. We therefore present a new inhomogeneous equation for L(r,t) that is in agreement withour data and propose that it should be considered for further studies of superfluid turbulence.

Dynamics of Quantized Vortices Before Reconnection

The main goal of this paper is to investigate numerically the dynamics of quantized vortex loops, just before the reconnection at finite temperature, when mutual friction essentially changes the evolution of lines. Modeling is performed on the base of vortex filament method using the full Biot–Savart equation. It was discovered that the initial position of vortices and the temperature strongly affect the dependence on time of the minimum distance

Numerical simulation of stochastic motion of vortex loops under action of random force. Evidence of the thermodynamic equilibrium state

\delta (t)

Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium

δ(t) between tips of two vortex loops. In particular, in some cases, the shrinking and collapse of vortex loops due to mutual friction occur earlier than the reconnection, thereby canceling the latter. However, this relationship takes a universal square-root form

Full Biot-Savart Numerical Simulation of Vortices in He II

\delta \left( t\right) =\sqrt{\left( \kappa /2\pi \right) \left( t_{*}-t\right) }