Reconnection of quantized vortex filaments and the Kolmogorov spectrum

Abstract

The energy spectrum of the 3D velocity field, induced by collapsing vortex filaments is studied. One of the aims of this work is to clarify the appearance of the Kolmogorov type energy spectrum $E(k)\varpropto k^{-5/3}$, observed in many numerical works on discrete vortex tubes (quantized vortex filaments in quantum fluids). Usually, explaining classical turbulent properties of quantum turbulence, the model of vortex bundles, is used. This model is necessary to mimic the vortex stretching, which is responsible for the energy transfer in classical turbulence. In our consideration we do not appeal to the possible "bundle arrangement" but explore alternative idea that the turbulent spectra appear from singular solution, which describe the collapsing line at moments of reconnection. One more aim is related to an important and intensively discussed topic - a role of hydrodynamic collapse in the formation of turbulent spectra. We demonstrated that the specific vortex filament configuration generated the spectrum $E(k)$ close to the Kolmogorov dependence and discussed the reason for this as well as the reason for deviation. We also discuss the obtained results from point of view of the both classical and quantum turbulence.