Abstract
This work investigates a quantized system of thin vortex rings with a flow in the core. Examples show that the set of permissible circulation values has a fractal structure. Circulation values in the domain of a round tube with a radius R${}_{0}$ in the shape of a torus of radius R${}_{1}\ensuremath{\gg}{R}_{0}$ are given by the accompanying expression where quantities ${\ensuremath{\zeta}}_{k}^{(l)}$ stand for zeros of the Bessel function J${}_{l}$(\ensuremath{\rho}). A general expression for the partition function of a turbulent flow is also suggested.
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