Quantum Turbulence: Vortex Bundle Collapse and Kolmogorov Spectrum

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 is not clarified and the source of the \(k^{-5/3}\) dependence is unclear. In this work, we concentrated on the nonuniform vortex bundles. This choice is related to the actively discussed question concerning a role of collapses in the vortex dynamics in formation of turbulent spectra. We demonstrate that the nonuniform vortex bundles, which appear in result of nonlinear vortex dynamics, generates an energy spectrum which is close to the Kolmogorov dependence \(\propto k^{-5/3}\).