Energy spectrum of the quantum vortices configurations

Abstract

The energy spectra of the 3D velocity field, induced by various vortex filaments configurations are reviewed. The especial attention is paid to configurations generating the Kolmogorov type energy spectrum E(k) ∝ k⁻⁵/³. The motivation of this work is related to the problem of modeling classical turbulence with a set of chaotic vortex filaments. The quantity <v(k)v(–k)> can be exactly calculated, provided that we know the probability distribution functional P({s(ξ,t)}) of vortex loops configurations. The knowledge of P({s(ξ,t)}) is identical to the full solution of the problem of quantum turbulence and, in general, P is unknown. One of the simplifications is to investigate various truthful vortex configurations which can be elements of real vortex tangles. These configurations are: the uniform and nonuniform vortex arrays, the straight lines with excited Kelvin waves on it and the reconnecting vortex filaments. We demonstrate that the spectra E(k), generated by the these configurations, are close to the Kolmogorov dependence ∝ k⁻⁵/³, and discuss the reason for this as well as the reason for deviation.