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

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 $\propto k^{-5/3}$.