Vortex bundle collapse and Kolmogorov spectrum. Talk given at the Low Temperature Conference, Kazan, 2015

TL;DR

This paper investigates how nonuniform vortex bundles in superfluids can generate energy spectra resembling classical turbulence, specifically the Kolmogorov $k^{-5/3}$ spectrum, through nonlinear vortex dynamics.

Contribution

It demonstrates that nonuniform vortex bundles resulting from nonlinear vortex interactions can produce energy spectra close to the Kolmogorov law in quantum turbulence.

Findings

Nonuniform vortex bundles generate $k^{-5/3}$ energy spectrum.

Vortex dynamics with nonlinear interactions lead to classical turbulence features.

Supports the idea of quantum turbulence mimicking classical turbulence spectra.

Abstract

The statement of problem is motivated by the idea of modeling the classical turbulence with a set of chaotic quantized vortex filaments in superfluids. Among various arguments supporting the idea of quasi-classic behavior of quantum turbulence, the strongest, probably, is the $k$ dependence of the spectra of energy, $E(k)\propto k^{-5/3}$ obtained in numerical simulations and experiments. At the same time the mechanism of classical vs quantum turbulence (QT) is not clarified and the source of the $k^{-5/3}$ dependence is unclear. In this work we concentrated on the nonuniform vortex vortex bundles. This choice is related to actively discussed question concerning a role of collapses in the vortex dynamics in formation of turbulent spectra. We demonstrate that the nonuniform vortex vortex bundles, which appear in result of nonlinear vortex dynamics generates the energy spectrum, which close to the Kolmogorov dependence $\propto k^{-5/3}$.