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

TL;DR

This paper introduces a simple model for quantized vortex rings with internal structure, calculating energy and circulation spectra, revealing fractal circulation values, and discussing implications for quantum turbulence theory.

Contribution

It proposes a new quantization scheme for vortex rings, incorporating interactions and internal structure, advancing the theoretical understanding of quantum turbulence.

Findings

Circulation spectrum exhibits fractal structure.

Partition function for turbulent flow is derived.

Model describes isolated and interacting vortex rings.

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.