Numerical study of decay of vortex tangles in superfluid helium at zero temperature

Abstract

We submit the results of the numerical experiment on the decay of the quantum turbulence in the absence of the normal component of the superfluid helium. Computations were fulfilled inside a fixed domain with the use of the vortex filament method. The purpose of this study was to ascertain the role of the various factors arising in the numerical procedure, such as change in length in the reconnection processes, the procedures regulating the amount of points on the lines, eliminations of very small loops below the space resolution as well as the evaporation of the loops from the volume. We would like to stress that the widely accepted mechanism-a cascadelike transfer of the energy by nonlinear Kelvin waves (and radiation of sound)-was not considered. One of the reasons is that the space resolution along the lines did not allow to detect generation of high harmonics, moreover, particularly to get harmonics, which really radiate sound. In addition, the use of the method assumes that the fluid is incompressible. Numerical simulations have been performed for the cubic domain with transparent walls embedded in an unbounded space, and for a cube with solid smooth walls. Calculations showed that in the case of unlimited space the decay of quantum turbulence caused by the evaporation of vortex loops, which is implemented in a diffusion-like manner. The rate of the attenuation of the vortex line density agrees with the one, predicted by the theory of diffusion of nonuniform vortex tangles. In the case of a cube with solid walls, the main decay is also due to the diffusion of the vortex loops to boundaries. The vortex loops, whose ends glide on a smooth wall, execute the sophisticated motion (especially when they jump from the one face to the other) with many subsequent reconnections. As a result, there appear smaller and smaller loops with a size of few spatial resolutions, which were removed from the calculation. Indirect comparison with the experiments shows that the time of decay agrees with the measured data.

A Note on the Propagation of Quantized Vortex Rings Through a Quantum Turbulence Tangle: Energy Transport or Energy Dissipation?

“…Figure 6 displays the the numerical data for the post-reconnection vortex ring circumferences and compares to the theoretical prediction given by Eq. (8). For our setup, we observe very good agreement between the numerical data and the theory.…”

Decay of Finite Temperature Superfluid Helium-4 Turbulence

“…1 (right), by this time, the spectral scaling structure of superfluid energy is lost, as the tangle becomes a very dilute system of vortices, that cannot be properly characterized as "turbulent". Notably, the mechanism of Kondaurova and Nemirovskii [16] of vortex line decay due to evaporation (or diffusion) of vortex loops from the bulk is not active here. This is because this mechanism is properly valid for T → 0 K temperatures, and relies on Kelvin waves generating many small loops in the system.…”

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

“…The results may be especially relevant in studies of strongly inhomogeneous flows, as for instance radial flows, flows in convergent or divergent channels [11][12][13][14], in the diffusion contribution to the decay of vortex tangles in narrow channels [18], or in entrance regions in channels. The results will be useful also in the study of mechanically generated turbulence.…”

“…However, experiments [11][12][13][14][15], and numerical results [9,[16][17][18] lead to consider inhomogeneous and anisotropic tangles, with special emphasis on the role of vortex diffusion. Here we will consider inhomogeneous situations, where the heat flux q (and consequently L) is inhomogeneous.…”

“…In this paper we consider inhomogeneous situations, where the tangle may still be described by L, but L may change from point to point in the volume of the tangle and an evolution equation for it must be written, taking explicitly into account the contributions of inhomogeneity, either as a diffusion flux of vortices [7][8][9]18], or as an additional contribution to vortex formation or destruction, which could arise in convergent or divergent channels, as it was observed in some early pioneering but relatively forgotten experiments some years ago [11][12][13][14][15].…”