Towards quantum turbulence theory: A simple model with interaction of the vortex loops

Abstract

This paper investigates quantized thin vortex rings with an internal structure. The quantization scheme of this dynamical system is based on an earlier the approach proposed by the author. Both energy spectrum and circulation spectrum are calculated. Examples show that the set of permissible circulation values has a fractal structure. The suggested model allows us to describe the system of isolated vortex rings as well as the vortex rings with interaction. Furthermore, the application to the quantum turbulence theory is discussed. The general expression for the partition function of a turbulent flow is suggested.

20 pages

References in corpus (3)

• Intermittency of velocity circulation in quantum turbulence
• Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization
• Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization

Cited by in corpus (3)

• The system of the vortex-like structures: the viewpoint on a turbulence modelling
• The quantum vortices dynamics: spatio-temporal scale hierarchy and origin of turbulence
• On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain