**Физика Низких Температур: ***Том ***41**, Выпуск **6** (Июнь 2015), c. 608-614
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### Energy spectrum of the quantum vortices configurations

**Sergey K. Nemirovskii**

Institute of Thermophysics, 1 Lavrentyev Ave., Novosibirsk 630090, Russia Novosibirsk State University, Novosibirsk, Russia

E-mail: nemir@itp.nsc.ru

*Received September 7, 2014*

**Аннотация**

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*)µ*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 µ*k*^{−5/3} and discuss the reason for this as well as the reason for deviation.

PACS: 67.25.dk Vortices and turbulence;

PACS: 47.37.+q Hydrodynamic aspects of superfluidity; quantum fluids;

PACS: 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow.

**Ключевые слова: **superfluidity, vortices, quantum turbulence.

**Published online:** *April 23, 2015*