Low Temperature Physics: 34, 293 (2008); https://doi.org/10.1063/1.2911641 (5 pages)
Energy spectrum of the velocity field induced by a fractal vortex line in superfluid helium
S.K. Nemirovskii and V.A. Andryuschenko
Kutateladze Institute of Thermophysics SB RAS, Novosibirsk 630090, Russia
Received November 29, 2007
The energy spectrum E(k) of the three-dimensional velocity field induced by fractal vortex line in superfluid helium is calculated by the use of the Gaussian model of vortex tangle induced by chaotic vortex lines. We studied the cases of various Haussdorf dimension HD. If the line is a purely fractal object with Haussdorf dimension HD, the E(k) is a power-like function E(k)~kHD-2 for large k, whereas for small k the spectrum has universal character E(k) ~ k2. For very small distance from the vortex line the characteristics are similar to those of a smooth line.
PACS: 67.25.dk Vortices and turbulence ;
Key words: model of the vortex tangle, fractal vortex line, superfluid helium.